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2013-11-22 22:04

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2D Elastic Pseudospectral Method

递进结构

2D-EPM.rar
（共32个文件 · 1.8MB）

Debug
ps_main.obj

5.6KB
PS2D.pdb

609KB
ps_output.obj

9.3KB
ps_check.obj

19.7KB
PS2D.exe

452.1KB
ps_evolution.obj

27.2KB
ps_input.obj

9.8KB
ps_oper.obj

8KB
DF60.PDB

25KB
ps_model.obj

8.9KB
ps_deriv.obj

26.8KB
ps_init.obj

12.2KB
ps_init.f

2.1KB
ps_deriv.f

25KB
PS2D.dsw

533B
_gauss

272KB
common.h

1KB
使用说明.docx

11.9KB
ps_main.f

720B
ps_output.f

1.1KB
params.h

162B
Wave propagation in three-dimensional spherical sections by the.pdf

1.5MB
ps_check.f

2.4KB
PS2D.plg

1.2KB
_src

0B
PS2D.dsp

3.4KB
ps_oper.f

1.1KB
ps_evolution.f

3.1KB
ps_input.f

881B
ps_model.f

794B

内容介绍

<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/622b67d33d2fbb0007481ba1/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/622b67d33d2fbb0007481ba1/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">W<span class="_ _0"></span>ave<span class="_ _1"> </span>propagation<span class="_ _1"> </span>in<span class="_ _2"> </span>three-dimensional<span class="_ _2"> </span>spherical<span class="_ _1"> </span>sections<span class="_ _2"> </span>by<span class="_ _1"> </span>the</div><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls1 ws0">Chebyshev<span class="_ _1"> </span>spectral<span class="_ _2"> </span>method</div><div class="t m0 x1 h3 y3 ff2 fs1 fc0 sc0 ls2 ws0">Heiner<span class="_ _1"> </span>I<span class="_ _0"></span>gel</div><div class="t m0 x1 h4 y4 ff3 fs2 fc0 sc0 ls3 ws0">Institute<span class="_ _3"> </span>of<span class="_ _3"> </span>Theoretical<span class="_ _3"> </span>Geophysics,<span class="_ _3"> </span>Department<span class="_ _3"> </span>of<span class="_ _3"> </span>Ear<span class="_ _0"></span>th<span class="_ _3"> </span>Sciences,<span class="_ _3"> </span>Cambridge,<span class="_ _3"> </span><span class="ff2 ls2">CB2<span class="_ _4"> </span>3EQ,<span class="_ _4"> </span></span><span class="ls4">UK.<span class="_ _3"> </span>E-mail:<span class="_ _3"> </span>heiner@esc.cam.ac.uk</span></div><div class="t m0 x1 h4 y5 ff2 fs2 fc0 sc0 ls2 ws0">Accept<span class="_ _5"></span>ed<span class="_ _3"> </span>1998<span class="_ _4"> </span>Sept<span class="_ _5"></span>ember<span class="_ _4"> </span>1<span class="_ _0"></span>7<span class="_ _0"></span>.<span class="_ _3"> </span>Rece<span class="_ _5"></span>ived<span class="_ _3"> </span>1998<span class="_ _4"> </span>August<span class="_ _4"> </span>24;<span class="_ _4"> </span>in<span class="_ _4"> </span>orig<span class="_ _5"></span>inal<span class="_ _4"> </span>form<span class="_ _3"> </span>1998<span class="_ _4"> </span>February<span class="_ _4"> </span>1<span class="_ _0"></span>6</div><div class="t m0 x2 h5 y6 ff1 fs3 fc0 sc0 ls5 ws0">SUMMAR<span class="_ _0"></span>Y</div><div class="t m0 x2 h6 y7 ff2 fs3 fc0 sc0 ls2 ws0">Th<span class="_ _5"></span>e<span class="_ _2"> </span>e<span class="_"> </span>l<span class="_ _5"></span>ast<span class="_ _5"></span>ic<span class="_ _6"> </span>wave<span class="_ _2"> </span>e<span class="_ _5"></span>quati<span class="_ _5"></span>on<span class="_ _6"> </span>in<span class="_ _6"> </span>sp<span class="_ _5"></span>her<span class="_ _5"></span>ica<span class="_ _5"></span>l<span class="_ _2"> </span>c<span class="_ _5"></span>oord<span class="_ _5"></span>inat<span class="_ _5"></span>es<span class="_ _6"> </span>is<span class="_ _6"> </span>so<span class="_"> </span>lve<span class="_ _5"></span>d<span class="_ _6"> </span>by<span class="_ _2"> </span>a<span class="_ _6"> </span>Cheby<span class="_ _5"></span>shev<span class="_ _6"> </span>sp<span class="_ _5"></span>ect<span class="_ _5"></span>ral</div><div class="t m0 x2 h6 y8 ff2 fs3 fc0 sc0 ls2 ws0">me<span class="_ _5"></span>thod.<span class="_ _7"> </span>In<span class="_ _7"> </span>the<span class="_ _7"> </span>algo<span class="_"> </span>r<span class="_ _5"></span>ith<span class="_ _5"></span>m<span class="_ _8"> </span>pre<span class="_ _5"></span>sen<span class="_ _5"></span>ted<span class="_ _7"> </span>the<span class="_ _8"> </span>s<span class="_ _5"></span>ing<span class="_ _5"></span>ula<span class="_ _5"></span>riti<span class="_ _5"></span>es<span class="_ _8"> </span>in<span class="_ _8"> </span>t<span class="_ _5"></span>he<span class="_ _8"> </span>gove<span class="_ _5"></span>rn<span class="_ _5"></span>ing<span class="_ _8"> </span>e<span class="_ _5"></span>quati<span class="_ _5"></span>ons<span class="_ _7"> </span>are</div><div class="t m0 x2 h6 y9 ff2 fs3 fc0 sc0 ls2 ws0">avoide<span class="_ _5"></span>d<span class="_ _9"> </span>by<span class="_ _9"> </span>ce<span class="_ _5"></span>ntr<span class="_ _5"></span>ing<span class="_ _9"> </span>t<span class="_ _5"></span>he<span class="_ _9"> </span>phys<span class="_ _5"></span>ical<span class="_ _a"> </span>do<span class="_ _5"></span>mai<span class="_ _5"></span>n<span class="_ _9"> </span>around<span class="_ _a"> </span>the<span class="_ _a"> </span>equato<span class="_ _5"></span>r.<span class="_ _8"> </span>T<span class="_ _5"></span>he<span class="_ _9"> </span>hig<span class="_ _5"></span>hly<span class="_ _9"> </span>ac<span class="_ _5"></span>curat<span class="_ _5"></span>e</div><div class="t m0 x2 h6 ya ff2 fs3 fc0 sc0 ls6 ws0">pseudospectral<span class="_ _8"> </span>(PS)<span class="_ _7"> </span>der<span class="ls2">ivative<span class="_ _9"> </span>op<span class="_ _5"></span>erator<span class="_"> </span>s<span class="_ _9"> </span>reduc<span class="_ _5"></span>e<span class="_ _7"> </span>the<span class="_ _9"> </span>requi<span class="_ _5"></span>red<span class="_ _9"> </span>grid<span class="_ _7"> </span>s<span class="_ _5"></span>ize<span class="_ _7"> </span>c<span class="_ _5"></span>omp<span class="_ _5"></span>are<span class="_ _5"></span>d<span class="_ _8"> </span>to</span></div><div class="t m0 x2 h6 yb ff2 fs3 fc0 sc0 ls6 ws0">¢nite<span class="_ _4"> </span>di¡<span class="_ _0"></span>erence<span class="_ _b"> </span>(FD)<span class="_ _b"> </span>algorithms.<span class="_ _3"> </span>The<span class="_ _4"> </span>non-staggered<span class="_ _b"> </span>grid<span class="_ _4"> </span>scheme<span class="_ _b"> </span>allows<span class="_ _4"> </span>easy<span class="_ _4"> </span>extension</div><div class="t m0 x2 h6 yc ff2 fs3 fc0 sc0 ls7 ws0">to<span class="_ _2"> </span>general<span class="_ _2"> </span>material<span class="_ _2"> </span>anisotropy<span class="_ _2"> </span>without<span class="_ _2"> </span>additional<span class="_ _2"> </span>interpolations<span class="_ _2"> </span>being<span class="_ _6"> </span>required<span class="_ _2"> </span>as<span class="_ _2"> </span>in</div><div class="t m0 x2 h6 yd ff2 fs3 fc0 sc0 ls2 ws0">stag<span class="_ _5"></span>ger<span class="_ _5"></span>ed<span class="_ _9"> </span>FD<span class="_ _7"> </span>s<span class="_ _5"></span>chem<span class="_ _5"></span>es.<span class="_ _8"> </span>Th<span class="_ _5"></span>e<span class="_ _7"> </span>bou<span class="_ _5"></span>nda<span class="_ _5"></span>ry<span class="_ _7"> </span>c<span class="_ _5"></span>ond<span class="_ _5"></span>itio<span class="_ _5"></span>ns<span class="_ _9"> </span>previ<span class="_ _5"></span>ously<span class="_ _7"> </span>d<span class="_ _5"></span>er<span class="_"> </span>ive<span class="_ _5"></span>d<span class="_ _7"> </span>for<span class="_ _9"> </span>cur<span class="_ _5"></span>vil<span class="_ _5"></span>ine<span class="_ _5"></span>ar</div><div class="t m0 x2 h6 ye ff2 fs3 fc0 sc0 ls8 ws0">coordinate<span class="_ _3"> </span>systems<span class="_ _4"> </span>can<span class="_ _4"> </span>be<span class="_ _4"> </span>applied<span class="_ _4"> </span>directly<span class="_ _3"> </span>to<span class="_ _4"> </span>the<span class="_ _4"> </span>velocit<span class="_ _0"></span>y<span class="_ _4"> </span>vect<span class="_ _0"></span>or<span class="_ _4"> </span>and<span class="_ _4"> </span>stress<span class="_ _4"> </span>tensor<span class="_ _4"> </span>in<span class="_ _4"> </span>the</div><div class="t m0 x2 h6 yf ff2 fs3 fc0 sc0 ls2 ws0">sph<span class="_ _5"></span>eri<span class="_ _5"></span>cal<span class="_ _9"> </span>basi<span class="_ _5"></span>s.<span class="_ _6"> </span>Th<span class="_ _5"></span>e<span class="_ _8"> </span>a<span class="_ _5"></span>lgor<span class="_ _5"></span>ith<span class="_ _5"></span>m<span class="_ _8"> </span>i<span class="_ _5"></span>s<span class="_ _7"> </span>appl<span class="_ _5"></span>ied<span class="_ _7"> </span>to<span class="_ _9"> </span>the<span class="_ _7"> </span>p<span class="_"> </span>robl<span class="_ _5"></span>em<span class="_ _7"> </span>o<span class="_ _5"></span>f<span class="_ _8"> </span>a<span class="_ _7"> </span>d<span class="_"> </span>ou<span class="_ _5"></span>ble<span class="_ _5"></span>-<span class="_ _5"></span>coup<span class="_ _5"></span>le<span class="_ _7"> </span>sou<span class="_ _5"></span>rce</div><div class="t m0 x2 h6 y10 ff2 fs3 fc0 sc0 ls2 ws0">lo<span class="_"> </span>c<span class="_ _5"></span>ated<span class="_ _2"> </span>in<span class="_ _1"> </span>a<span class="_ _2"> </span>hig<span class="_ _5"></span>h-ve<span class="_"> </span>l<span class="_ _5"></span>ocity<span class="_ _1"> </span>r<span class="_ _5"></span>egi<span class="_ _5"></span>on<span class="_ _1"> </span>at<span class="_ _1"> </span>t<span class="_ _5"></span>he<span class="_ _1"> </span>to<span class="_ _5"></span>p<span class="_ _1"> </span>of<span class="_ _1"> </span>th<span class="_ _5"></span>e<span class="_ _1"> </span>ma<span class="_ _5"></span>ntl<span class="_ _5"></span>e<span class="_ _1"> </span>(slab).<span class="_ _b"> </span>T<span class="_ _5"></span>he<span class="_ _1"> </span>sy<span class="_ _5"></span>nth<span class="_ _5"></span>eti<span class="_ _5"></span>c<span class="_ _1"> </span>se<span class="_"> </span>i<span class="_ _5"></span>smo<span class="_ _5"></span>-</div><div class="t m0 x2 h6 y11 ff2 fs3 fc0 sc0 ls2 ws0">gra<span class="_"> </span>m<span class="_ _5"></span>s<span class="_ _1"> </span>show<span class="_ _1"> </span>azimu<span class="_ _5"></span>th<span class="_ _5"></span>-de<span class="_ _5"></span>pe<span class="_ _5"></span>nde<span class="_ _5"></span>nt<span class="_ _1"> </span>travelti<span class="_ _5"></span>me<span class="_ _1"> </span>and<span class="_ _1"> </span>waveform<span class="_ _1"> </span>e¡ects<span class="_ _1"> </span>whi<span class="_ _5"></span>ch<span class="_ _b"> </span>a<span class="_ _5"></span>re<span class="_ _1"> </span>like<span class="_ _5"></span>ly<span class="_ _1"> </span>to<span class="_ _b"> </span>be</div><div class="t m0 x2 h6 y12 ff2 fs3 fc0 sc0 ls2 ws0">obse<span class="_ _5"></span>rvabl<span class="_ _5"></span>e<span class="_ _1"> </span>in<span class="_ _2"> </span>reg<span class="_ _5"></span>ion<span class="_ _5"></span>s<span class="_ _1"> </span>whe<span class="_ _5"></span>re<span class="_ _1"> </span>s<span class="_ _5"></span>ubdu<span class="_ _5"></span>cti<span class="_ _5"></span>on<span class="_ _1"> </span>t<span class="_ _5"></span>akes<span class="_ _2"> </span>pla<span class="_ _5"></span>ce.<span class="_ _1"> </span>Su<span class="_ _5"></span>ch<span class="_ _1"> </span>t<span class="_"> </span>e<span class="_ _5"></span>chni<span class="_ _5"></span>que<span class="_"> </span>s<span class="_ _2"> </span>ar<span class="_ _5"></span>e<span class="_ _1"> </span>im<span class="_ _5"></span>por<span class="_ _5"></span>tan<span class="_ _5"></span>t<span class="_ _1"> </span>in</div><div class="t m0 x2 h6 y13 ff2 fs3 fc0 sc0 ls2 ws0">mod<span class="_ _5"></span>ell<span class="_ _5"></span>ing<span class="_ _6"> </span>t<span class="_ _5"></span>he<span class="_ _6"> </span>full<span class="_ _5"></span>-wave<span class="_ _6"> </span>chara<span class="_ _5"></span>cter<span class="_ _5"></span>ist<span class="_ _5"></span>ics<span class="_ _6"> </span>o<span class="_ _5"></span>f<span class="_ _2"> </span>t<span class="_ _5"></span>he<span class="_ _6"> </span>Ea<span class="_ _5"></span>rth's<span class="_ _6"> </span>3-D<span class="_ _6"> </span>s<span class="_ _5"></span>tru<span class="_ _5"></span>ctur<span class="_ _5"></span>e<span class="_ _6"> </span>and<span class="_ _6"> </span>i<span class="_"> </span>n<span class="_ _8"> </span>provid<span class="_ _5"></span>ing</div><div class="t m0 x2 h6 y14 ff2 fs3 fc0 sc0 ls2 ws0">acc<span class="_ _5"></span>urate<span class="_ _1"> </span>refer<span class="_ _5"></span>en<span class="_ _5"></span>ce<span class="_ _b"> </span>s<span class="_ _5"></span>olu<span class="_ _5"></span>tio<span class="_ _5"></span>ns<span class="_ _1"> </span>for<span class="_ _b"> </span>3<span class="_ _5"></span>-D<span class="_ _b"> </span>gl<span class="_ _5"></span>obal<span class="_ _1"> </span>mo<span class="_ _5"></span>dels.</div><div class="t m0 x2 h6 y15 ff1 fs3 fc0 sc0 ls9 ws0">Key<span class="_ _b"> </span>words:<span class="_ _a"> </span><span class="ff2 lsa">Chebyshev<span class="_ _b"> </span>spectral<span class="_ _b"> </span>method,<span class="_ _1"> </span>synthetic<span class="_ _b"> </span>seismograms,<span class="_ _b"> </span>wave<span class="_ _b"> </span>propagatio<span class="_"> </span>n.</span></div><div class="t m0 x1 h7 y16 ff1 fs4 fc0 sc0 lsb ws0">1<span class="_ _c"> </span>INTRO<span class="_ _0"></span>DUCTION</div><div class="t m0 x1 h8 y17 ff2 fs4 fc0 sc0 ls2 ws0">Under<span class="_ _5"></span>stan<span class="_ _5"></span>din<span class="_ _5"></span>g<span class="_ _d"> </span>the<span class="_ _e"> </span>glob<span class="_ _5"></span>al<span class="_ _d"> </span>up<span class="_ _5"></span>per-m<span class="_ _5"></span>antl<span class="_ _5"></span>e<span class="_ _d"> </span>str<span class="_ _5"></span>uctu<span class="_"> </span>r<span class="_ _5"></span>e<span class="_ _d"> </span>an<span class="_ _5"></span>d<span class="_ _d"> </span>the</div><div class="t m0 x1 h8 y18 ff2 fs4 fc0 sc0 ls2 ws0">rel<span class="_ _5"></span>ated<span class="_ _8"> </span>geo<span class="_ _5"></span>dynam<span class="_ _5"></span>ical<span class="_ _8"> </span>featur<span class="_ _5"></span>es<span class="_ _6"> </span>i<span class="_ _5"></span>s<span class="_ _6"> </span>o<span class="_ _5"></span>ne<span class="_ _8"> </span>of<span class="_ _6"> </span>th<span class="_ _5"></span>e<span class="_ _6"> </span>m<span class="_ _5"></span>ost<span class="_ _8"> </span>imp<span class="_ _5"></span>orta<span class="_ _5"></span>nt</div><div class="t m0 x1 h8 y19 ff2 fs4 fc0 sc0 ls2 ws0">goal<span class="_ _5"></span>s<span class="_ _6"> </span>in<span class="_ _6"> </span>s<span class="_ _5"></span>eis<span class="_ _5"></span>molo<span class="_ _5"></span>gy<span class="_ _6"> </span>tod<span class="_ _5"></span>ay<span class="_ _f"></span>.<span class="_ _6"> </span>In<span class="_ _8"> </span>orde<span class="_ _5"></span>r<span class="_ _6"> </span>to<span class="_ _6"> </span>und<span class="_ _5"></span>ers<span class="_"> </span>t<span class="_ _5"></span>and<span class="_ _6"> </span>t<span class="_ _5"></span>he<span class="_ _6"> </span>m<span class="_ _5"></span>ass</div><div class="t m0 x1 h8 y1a ff2 fs4 fc0 sc0 lsc ws0">£ux<span class="_ _2"> </span>into<span class="_ _6"> </span>and<span class="_ _2"> </span>out<span class="_ _2"> </span>of<span class="_ _2"> </span>the<span class="_ _6"> </span>mantle,<span class="_ _2"> </span>a<span class="_ _2"> </span>detailed<span class="_ _6"> </span>understanding<span class="_ _2"> </span>of</div><div class="t m0 x1 h8 y1b ff2 fs4 fc0 sc0 lsd ws0">the<span class="_ _a"> </span>structure<span class="_ _a"> </span>of<span class="_ _a"> </span>subduction<span class="_ _d"> </span>zones,<span class="_ _a"> </span>hotspots,<span class="_ _a"> </span>upper-mantle</div><div class="t m0 x1 h8 y1c ff2 fs4 fc0 sc0 ls2 ws0">dis<span class="_ _5"></span>cont<span class="_ _5"></span>inu<span class="_ _5"></span>ities,<span class="_ _4"> </span>e<span class="_ _5"></span>tc.,<span class="_ _4"> </span>i<span class="_ _5"></span>s<span class="_ _4"> </span>nece<span class="_ _5"></span>ssa<span class="_"> </span>r<span class="_ _5"></span>y<span class="_ _f"></span>.<span class="_ _4"> </span>Much<span class="_ _b"> </span>of<span class="_ _4"> </span>the<span class="_ _b"> </span>cur<span class="_ _5"></span>ren<span class="_ _5"></span>t<span class="_ _4"> </span>imagi<span class="_ _5"></span>ng</div><div class="t m0 x1 h8 y1d ff2 fs4 fc0 sc0 lse ws0">and<span class="_ _1"> </span>modelling<span class="_ _1"> </span>of<span class="_ _1"> </span>upp<span class="_"> </span>er-mantle<span class="_ _1"> </span>structure<span class="_ _1"> </span>is<span class="_ _1"> </span>un<span class="_"> </span>dertaken<span class="_ _1"> </span>using</div><div class="t m0 x1 h8 y1e ff2 fs4 fc0 sc0 ls2 ws0">ray-bas<span class="_ _5"></span>ed<span class="_ _7"> </span>approxi<span class="_ _5"></span>matio<span class="_ _5"></span>ns<span class="_ _7"> </span>or<span class="_ _7"> </span>lon<span class="_ _5"></span>g-p<span class="_ _5"></span>eri<span class="_"> </span>o<span class="_ _5"></span>d<span class="_ _8"> </span>s<span class="_ _5"></span>eism<span class="_ _5"></span>ogra<span class="_"> </span>ms<span class="_ _9"> </span>with</div><div class="t m0 x1 h8 y1f ff2 fs4 fc0 sc0 ls2 ws0">oth<span class="_ _5"></span>er<span class="_ _a"> </span>(li<span class="_ _5"></span>near<span class="_ _5"></span>ized<span class="_ _5"></span>)<span class="_ _9"> </span>app<span class="_ _5"></span>roximat<span class="_ _5"></span>ions<span class="_ _a"> </span>i<span class="_"> </span>nvolved.<span class="_ _9"> </span>Th<span class="_ _5"></span>ese<span class="_ _a"> </span>app<span class="_"> </span>roxi<span class="_ _5"></span>-</div><div class="t m0 x1 h8 y20 ff2 fs4 fc0 sc0 ls2 ws0">mati<span class="_ _5"></span>ons<span class="_ _b"> </span>are<span class="_ _b"> </span>n<span class="_ _5"></span>ot<span class="_ _4"> </span>va<span class="_"> </span>l<span class="_ _5"></span>id<span class="_ _4"> </span>wh<span class="_ _5"></span>en<span class="_ _4"> </span>t<span class="_ _5"></span>he<span class="_ _4"> </span>wavel<span class="_ _5"></span>engt<span class="_ _5"></span>h<span class="_ _4"> </span>of<span class="_ _b"> </span>the<span class="_ _b"> </span>prop<span class="_ _5"></span>agatin<span class="_ _5"></span>g</div><div class="t m0 x1 h8 y21 ff2 fs4 fc0 sc0 ls2 ws0">wave¢el<span class="_ _5"></span>d<span class="_ _8"> </span>is<span class="_ _8"> </span>of<span class="_ _8"> </span>the<span class="_ _8"> </span>s<span class="_ _5"></span>ame<span class="_ _8"> </span>o<span class="_"> </span>rd<span class="_ _5"></span>er<span class="_ _8"> </span>as<span class="_ _8"> </span>th<span class="_ _5"></span>e<span class="_ _6"> </span>s<span class="_ _5"></span>tru<span class="_ _5"></span>cture<span class="_ _5"></span>s<span class="_ _8"> </span>of<span class="_ _8"> </span>int<span class="_ _5"></span>eres<span class="_ _5"></span>t.</div><div class="t m0 x1 h8 y22 ff2 fs4 fc0 sc0 lsf ws0">Scattering<span class="_ _8"> </span>e¡ects<span class="_ _7"> </span>will<span class="_ _7"> </span>then<span class="_ _7"> </span>be<span class="_ _7"> </span>important,<span class="_ _7"> </span>and<span class="_ _7"> </span>may<span class="_ _7"> </span>contain</div><div class="t m0 x1 h8 y23 ff2 fs4 fc0 sc0 ls10 ws0">important<span class="_ _d"> </span>information<span class="_ _d"> </span>on<span class="_ _d"> </span>these<span class="_ _d"> </span>structures.<span class="_ _a"> </span>Modern<span class="_ _d"> </span>high-</div><div class="t m0 x1 h8 y24 ff2 fs4 fc0 sc0 ls2 ws0">qual<span class="_ _5"></span>ity<span class="_ _9"> </span>broad<span class="_ _5"></span>-ban<span class="_ _5"></span>d<span class="_ _9"> </span>r<span class="_ _5"></span>eco<span class="_ _5"></span>rding<span class="_ _5"></span>s<span class="_ _a"> </span>cont<span class="_ _5"></span>ain<span class="_ _a"> </span>i<span class="_ _5"></span>nformat<span class="_ _5"></span>ion<span class="_ _a"> </span>t<span class="_ _5"></span>hat<span class="_ _a"> </span>is</div><div class="t m0 x1 h8 y25 ff2 fs4 fc0 sc0 ls11 ws0">currently<span class="_ _3"> </span>not<span class="_ _4"> </span>accounted<span class="_ _4"> </span>fo<span class="_ _f"></span>r<span class="_ _4"> </span>by<span class="_ _3"> </span>essentially<span class="_ _4"> </span>ra<span class="_ _0"></span>y-based<span class="_ _3"> </span>modelling</div><div class="t m0 x1 h8 y26 ff2 fs4 fc0 sc0 ls2 ws0">algo<span class="_ _5"></span>rith<span class="_ _5"></span>ms.<span class="_ _4"> </span>T<span class="_ _5"></span>here<span class="_ _5"></span>fore,<span class="_ _1"> </span>the<span class="_ _1"> </span>deve<span class="_ _5"></span>lopm<span class="_ _5"></span>ent<span class="_ _1"> </span>of<span class="_ _b"> </span>for<span class="_ _5"></span>ward<span class="_ _1"> </span>mod<span class="_ _5"></span>elli<span class="_ _5"></span>ng</div><div class="t m0 x1 h8 y27 ff2 fs4 fc0 sc0 ls2 ws0">tool<span class="_ _5"></span>s<span class="_ _7"> </span>th<span class="_ _5"></span>atöi<span class="_ _5"></span>n<span class="_ _7"> </span>the<span class="_ _9"> </span>not<span class="_ _9"> </span>too<span class="_ _7"> </span>d<span class="_ _5"></span>istan<span class="_ _5"></span>t<span class="_ _9"> </span>futureöw<span class="_ _5"></span>ill<span class="_ _9"> </span>allow<span class="_ _9"> </span>us<span class="_ _7"> </span>to</div><div class="t m0 x1 h8 y28 ff2 fs4 fc0 sc0 ls2 ws0">simu<span class="_ _5"></span>late<span class="_ _3"> </span>3<span class="_ _5"></span>-D<span class="_ _3"> </span>glob<span class="_ _5"></span>al<span class="_ _3"> </span>eart<span class="_ _5"></span>h<span class="_ _3"> </span>mo<span class="_ _5"></span>dels<span class="_ _3"> </span>w<span class="_ _5"></span>ith<span class="_ _3"> </span>hig<span class="_ _5"></span>h<span class="_ _3"> </span>enoug<span class="_ _5"></span>h<span class="_ _3"> </span>frequ<span class="_ _5"></span>enci<span class="_ _5"></span>es</div><div class="t m0 x1 h8 y29 ff2 fs4 fc0 sc0 ls2 ws0">is<span class="_ _9"> </span>an<span class="_ _a"> </span>imp<span class="_ _5"></span>ort<span class="_ _5"></span>ant<span class="_ _9"> </span>st<span class="_ _5"></span>ep<span class="_ _9"> </span>toward<span class="_ _5"></span>s<span class="_ _9"> </span>solv<span class="_ _5"></span>ing<span class="_ _a"> </span>some<span class="_ _a"> </span>of<span class="_ _9"> </span>th<span class="_ _5"></span>e<span class="_ _9"> </span>cu<span class="_ _5"></span>rren<span class="_ _5"></span>t</div><div class="t m0 x1 h8 y2a ff2 fs4 fc0 sc0 ls2 ws0">geo<span class="_ _5"></span>dyna<span class="_"> </span>mi<span class="_ _5"></span>cal<span class="_ _b"> </span>p<span class="_"> </span>robl<span class="_ _5"></span>ems.</div><div class="t m0 x3 h8 y2b ff2 fs4 fc0 sc0 ls2 ws0">In<span class="_ _2"> </span>the<span class="_ _2"> </span>pa<span class="_ _5"></span>st<span class="_ _2"> </span>dec<span class="_ _5"></span>ade<span class="_ _2"> </span>dis<span class="_ _5"></span>cre<span class="_"> </span>t<span class="_ _5"></span>e<span class="_ _1"> </span>g<span class="_ _5"></span>rid<span class="_ _2"> </span>met<span class="_ _5"></span>hods<span class="_ _2"> </span>h<span class="_ _5"></span>ave<span class="_ _1"> </span>been<span class="_ _2"> </span>wi<span class="_ _5"></span>dely</div><div class="t m0 x1 h8 y2c ff2 fs4 fc0 sc0 ls2 ws0">use<span class="_ _5"></span>d<span class="_ _4"> </span>in<span class="_ _3"> </span>t<span class="_ _5"></span>he<span class="_ _4"> </span>¢eld<span class="_ _4"> </span>of<span class="_ _4"> </span>seis<span class="_ _5"></span>mic<span class="_ _4"> </span>wave<span class="_ _4"> </span>propagati<span class="_ _5"></span>on.<span class="_ _4"> </span>Early<span class="_ _4"> </span>algor<span class="_ _5"></span>ithm<span class="_ _5"></span>s</div><div class="t m0 x1 h8 y2d ff2 fs4 fc0 sc0 ls2 ws0">(e.g.<span class="_ _b"> </span>Vir<span class="_ _5"></span>ieu<span class="_"> </span>x<span class="_ _2"> </span>1984<span class="_ _5"></span>,<span class="_ _2"> </span>1986)<span class="_ _6"> </span>solved<span class="_ _6"> </span>th<span class="_ _5"></span>e<span class="_ _6"> </span>equatio<span class="_ _5"></span>ns<span class="_ _6"> </span>in<span class="_ _6"> </span>two<span class="_ _6"> </span>di<span class="_ _5"></span>men-</div><div class="t m0 x1 h8 y2e ff2 fs4 fc0 sc0 ls2 ws0">sio<span class="_ _5"></span>ns<span class="_ _6"> </span>usi<span class="_ _5"></span>ng<span class="_ _6"> </span>low-ord<span class="_ _5"></span>er<span class="_ _6"> </span>approxim<span class="_ _5"></span>ation<span class="_ _5"></span>s<span class="_ _2"> </span>to<span class="_ _6"> </span>t<span class="_ _5"></span>he<span class="_ _6"> </span>spac<span class="_ _5"></span>e<span class="_ _6"> </span>and<span class="_ _6"> </span>tim<span class="_ _5"></span>e</div><div class="t m0 x1 h8 y2f ff2 fs4 fc0 sc0 ls2 ws0">der<span class="_ _5"></span>ivatives.<span class="_ _8"> </span>Lat<span class="_ _5"></span>er<span class="_ _8"> </span>th<span class="_ _5"></span>ese<span class="_ _8"> </span>a<span class="_ _5"></span>lgor<span class="_"> </span>it<span class="_ _5"></span>hm<span class="_ _5"></span>s<span class="_ _8"> </span>wer<span class="_ _5"></span>e<span class="_ _8"> </span>exten<span class="_ _5"></span>ded<span class="_ _8"> </span>to<span class="_ _8"> </span>h<span class="_ _5"></span>ighe<span class="_ _5"></span>r</div><div class="t m0 x4 h8 y30 ff2 fs4 fc0 sc0 ls2 ws0">orde<span class="_ _5"></span>rs<span class="_ _6"> </span>(e.g.<span class="_ _8"> </span>Levan<span class="_ _5"></span>der<span class="_ _6"> </span>1988),<span class="_ _6"> </span>to<span class="_ _6"> </span>t<span class="_ _5"></span>hree<span class="_ _8"> </span>dime<span class="_ _5"></span>nsi<span class="_ _5"></span>ons<span class="_ _6"> </span>(e.g<span class="_ _5"></span>.<span class="_ _6"> </span>Mora</div><div class="t m0 x4 h8 y31 ff2 fs4 fc0 sc0 ls2 ws0">1989)<span class="_ _b"> </span>a<span class="_ _5"></span>nd<span class="_ _b"> </span>to<span class="_ _b"> </span>t<span class="_ _5"></span>he<span class="_ _b"> </span>ge<span class="_ _5"></span>neral<span class="_ _1"> </span>aniso<span class="_ _5"></span>tropi<span class="_ _5"></span>c<span class="_ _4"> </span>c<span class="_ _5"></span>ase<span class="_ _1"> </span>(e.g.<span class="_ _b"> </span>Igel<span class="_ _1"> </span><span class="ff3 ls12">et<span class="_ _4"> </span>al.<span class="_ _4"> </span></span><span class="ls13">199<span class="_ _5"></span>5<span class="_ _5"></span>;</span></div><div class="t m0 x4 h8 y32 ff2 fs4 fc0 sc0 ls2 ws0">T<span class="_ _f"></span>es<span class="_ _5"></span>smer<span class="_ _4"> </span>1995).</div><div class="t m0 x5 h8 y33 ff2 fs4 fc0 sc0 ls2 ws0">An<span class="_ _d"> </span>al<span class="_ _5"></span>ter<span class="_ _5"></span>native<span class="_ _d"> </span>to<span class="_ _e"> </span>the<span class="_ _d"> </span><span class="ff3 ls14">local<span class="_ _e"> </span></span>derivat<span class="_ _5"></span>ive<span class="_ _d"> </span>op<span class="_ _5"></span>erator<span class="_ _5"></span>s<span class="_ _d"> </span>of<span class="_ _d"> </span>FD</div><div class="t m0 x4 h8 y34 ff2 fs4 fc0 sc0 ls2 ws0">schem<span class="_ _5"></span>es<span class="_ _10"> </span>is<span class="_ _10"> </span>pse<span class="_ _5"></span>udo<span class="_ _5"></span>spe<span class="_ _5"></span>ctral<span class="_ _10"> </span>(P<span class="_ _5"></span>S)<span class="_ _10"> </span>techn<span class="_ _5"></span>iques.<span class="_ _10"> </span>PS<span class="_ _10"> </span>me<span class="_ _5"></span>thod<span class="_ _5"></span>s</div><div class="t m0 x4 h8 y35 ff2 fs4 fc0 sc0 ls2 ws0">have<span class="_ _d"> </span>bee<span class="_ _5"></span>n<span class="_ _d"> </span>widely<span class="_ _e"> </span>us<span class="_ _5"></span>ed<span class="_ _d"> </span>in<span class="_ _e"> </span>num<span class="_ _5"></span>eri<span class="_"> </span>ca<span class="_ _5"></span>l<span class="_ _d"> </span>a<span class="_ _5"></span>lgorit<span class="_ _5"></span>hms<span class="_ _e"> </span>for<span class="_ _d"> </span>wave</div><div class="t m0 x4 h8 y36 ff2 fs4 fc0 sc0 lsd ws0">propaga<span class="_ _0"></span>tion,<span class="_ _6"> </span>computational<span class="_ _6"> </span>£uid<span class="_ _6"> </span>dynamics<span class="_ _6"> </span>and<span class="_ _6"> </span>other<span class="_ _2"> </span>¢el<span class="_"> </span>ds.</div><div class="t m0 x4 h8 y37 ff2 fs4 fc0 sc0 ls2 ws0">F<span class="_ _f"></span>o<span class="_ _5"></span>r<span class="_ _4"> </span>t<span class="_ _5"></span>he<span class="_ _b"> </span>fundam<span class="_ _5"></span>ent<span class="_ _5"></span>als<span class="_ _b"> </span>of<span class="_ _b"> </span>pse<span class="_ _5"></span>udos<span class="_ _5"></span>pe<span class="_ _5"></span>ctral<span class="_ _b"> </span>me<span class="_ _5"></span>thod<span class="_ _5"></span>s<span class="_ _4"> </span>t<span class="_ _5"></span>he<span class="_ _4"> </span>r<span class="_ _5"></span>eade<span class="_ _5"></span>r<span class="_ _4"> </span>i<span class="_"> </span>s</div><div class="t m0 x4 h8 y38 ff2 fs4 fc0 sc0 ls2 ws0">referr<span class="_ _5"></span>ed<span class="_ _8"> </span>to<span class="_ _6"> </span>t<span class="_ _5"></span>he<span class="_ _8"> </span>excell<span class="_ _5"></span>ent<span class="_ _8"> </span>book<span class="_ _6"> </span>by<span class="_ _8"> </span>F<span class="_ _0"></span>or<span class="_ _5"></span>nber<span class="_ _5"></span>g<span class="_ _6"> </span>(1996).<span class="_ _8"> </span>Previ<span class="_ _5"></span>ous</div><div class="t m0 x4 h8 y39 ff2 fs4 fc0 sc0 ls2 ws0">appl<span class="_ _5"></span>icati<span class="_ _5"></span>ons<span class="_ _6"> </span>to<span class="_ _8"> </span>wave<span class="_ _6"> </span>propaga<span class="_ _5"></span>tion<span class="_ _8"> </span>problem<span class="_ _5"></span>s<span class="_ _6"> </span>can<span class="_ _8"> </span>be<span class="_ _6"> </span>foun<span class="_ _5"></span>d<span class="_ _6"> </span>in</div><div class="t m0 x4 h8 y3a ff2 fs4 fc0 sc0 ls15 ws0">Kos<span class="_ _5"></span>l<span class="_ _5"></span>o¡<span class="_ _6"> </span><span class="ff3 ls12">et<span class="_ _1"> </span>al.<span class="_ _6"> </span></span><span class="ls16">(1<span class="_ _f"></span>990),<span class="_ _2"> </span>K<span class="_ _0"></span>oslo¡<span class="_ _2"> </span>&<span class="_ _2"> </span>T<span class="_ _f"></span>al-Ezer<span class="_ _2"> </span>(1<span class="_ _f"></span>993),<span class="_ _1"> </span>Carcione<span class="_ _2"> </span>&</span></div><div class="t m0 x4 h8 y3b ff2 fs4 fc0 sc0 ls2 ws0">W<span class="_ _f"></span>a<span class="_"> </span>n<span class="_ _5"></span>g<span class="_ _a"> </span>(1993),<span class="_ _a"> </span>C<span class="_ _5"></span>arci<span class="_ _5"></span>one<span class="_ _d"> </span>(1<span class="_ _0"></span>994<span class="_ _5"></span>),<span class="_ _9"> </span>T<span class="_ _f"></span>ess<span class="_"> </span>m<span class="_ _5"></span>er<span class="_ _d"> </span>&<span class="_ _a"> </span>Kos<span class="_ _5"></span>lo¡<span class="_ _d"> </span>(1<span class="_ _0"></span>994),</div><div class="t m0 x4 h8 y3c ff2 fs4 fc0 sc0 ls2 ws0">T<span class="_ _f"></span>es<span class="_ _5"></span>smer<span class="_ _b"> </span>(1995)<span class="_ _4"> </span>an<span class="_ _5"></span>d<span class="_ _4"> </span>Komat<span class="_ _5"></span>itsch<span class="_ _b"> </span><span class="ff3 ls12">et<span class="_ _3"> </span>a<span class="_"> </span>l<span class="_"> </span>.<span class="_ _b"> </span></span>(1996).</div><div class="t m0 x5 h8 y3d ff2 fs4 fc0 sc0 ls17 ws0">In<span class="_ _4"> </span>PS<span class="_ _4"> </span>techniques<span class="_ _3"> </span>the<span class="_ _4"> </span>space-dep<span class="_"> </span>endent<span class="_ _4"> </span>¢elds<span class="_ _4"> </span>are<span class="_ _4"> </span>expanded<span class="_ _4"> </span>in</div><div class="t m0 x4 h8 y3e ff2 fs4 fc0 sc0 ls2 ws0">a<span class="_ _3"> </span>set<span class="_ _11"> </span>of<span class="_ _11"> </span>orth<span class="_ _5"></span>ogon<span class="_ _5"></span>al<span class="_ _11"> </span>ba<span class="_ _5"></span>sis<span class="_ _11"> </span>func<span class="_ _5"></span>tio<span class="_ _5"></span>ns<span class="_ _11"> </span>whi<span class="_ _5"></span>ch<span class="_ _11"> </span>are<span class="_ _3"> </span>know<span class="_ _5"></span>n<span class="_ _11"> </span><span class="ff3">exa<span class="_ _5"></span>ctl<span class="_ _5"></span>y<span class="_ _11"> </span></span>at<span class="_ _11"> </span>a</div><div class="t m0 x4 h8 y3f ff2 fs4 fc0 sc0 ls2 ws0">dis<span class="_ _5"></span>cret<span class="_ _5"></span>e<span class="_ _4"> </span>set<span class="_ _4"> </span>of<span class="_ _4"> </span>poin<span class="_ _5"></span>ts.<span class="_ _11"> </span>T<span class="_ _5"></span>hese<span class="_ _4"> </span>b<span class="_ _5"></span>asis<span class="_ _4"> </span>func<span class="_ _5"></span>tio<span class="_"> </span>n<span class="_ _5"></span>s<span class="_ _4"> </span>can<span class="_ _4"> </span>be<span class="_ _4"> </span>for<span class="_ _4"> </span>exam<span class="_ _5"></span>ple</div><div class="t m0 x4 h8 y40 ff2 fs4 fc0 sc0 ls2 ws0">F<span class="_ _f"></span>ou<span class="_ _5"></span>rie<span class="_ _5"></span>r<span class="_ _1"> </span>ser<span class="_ _5"></span>ies<span class="_ _1"> </span>(r<span class="_ _5"></span>egu<span class="_ _5"></span>lar<span class="_ _1"> </span>g<span class="_ _5"></span>rid)<span class="_ _2"> </span>or<span class="_ _1"> </span>C<span class="_ _5"></span>hebysh<span class="_ _5"></span>ev<span class="_ _1"> </span>poly<span class="_ _5"></span>nomi<span class="_ _5"></span>als<span class="_ _2"> </span>(non-</div><div class="t m0 x4 h8 y41 ff2 fs4 fc0 sc0 lsd ws0">uniform<span class="_ _3"> </span>grid<span class="_ _4"> </span>de¢ned<span class="_ _3"> </span>between<span class="_ _4"> </span>[<span class="ff4 ls2">{</span><span class="lsc">1<span class="_ _f"></span>,<span class="_ _1"> </span>1<span class="_ _0"></span>]<span class="_ _3"> </span>with<span class="_ _4"> </span>denser<span class="_ _3"> </span>grid<span class="_ _4"> </span>near<span class="_ _3"> </span>the</span></div><div class="t m0 x4 h8 y42 ff2 fs4 fc0 sc0 ls2 ws0">boun<span class="_ _5"></span>dari<span class="_ _5"></span>es).<span class="_ _d"> </span>Th<span class="_ _5"></span>e<span class="_ _e"> </span>PS<span class="_ _12"> </span>tech<span class="_ _5"></span>niqu<span class="_ _5"></span>es<span class="_ _e"> </span>h<span class="_ _5"></span>ave<span class="_ _e"> </span>the<span class="_ _12"> </span>advan<span class="_ _5"></span>tage<span class="_ _12"> </span>that</div><div class="t m0 x4 h8 y43 ff2 fs4 fc0 sc0 ls2 ws0">the<span class="_ _4"> </span>der<span class="_ _5"></span>ivatives<span class="_ _4"> </span>can<span class="_ _4"> </span>be<span class="_ _4"> </span>cal<span class="_ _5"></span>culat<span class="_ _5"></span>ed<span class="_ _4"> </span>with<span class="_ _4"> </span>nume<span class="_ _5"></span>ric<span class="_"> </span>al<span class="_ _4"> </span>p<span class="_ _5"></span>reci<span class="_ _5"></span>sion.<span class="_ _3"> </span>T<span class="_ _5"></span>he</div><div class="t m0 x4 h8 y44 ff2 fs4 fc0 sc0 ls2 ws0">Chebys<span class="_ _5"></span>hev<span class="_ _d"> </span>met<span class="_ _5"></span>hod<span class="_ _d"> </span>furt<span class="_ _5"></span>herm<span class="_ _5"></span>ore<span class="_ _d"> </span>al<span class="_ _5"></span>lows<span class="_ _d"> </span>an<span class="_ _d"> </span>imp<span class="_ _5"></span>lem<span class="_ _5"></span>entat<span class="_ _5"></span>ion</div><div class="t m0 x4 h8 y45 ff2 fs4 fc0 sc0 ls2 ws0">of<span class="_ _8"> </span>bound<span class="_ _5"></span>ary<span class="_ _8"> </span>c<span class="_ _5"></span>ondit<span class="_ _5"></span>ions<span class="_ _8"> </span>(e.g<span class="_ _5"></span>.<span class="_ _8"> </span>tract<span class="_ _5"></span>ion-<span class="_ _5"></span>free<span class="_ _8"> </span>or<span class="_ _7"> </span>no<span class="_ _5"></span>n-re<span class="_ _5"></span>£ect<span class="_ _5"></span>ing)</div><div class="t m0 x4 h8 y46 ff2 fs4 fc0 sc0 ls2 ws0">with<span class="_ _6"> </span>th<span class="_ _5"></span>e<span class="_ _6"> </span>same<span class="_ _6"> </span>ac<span class="_ _5"></span>cura<span class="_ _5"></span>cy<span class="_ _2"> </span>as<span class="_ _6"> </span>w<span class="_ _5"></span>ithin<span class="_ _6"> </span>t<span class="_ _5"></span>he<span class="_ _6"> </span>med<span class="_ _5"></span>ium.<span class="_ _2"> </span>Th<span class="_ _5"></span>is<span class="_ _6"> </span>is<span class="_ _6"> </span>mo<span class="_ _5"></span>re</div><div class="t m0 x4 h8 y47 ff2 fs4 fc0 sc0 ls10 ws0">di¤cult<span class="_ _9"> </span>when<span class="_ _7"> </span>FD<span class="_ _9"> </span>techniques<span class="_ _7"> </span>are<span class="_ _7"> </span>applied,<span class="_ _9"> </span>where<span class="_ _7"> </span>boundary</div><div class="t m0 x4 h8 y48 ff2 fs4 fc0 sc0 ls10 ws0">conditions<span class="_ _b"> </span>are<span class="_ _1"> </span>usually<span class="_ _b"> </span>implemented<span class="_ _b"> </span>with<span class="_ _1"> </span>lower<span class="_ _4"> </span>accuracy<span class="_ _b"> </span>than</div><div class="t m0 x4 h8 y49 ff2 fs4 fc0 sc0 ls2 ws0">the<span class="_ _b"> </span>d<span class="_ _5"></span>i¡ere<span class="_ _5"></span>ntia<span class="_ _5"></span>l<span class="_ _4"> </span>o<span class="_ _5"></span>perato<span class="_ _5"></span>rs<span class="_ _b"> </span>ins<span class="_ _5"></span>ide<span class="_ _b"> </span>th<span class="_ _5"></span>e<span class="_ _4"> </span>me<span class="_ _5"></span>diu<span class="_ _5"></span>m.<span class="_ _4"> </span>The<span class="_ _b"> </span>drawba<span class="_ _5"></span>ck<span class="_ _4"> </span>of</div><div class="t m0 x4 h8 y4a ff2 fs4 fc0 sc0 ls2 ws0">the<span class="_ _1"> </span>P<span class="_ _5"></span>S<span class="_ _1"> </span>tec<span class="_ _5"></span>hniqu<span class="_ _5"></span>e<span class="_ _1"> </span>is<span class="_ _1"> </span>th<span class="_ _5"></span>at<span class="_ _1"> </span>owing<span class="_ _2"> </span>to<span class="_ _1"> </span>th<span class="_ _5"></span>e<span class="_ _1"> </span>len<span class="_ _5"></span>gth<span class="_ _1"> </span>o<span class="_ _5"></span>f<span class="_ _1"> </span>the<span class="_ _1"> </span>d<span class="_"> </span>e<span class="_ _5"></span>rivative</div><div class="t m0 x6 h4 y4b ff3 fs2 fc0 sc0 ls18 ws0">Geophys.<span class="_ _11"> </span>J.<span class="_ _3"> </span>Int.<span class="_ _11"> </span><span class="ff2 ls2">(19<span class="_ _5"></span>99)<span class="_ _4"> </span><span class="ff1 ls19">136,<span class="_ _4"> </span></span>559^5<span class="_ _5"></span>66</span></div><div class="t m0 x1 h4 y4c ff2 fs2 fc0 sc0 ls1a ws0">ß1<span class="_ _13"></span>9<span class="_ _14"></span>9<span class="_ _13"></span>9R<span class="_ _14"></span>A<span class="_ _14"></span>S</div><div class="t m0 x7 h6 y4d ff2 fs3 fc0 sc0 ls2 ws0">559</div><div class="t m1 x8 h9 y4e ff5 fs5 fc0 sc0 ls2 ws0"> by guest on November 22, 2013<span class="_ _15"></span><span class="fc1">http://gji.oxfordjournals.org/<span class="_ _16"></span><span class="fc0">Downloaded from </span></span></div><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div> </body> </html>

<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/622b67d33d2fbb0007481ba1/bg2.jpg"><div class="t m0 x1 h8 y4f ff2 fs4 fc0 sc0 ls2 ws0">op<span class="_ _5"></span>erator,<span class="_ _7"> </span>mo<span class="_ _5"></span>re<span class="_ _7"> </span>num<span class="_ _5"></span>eri<span class="_ _5"></span>cal<span class="_ _7"> </span>op<span class="_ _5"></span>erati<span class="_ _5"></span>ons<span class="_ _7"> </span>a<span class="_ _5"></span>re<span class="_ _7"> </span>nee<span class="_ _5"></span>ded.<span class="_ _7"> </span>Howeve<span class="_ _5"></span>r,</div><div class="t m0 x1 h8 y50 ff2 fs4 fc0 sc0 ls2 ws0">the<span class="_ _17"> </span>overal<span class="_ _5"></span>l<span class="_ _12"> </span>pe<span class="_ _5"></span>rforma<span class="_ _5"></span>nce<span class="_ _5"></span>s<span class="_ _12"> </span>of<span class="_ _12"> </span>the<span class="_ _17"> </span>FD<span class="_ _12"> </span>a<span class="_ _5"></span>nd<span class="_ _12"> </span>PS<span class="_ _12"> </span>m<span class="_ _5"></span>eth<span class="_ _5"></span>odsö</div><div class="t m0 x1 h8 y51 ff2 fs4 fc0 sc0 ls2 ws0">ass<span class="_ _5"></span>umin<span class="_ _5"></span>g<span class="_ _2"> </span>t<span class="_ _5"></span>he<span class="_ _6"> </span>sam<span class="_ _5"></span>e<span class="_ _2"> </span>a<span class="_ _5"></span>ccu<span class="_"> </span>rac<span class="_ _5"></span>yö<span class="_"> </span>ar<span class="_ _5"></span>e<span class="_ _6"> </span>simi<span class="_ _5"></span>lar,<span class="_ _6"> </span>dep<span class="_ _5"></span>end<span class="_ _5"></span>ing<span class="_ _6"> </span>mo<span class="_ _5"></span>stly</div><div class="t m0 x1 h8 y52 ff2 fs4 fc0 sc0 ls2 ws0">on<span class="_ _b"> </span>hardwa<span class="_ _5"></span>re.</div><div class="t m0 x3 h8 y53 ff2 fs4 fc0 sc0 ls2 ws0">One<span class="_ _2"> </span>m<span class="_"> </span>aj<span class="_ _5"></span>or<span class="_ _1"> </span>a<span class="_ _5"></span>dvantag<span class="_ _5"></span>e<span class="_ _1"> </span>o<span class="_ _5"></span>f<span class="_ _1"> </span>th<span class="_ _5"></span>e<span class="_ _1"> </span>P<span class="_ _5"></span>S<span class="_ _1"> </span>t<span class="_ _5"></span>echni<span class="_ _5"></span>que<span class="_ _2"> </span>is<span class="_ _2"> </span>in<span class="_ _2"> </span>co<span class="_"> </span>n<span class="_ _5"></span>nec<span class="_"> </span>t<span class="_ _5"></span>ion</div><div class="t m0 x1 h8 y54 ff2 fs4 fc0 sc0 ls2 ws0">with<span class="_ _8"> </span>an<span class="_ _5"></span>iso<span class="_ _5"></span>tropy:<span class="_ _6"> </span>W<span class="_ _5"></span>hile<span class="_ _8"> </span>s<span class="_ _5"></span>tagge<span class="_ _5"></span>red<span class="_ _8"> </span>gri<span class="_ _5"></span>ds<span class="_ _8"> </span>are<span class="_ _8"> </span>pr<span class="_ _5"></span>eferre<span class="_ _5"></span>d<span class="_ _8"> </span>in<span class="_ _8"> </span>FD</div><div class="t m0 x1 h8 y55 ff2 fs4 fc0 sc0 ls2 ws0">algo<span class="_ _5"></span>rith<span class="_ _5"></span>ms,<span class="_ _b"> </span>they<span class="_ _b"> </span>are<span class="_ _b"> </span>n<span class="_ _5"></span>ot<span class="_ _b"> </span>requ<span class="_ _5"></span>ired<span class="_ _b"> </span>wit<span class="_ _5"></span>h<span class="_ _4"> </span>th<span class="_ _5"></span>e<span class="_ _4"> </span>P<span class="_ _5"></span>S<span class="_ _4"> </span>te<span class="_ _5"></span>chniqu<span class="_ _5"></span>e.<span class="_ _4"> </span>Si<span class="_ _5"></span>nce</div><div class="t m0 x1 h8 y56 ff2 fs4 fc0 sc0 ls2 ws0">stag<span class="_ _5"></span>geri<span class="_ _5"></span>ng<span class="_ _9"> </span>involves<span class="_ _9"> </span>ele<span class="_ _5"></span>men<span class="_ _5"></span>ts<span class="_ _9"> </span>of<span class="_ _9"> </span>stres<span class="_ _5"></span>s,<span class="_ _9"> </span>strai<span class="_ _5"></span>n<span class="_ _9"> </span>and<span class="_ _9"> </span>the<span class="_ _9"> </span>s<span class="_ _5"></span>ti¡-</div><div class="t m0 x1 h8 y57 ff2 fs4 fc0 sc0 ls2 ws0">nes<span class="_ _5"></span>s<span class="_ _12"> </span>tens<span class="_ _5"></span>or<span class="_ _e"> </span>b<span class="_ _5"></span>ein<span class="_ _5"></span>g<span class="_ _e"> </span>d<span class="_ _5"></span>e¢n<span class="_ _5"></span>ed<span class="_ _12"> </span>at<span class="_ _12"> </span>di¡er<span class="_ _5"></span>ent<span class="_ _12"> </span>lo<span class="_ _5"></span>catio<span class="_ _5"></span>ns,<span class="_ _12"> </span>Hooke's</div><div class="t m0 x1 h8 y58 ff2 fs4 fc0 sc0 ls1b ws0">law<span class="_ _6"> </span>requires<span class="_ _6"> </span>(numerical)<span class="_ _8"> </span>interpolations<span class="_ _6"> </span>to<span class="_ _6"> </span>be<span class="_ _8"> </span>carried<span class="_ _8"> </span>out<span class="_ _6"> </span>in</div><div class="t m0 x1 h8 y59 ff2 fs4 fc0 sc0 ls2 ws0">the<span class="_ _a"> </span>gen<span class="_ _5"></span>eral<span class="_ _a"> </span>anis<span class="_ _5"></span>otrop<span class="_ _5"></span>ic<span class="_ _9"> </span>ca<span class="_ _5"></span>se,<span class="_ _9"> </span>furt<span class="_ _5"></span>her<span class="_ _9"> </span>deg<span class="_ _5"></span>radi<span class="_ _5"></span>ng<span class="_ _9"> </span>t<span class="_"> </span>h<span class="_ _5"></span>e<span class="_ _9"> </span>overa<span class="_ _5"></span>ll</div><div class="t m0 x1 h8 y5a ff2 fs4 fc0 sc0 ls2 ws0">acc<span class="_ _5"></span>uracy<span class="_ _4"> </span>(Igel<span class="_ _4"> </span><span class="ff3">et<span class="_ _11"> </span>al<span class="_ _5"></span>.<span class="_ _11"> </span></span>1995).<span class="_ _3"> </span>B<span class="_ _5"></span>ecau<span class="_ _5"></span>se<span class="_ _3"> </span>of<span class="_ _4"> </span>the<span class="_ _3"> </span>no<span class="_ _5"></span>n-s<span class="_"> </span>t<span class="_ _5"></span>agger<span class="_ _5"></span>ed<span class="_ _3"> </span>g<span class="_ _5"></span>rid<span class="_ _3"> </span>i<span class="_ _5"></span>n</div><div class="t m0 x1 h8 y5b ff2 fs4 fc0 sc0 ls1c ws0">the<span class="_ _4"> </span>PS<span class="_ _4"> </span>method<span class="_ _4"> </span>no<span class="_ _b"> </span>such<span class="_ _4"> </span>interpolations<span class="_ _4"> </span>are<span class="_ _4"> </span>necessary<span class="_ _f"></span>.</div><div class="t m0 x3 h8 y5c ff2 fs4 fc0 sc0 ls2 ws0">In<span class="_ _1"> </span>t<span class="_ _5"></span>his<span class="_ _2"> </span>pap<span class="_ _5"></span>er<span class="_ _1"> </span>we<span class="_ _2"> </span>propo<span class="_ _5"></span>se<span class="_ _1"> </span>a<span class="_ _2"> </span>sol<span class="_ _5"></span>utio<span class="_ _5"></span>n<span class="_ _1"> </span>to<span class="_ _1"> </span>t<span class="_ _5"></span>he<span class="_ _1"> </span>el<span class="_ _5"></span>asti<span class="_ _5"></span>c<span class="_ _1"> </span>is<span class="_ _5"></span>otropi<span class="_ _5"></span>c</div><div class="t m0 x1 h8 y5d ff2 fs4 fc0 sc0 ls2 ws0">wave<span class="_ _a"> </span>equat<span class="_ _5"></span>ion<span class="_ _a"> </span>for<span class="_ _d"> </span>sph<span class="_ _5"></span>erica<span class="_ _5"></span>l<span class="_ _a"> </span>sec<span class="_ _5"></span>tio<span class="_ _5"></span>ns<span class="_ _a"> </span>us<span class="_ _5"></span>ing<span class="_ _a"> </span>t<span class="_ _5"></span>he<span class="_ _a"> </span>C<span class="_ _5"></span>hebyshev</div><div class="t m0 x1 h8 y5e ff2 fs4 fc0 sc0 ls1b ws0">method.<span class="_ _3"> </span>This<span class="_ _4"> </span>can<span class="_ _4"> </span>be<span class="_ _4"> </span>seen<span class="_ _4"> </span>as<span class="_ _b"> </span>a<span class="_ _4"> </span>special<span class="_ _4"> </span>case<span class="_ _b"> </span>of<span class="_ _4"> </span>the<span class="_ _4"> </span>more<span class="_ _4"> </span>general</div><div class="t m0 x1 h8 y5f ff2 fs4 fc0 sc0 ls1d ws0">form<span class="_ _0"></span>ulation<span class="_ _8"> </span>of<span class="_ _6"> </span>Carcione<span class="_ _8"> </span>(1<span class="_ _f"></span>994)<span class="_ _8"> </span>for<span class="_ _6"> </span>generalized<span class="_ _6"> </span>c<span class="_"> </span>oordinates.</div><div class="t m0 x1 h8 y60 ff2 fs4 fc0 sc0 ls2 ws0">However,<span class="_ _2"> </span>th<span class="_ _5"></span>e<span class="_ _2"> </span>di<span class="_ _5"></span>rect<span class="_ _6"> </span>impl<span class="_ _5"></span>eme<span class="_"> </span>n<span class="_ _5"></span>tati<span class="_ _5"></span>on<span class="_ _2"> </span>of<span class="_ _2"> </span>t<span class="_ _5"></span>he<span class="_ _2"> </span>wave<span class="_ _2"> </span>e<span class="_ _5"></span>quatio<span class="_ _5"></span>n<span class="_ _2"> </span>in</div><div class="t m0 x1 h8 y61 ff2 fs4 fc0 sc0 ls2 ws0">sph<span class="_ _5"></span>eric<span class="_ _5"></span>al<span class="_ _9"> </span>co<span class="_ _5"></span>ordi<span class="_ _5"></span>nates<span class="_ _a"> </span>is<span class="_ _a"> </span>far<span class="_ _9"> </span>m<span class="_ _5"></span>ore<span class="_ _a"> </span>conven<span class="_ _5"></span>ient<span class="_ _a"> </span>tha<span class="_ _5"></span>n<span class="_ _9"> </span>sta<span class="_ _5"></span>rtin<span class="_ _5"></span>g</div><div class="t m0 x1 h8 y62 ff2 fs4 fc0 sc0 ls2 ws0">from<span class="_ _2"> </span>a<span class="_ _6"> </span>Car<span class="_ _5"></span>tesi<span class="_ _5"></span>an<span class="_ _2"> </span>fra<span class="_ _5"></span>me.<span class="_ _2"> </span>Fur<span class="_ _5"></span>ther<span class="_ _5"></span>more,<span class="_ _6"> </span>it<span class="_ _2"> </span>al<span class="_ _5"></span>lows<span class="_ _2"> </span>t<span class="_ _5"></span>he<span class="_ _2"> </span>a<span class="_ _5"></span>dditi<span class="_ _5"></span>on</div><div class="t m0 x1 h8 y63 ff2 fs4 fc0 sc0 ls2 ws0">of<span class="_ _7"> </span>smal<span class="_ _5"></span>l<span class="_ _7"> </span>pe<span class="_ _5"></span>rturbat<span class="_ _5"></span>ions<span class="_ _7"> </span>to<span class="_ _7"> </span>t<span class="_ _5"></span>he<span class="_ _7"> </span>sph<span class="_ _5"></span>eric<span class="_ _5"></span>al<span class="_ _7"> </span>gri<span class="_ _5"></span>d<span class="_ _8"> </span>(e.g<span class="_ _5"></span>.<span class="_ _8"> </span>e<span class="_ _5"></span>llip<span class="_ _5"></span>ticity<span class="_ _f"></span>,</div><div class="t m0 x1 h8 y64 ff2 fs4 fc0 sc0 ls2 ws0">sur<span class="_ _5"></span>face<span class="_ _9"> </span>topo<span class="_ _5"></span>graphy<span class="_ _f"></span>,<span class="_ _9"> </span>topo<span class="_ _5"></span>graphy<span class="_ _7"> </span>of<span class="_ _9"> </span>int<span class="_ _5"></span>ern<span class="_ _5"></span>al<span class="_ _9"> </span>bound<span class="_ _5"></span>arie<span class="_ _5"></span>s)<span class="_ _7"> </span>by</div><div class="t m0 x1 h8 y65 ff2 fs4 fc0 sc0 ls2 ws0">de¢<span class="_ _5"></span>nin<span class="_ _5"></span>g<span class="_ _4"> </span>app<span class="_ _5"></span>ropri<span class="_ _5"></span>ate<span class="_ _4"> </span>st<span class="_ _5"></span>retch<span class="_ _5"></span>ing<span class="_ _b"> </span>func<span class="_ _5"></span>tion<span class="_ _5"></span>s.</div><div class="t m0 x3 h8 y66 ff2 fs4 fc0 sc0 ls2 ws0">In<span class="_ _2"> </span>the<span class="_ _1"> </span>fol<span class="_ _5"></span>lowi<span class="_ _5"></span>ng<span class="_ _1"> </span>w<span class="_ _5"></span>e<span class="_ _1"> </span>wil<span class="_ _5"></span>l<span class="_ _1"> </span>in<span class="_"> </span>t<span class="_ _5"></span>roduce<span class="_ _2"> </span>the<span class="_ _2"> </span>gover<span class="_ _5"></span>ning<span class="_ _2"> </span>equat<span class="_ _5"></span>ion<span class="_ _5"></span>s</div><div class="t m0 x1 h8 y67 ff2 fs4 fc0 sc0 ls1e ws0">and<span class="_ _7"> </span>describe<span class="_ _9"> </span>the<span class="_ _7"> </span>numerical<span class="_ _7"> </span>techniques<span class="_ _7"> </span>to<span class="_ _9"> </span>sol<span class="_ _0"></span>ve<span class="_ _7"> </span>them<span class="_ _9"> </span>on<span class="_ _7"> </span>a</div><div class="t m0 x1 h8 y68 ff2 fs4 fc0 sc0 ls2 ws0">sph<span class="_ _5"></span>eric<span class="_ _5"></span>al<span class="_ _3"> </span>s<span class="_"> </span>e<span class="_ _5"></span>cti<span class="_ _5"></span>on.<span class="_ _3"> </span>Fin<span class="_ _5"></span>ally<span class="_ _f"></span>,<span class="_ _4"> </span>the<span class="_ _3"> </span>a<span class="_ _5"></span>lgorit<span class="_ _5"></span>hm<span class="_ _3"> </span>w<span class="_ _5"></span>ill<span class="_ _3"> </span>b<span class="_ _5"></span>e<span class="_ _3"> </span>app<span class="_ _5"></span>lied<span class="_ _4"> </span>to<span class="_ _11"> </span>wave</div><div class="t m0 x1 h8 y69 ff2 fs4 fc0 sc0 ls2 ws0">propagat<span class="_ _5"></span>ion<span class="_ _1"> </span>i<span class="_ _5"></span>n<span class="_ _1"> </span>the<span class="_ _1"> </span>E<span class="_ _5"></span>arth's<span class="_ _1"> </span>man<span class="_ _5"></span>tle<span class="_ _1"> </span>an<span class="_ _5"></span>d<span class="_ _1"> </span>to<span class="_ _1"> </span>th<span class="_"> </span>e<span class="_ _2"> </span>3-D<span class="_ _1"> </span>e<span class="_ _5"></span>¡ects<span class="_ _1"> </span>of<span class="_ _1"> </span>a</div><div class="t m0 x1 h8 y6a ff2 fs4 fc0 sc0 ls2 ws0">sim<span class="_ _5"></span>pli¢<span class="_ _5"></span>ed<span class="_ _b"> </span>slab<span class="_ _4"> </span>g<span class="_ _5"></span>eom<span class="_ _5"></span>etry<span class="_ _4"> </span>o<span class="_"> </span>n<span class="_ _b"> </span>l<span class="_ _5"></span>ong-p<span class="_ _5"></span>er<span class="_ _5"></span>iod<span class="_ _4"> </span>waves.</div><div class="t m0 x1 h7 y6b ff1 fs4 fc0 sc0 ls1f ws0">2<span class="_ _c"> </span>THE<span class="_ _b"> </span>WA<span class="_ _f"></span>VE<span class="_ _4"> </span>EQU<span class="_ _f"></span>ATION</div><div class="t m0 x1 h8 y6c ff2 fs4 fc0 sc0 ls2 ws0">F<span class="_ _0"></span>ol<span class="_"> </span>l<span class="_ _5"></span>owin<span class="_ _5"></span>g<span class="_ _6"> </span>the<span class="_ _8"> </span>approach<span class="_ _8"> </span>of<span class="_ _6"> </span>prev<span class="_ _5"></span>ious<span class="_ _6"> </span>a<span class="_"> </span>l<span class="_ _5"></span>gorit<span class="_ _5"></span>hms<span class="_ _8"> </span>(e.g.<span class="_ _1"> </span>Virieu<span class="_ _5"></span>x</div><div class="t m0 x1 h8 y6d ff2 fs4 fc0 sc0 ls12 ws0">1<span class="_ _0"></span>986;<span class="_ _b"> </span>Carcione<span class="_ _4"> </span>1994<span class="_ _0"></span>;<span class="_ _4"> </span>T<span class="_ _f"></span>essmer<span class="_ _1"> </span>&<span class="_ _4"> </span>Koslo¡<span class="_ _b"> </span>19<span class="_ _0"></span>94;<span class="_ _4"> </span>T<span class="_ _f"></span>essmer<span class="_ _4"> </span>1995)<span class="_ _f"></span>,</div><div class="t m0 x1 h8 y6e ff2 fs4 fc0 sc0 ls2 ws0">we<span class="_ _2"> </span>wr<span class="_ _5"></span>ite<span class="_ _2"> </span>the<span class="_ _2"> </span>gover<span class="_ _5"></span>ni<span class="_ _5"></span>ng<span class="_ _2"> </span>equat<span class="_ _5"></span>ions<span class="_ _2"> </span>as<span class="_ _6"> </span>a<span class="_ _1"> </span>¢<span class="_ _5"></span>rst-o<span class="_ _5"></span>rder<span class="_ _2"> </span>s<span class="_"> </span>yst<span class="_ _5"></span>em.<span class="_ _1"> </span>W<span class="_ _0"></span>e</div><div class="t m0 x1 h8 y6f ff2 fs4 fc0 sc0 ls20 ws0">denote<span class="_ _4"> </span><span class="ff6 ls2">p</span></div><div class="t m0 x9 ha y70 ff3 fs6 fc0 sc0 ls21 ws0">ij</div><div class="t m0 xa h8 y71 ff2 fs4 fc0 sc0 ls1d ws0">and<span class="_ _4"> </span><span class="ff7 ls2">o</span></div><div class="t m0 xb ha y70 ff3 fs6 fc0 sc0 ls2 ws0">i</div><div class="t m0 xc h8 y71 ff2 fs4 fc0 sc0 ls10 ws0">the<span class="_ _b"> </span>elements<span class="_ _4"> </span>of<span class="_ _b"> </span>the<span class="_ _b"> </span>stress<span class="_ _b"> </span>tensor<span class="_ _b"> </span>and<span class="_ _b"> </span>velocity</div><div class="t m0 x1 h8 y72 ff2 fs4 fc0 sc0 ls2 ws0">vecto<span class="_ _5"></span>r,<span class="_ _1"> </span>re<span class="_ _5"></span>spec<span class="_ _5"></span>tively.<span class="_ _1"> </span>In<span class="_ _2"> </span>gen<span class="_ _5"></span>eral<span class="_ _2"> </span>form<span class="_ _2"> </span>the<span class="_ _2"> </span>e<span class="_ _5"></span>quatio<span class="_ _5"></span>ns<span class="_ _1"> </span>o<span class="_ _5"></span>f<span class="_ _1"> </span>m<span class="_ _5"></span>otio<span class="_ _5"></span>n</div><div class="t m0 x1 h8 y73 ff2 fs4 fc0 sc0 ls22 ws0">are</div><div class="t m0 x1 hb y74 ff6 fs4 fc0 sc0 ls2 ws0">oL</div><div class="t m0 x3 hc y75 ff2 fs6 fc0 sc0 ls2 ws0">t</div><div class="t m0 xd hd y76 ff7 fs4 fc0 sc0 ls2 ws0">o</div><div class="t m0 xe ha y75 ff3 fs6 fc0 sc0 ls2 ws0">i</div><div class="t m0 xf hb y76 ff4 fs4 fc0 sc0 ls2 ws0">~<span class="ff6">+</span></div><div class="t m0 x9 ha y75 ff3 fs6 fc0 sc0 ls2 ws0">j</div><div class="t m0 x10 h8 y76 ff2 fs4 fc0 sc0 ls2 ws0">(<span class="ff6">p</span></div><div class="t m0 x11 ha y75 ff3 fs6 fc0 sc0 ls23 ws0">ij</div><div class="t m0 x12 he y76 ff4 fs4 fc0 sc0 ls2 ws0">z<span class="ff3">M</span></div><div class="t m0 xc ha y75 ff3 fs6 fc0 sc0 ls23 ws0">ij</div><div class="t m0 x13 h8 y76 ff2 fs4 fc0 sc0 ls2 ws0">)<span class="ff4">z<span class="ff3">f</span></span></div><div class="t m0 x14 ha y75 ff3 fs6 fc0 sc0 ls2 ws0">i</div><div class="t m0 x15 h8 y76 ff2 fs4 fc0 sc0 ls2 ws0">,</div><div class="t m0 x1 hb y77 ff6 fs4 fc0 sc0 ls2 ws0">L</div><div class="t m0 x16 hc y78 ff2 fs6 fc0 sc0 ls2 ws0">t</div><div class="t m0 x17 hb y79 ff6 fs4 fc0 sc0 ls2 ws0">p</div><div class="t m0 xd ha y78 ff3 fs6 fc0 sc0 ls23 ws0">ij</div><div class="t m0 xe he y79 ff4 fs4 fc0 sc0 ls2 ws0">~<span class="ff3">c</span></div><div class="t m0 x18 ha y78 ff3 fs6 fc0 sc0 ls24 ws0">ijkl</div><div class="t m0 x19 hb y79 ff6 fs4 fc0 sc0 ls2 ws0">L</div><div class="t m0 x11 hc y78 ff2 fs6 fc0 sc0 ls2 ws0">t</div><div class="t m0 x1a hf y79 ff8 fs4 fc0 sc0 ls2 ws0"></div><div class="t m0 x1b ha y78 ff3 fs6 fc0 sc0 ls25 ws0">kl</div><div class="t m0 x1c h8 y79 ff2 fs4 fc0 sc0 ls2 ws0">,<span class="_ _18"> </span>(1)</div><div class="t m0 x1 h8 y7a ff2 fs4 fc0 sc0 ls26 ws0">where<span class="_ _b"> </span><span class="ff3 ls2">c</span></div><div class="t m0 x18 ha y7b ff3 fs6 fc0 sc0 ls27 ws0">ijkl</div><div class="t m0 x1d h8 y7c ff2 fs4 fc0 sc0 ls28 ws0">are<span class="_ _b"> </span>the<span class="_ _1"> </span>elements<span class="_ _b"> </span>of<span class="_ _b"> </span>the<span class="_ _1"> </span>sti¡ness<span class="_ _1"> </span>tensor<span class="_ _4"> </span>a<span class="_"> </span>nd<span class="_ _1"> </span><span class="ff3 ls2">M</span></div><div class="t m0 x1e ha y7b ff3 fs6 fc0 sc0 ls23 ws0">ij</div><div class="t m0 x1f h8 y7c ff2 fs4 fc0 sc0 ls22 ws0">are</div><div class="t m0 x1 h8 y7d ff2 fs4 fc0 sc0 ls29 ws0">the<span class="_ _4"> </span>el<span class="_"> </span>ements<span class="_ _b"> </span>of<span class="_ _4"> </span>the<span class="_ _b"> </span>source<span class="_ _4"> </span>moment<span class="_ _b"> </span>tensor,<span class="_ _4"> </span><span class="ff3 ls2">f</span></div><div class="t m0 x20 ha y7e ff3 fs6 fc0 sc0 ls2 ws0">i</div><div class="t m0 x21 h8 y7f ff2 fs4 fc0 sc0 ls2 ws0">bei<span class="_ _5"></span>ng<span class="_ _b"> </span>volu<span class="_ _5"></span>metr<span class="_ _5"></span>ic</div><div class="t m0 x1 h8 y80 ff2 fs4 fc0 sc0 ls12 ws0">forces<span class="_ _f"></span>.</div><div class="t m0 x3 h8 y81 ff2 fs4 fc0 sc0 ls2 ws0">In<span class="_ _2"> </span>sp<span class="_ _5"></span>heri<span class="_ _5"></span>cal<span class="_ _2"> </span>coo<span class="_ _5"></span>rdin<span class="_ _5"></span>ates<span class="_ _2"> </span>[<span class="ff3">r</span>,<span class="_ _b"> </span><span class="ff6">h</span>,<span class="_ _b"> </span><span class="ff6">r</span>]<span class="_ _2"> </span>thes<span class="_ _5"></span>e<span class="_ _1"> </span>e<span class="_ _5"></span>quati<span class="_"> </span>o<span class="_ _5"></span>ns<span class="_ _2"> </span>(time<span class="_ _2"> </span>an<span class="_ _5"></span>d</div><div class="t m0 x1 h8 y82 ff2 fs4 fc0 sc0 ls2 ws0">spa<span class="_ _5"></span>ce<span class="_ _7"> </span>dep<span class="_ _5"></span>end<span class="_ _5"></span>ence<span class="_ _7"> </span>im<span class="_ _5"></span>plic<span class="_ _5"></span>it)<span class="_ _8"> </span>t<span class="_ _5"></span>ake<span class="_ _8"> </span>t<span class="_ _5"></span>he<span class="_ _8"> </span>for<span class="_ _5"></span>m<span class="_ _8"> </span>(e.g<span class="_ _5"></span>.<span class="_ _8"> </span>Lap<span class="_ _5"></span>wood<span class="_ _7"> </span>&</div><div class="t m0 x1 h8 y83 ff2 fs4 fc0 sc0 ls2 ws0">Usami<span class="_ _4"> </span>1981<span class="_ _f"></span>,<span class="_ _b"> </span>pp.<span class="_ _1"> </span>2<span class="_ _5"></span>8<span class="_ _4"> </span>an<span class="_ _5"></span>d<span class="_ _4"> </span>78)</div><div class="t m0 x1 hb y84 ff6 fs4 fc0 sc0 ls2 ws0">oL</div><div class="t m0 x3 hc y85 ff2 fs6 fc0 sc0 ls2 ws0">t</div><div class="t m0 xd hd y86 ff7 fs4 fc0 sc0 ls2 ws0">o</div><div class="t m0 xe ha y85 ff3 fs6 fc0 sc0 ls2 ws0">r</div><div class="t m0 xf hb y86 ff4 fs4 fc0 sc0 ls2 ws0">~<span class="ff6">L</span></div><div class="t m0 x22 ha y85 ff3 fs6 fc0 sc0 ls2 ws0">r</div><div class="t m0 x10 hb y86 ff6 fs4 fc0 sc0 ls2 ws0">p</div><div class="t m0 xa ha y85 ff3 fs6 fc0 sc0 ls2a ws0">rr</div><div class="t m0 x1a h10 y86 ff4 fs4 fc0 sc0 ls2 ws0">z</div><div class="t m0 x23 h8 y87 ff2 fs4 fc0 sc0 ls2 ws0">1</div><div class="t m0 x23 he y88 ff3 fs4 fc0 sc0 ls2 ws0">r</div><div class="t m0 x24 hb y89 ff6 fs4 fc0 sc0 ls2 ws0">L</div><div class="t m0 x25 h11 y85 ff6 fs6 fc0 sc0 ls2 ws0">h</div><div class="t m0 x26 hb y86 ff6 fs4 fc0 sc0 ls2 ws0">p</div><div class="t m0 x27 ha y85 ff3 fs6 fc0 sc0 ls2 ws0">r<span class="ff6">h</span></div><div class="t m0 x28 h10 y86 ff4 fs4 fc0 sc0 ls2 ws0">z</div><div class="t m0 x29 h8 y87 ff2 fs4 fc0 sc0 ls2 ws0">1</div><div class="t m0 x2a h8 y88 ff3 fs4 fc0 sc0 ls2 ws0">r<span class="_ _11"> </span><span class="ff2 ls2b">sin<span class="_ _19"> </span></span><span class="ff6">h</span></div><div class="t m0 x2b hb y89 ff6 fs4 fc0 sc0 ls2 ws0">L</div><div class="t m0 x2c h11 y85 ff6 fs6 fc0 sc0 ls2 ws0">r</div><div class="t m0 x2d hb y86 ff6 fs4 fc0 sc0 ls2 ws0">p</div><div class="t m0 x2 ha y85 ff3 fs6 fc0 sc0 ls2 ws0">r<span class="ff6">r</span></div><div class="t m0 x2e h10 y8a ff4 fs4 fc0 sc0 ls2 ws0">z</div><div class="t m0 x19 h8 y8b ff2 fs4 fc0 sc0 ls2 ws0">1</div><div class="t m0 x19 he y8c ff3 fs4 fc0 sc0 ls2 ws0">r</div><div class="t m0 x1a h8 y8d ff2 fs4 fc0 sc0 ls2 ws0">(2<span class="ff6">p</span></div><div class="t m0 x2f ha y8e ff3 fs6 fc0 sc0 ls2c ws0">rr</div><div class="t m0 x24 hb y8a ff4 fs4 fc0 sc0 ls2 ws0">{<span class="ff6">p</span></div><div class="t m0 x30 h11 y8e ff6 fs6 fc0 sc0 ls2d ws0">hh</div><div class="t m0 x14 hb y8a ff4 fs4 fc0 sc0 ls2 ws0">{<span class="ff6">p</span></div><div class="t m0 x31 h11 y8e ff6 fs6 fc0 sc0 ls2d ws0">rr</div><div class="t m0 x32 hb y8a ff4 fs4 fc0 sc0 ls2 ws0">z<span class="ff6">p</span></div><div class="t m0 x33 ha y8e ff3 fs6 fc0 sc0 ls2 ws0">r<span class="ff6">h</span></div><div class="t m0 x34 h8 y8a ff2 fs4 fc0 sc0 ls2e ws0">cot<span class="_ _19"> </span><span class="ff6 ls2">h<span class="ff2">)<span class="ff4">z<span class="ff3">f</span></span></span></span></div><div class="t m0 x35 ha y8e ff3 fs6 fc0 sc0 ls2 ws0">r</div><div class="t m0 x36 h8 y8a ff2 fs4 fc0 sc0 ls2 ws0">,</div><div class="t m0 x1 hb y8f ff6 fs4 fc0 sc0 ls2 ws0">oL</div><div class="t m0 x3 hc y90 ff2 fs6 fc0 sc0 ls2 ws0">t</div><div class="t m0 xd hd y91 ff7 fs4 fc0 sc0 ls2 ws0">o</div><div class="t m0 xe h11 y92 ff6 fs6 fc0 sc0 ls2 ws0">h</div><div class="t m0 x37 hb y91 ff4 fs4 fc0 sc0 ls2 ws0">~<span class="ff6">L</span></div><div class="t m0 x9 ha y90 ff3 fs6 fc0 sc0 ls2 ws0">r</div><div class="t m0 x10 hb y91 ff6 fs4 fc0 sc0 ls2 ws0">p</div><div class="t m0 x38 ha y92 ff3 fs6 fc0 sc0 ls2 ws0">r<span class="ff6">h</span></div><div class="t m0 x39 h10 y91 ff4 fs4 fc0 sc0 ls2 ws0">z</div><div class="t m0 x3a h8 y93 ff2 fs4 fc0 sc0 ls2 ws0">1</div><div class="t m0 x3a he y94 ff3 fs4 fc0 sc0 ls2 ws0">r</div><div class="t m0 x3b hb y95 ff6 fs4 fc0 sc0 ls2 ws0">L</div><div class="t m0 x13 h11 y92 ff6 fs6 fc0 sc0 ls2 ws0">h</div><div class="t m0 x3c hb y91 ff6 fs4 fc0 sc0 ls2 ws0">p</div><div class="t m0 x30 h11 y92 ff6 fs6 fc0 sc0 ls2d ws0">hh</div><div class="t m0 x14 h10 y91 ff4 fs4 fc0 sc0 ls2 ws0">z</div><div class="t m0 x3d h8 y93 ff2 fs4 fc0 sc0 ls2 ws0">1</div><div class="t m0 x3e h8 y94 ff3 fs4 fc0 sc0 ls2 ws0">r<span class="_ _11"> </span><span class="ff2 ls2b">sin<span class="_ _19"> </span></span><span class="ff6">h</span></div><div class="t m0 x3f hb y95 ff6 fs4 fc0 sc0 ls2 ws0">L</div><div class="t m0 x40 h11 y90 ff6 fs6 fc0 sc0 ls2 ws0">r</div><div class="t m0 x41 hb y91 ff6 fs4 fc0 sc0 ls2 ws0">p</div><div class="t m0 x42 h11 y92 ff6 fs6 fc0 sc0 ls2d ws0">hr</div><div class="t m0 x43 h10 y96 ff4 fs4 fc0 sc0 ls2 ws0">z</div><div class="t m0 x19 h8 y97 ff2 fs4 fc0 sc0 ls2 ws0">1</div><div class="t m0 x44 he y98 ff3 fs4 fc0 sc0 ls2 ws0">r</div><div class="t m0 x39 h8 y99 ff2 fs4 fc0 sc0 ls2 ws0">[(<span class="ff6">p</span></div><div class="t m0 x1c h11 y9a ff6 fs6 fc0 sc0 ls2d ws0">hh</div><div class="t m0 x24 hb y96 ff4 fs4 fc0 sc0 ls2 ws0">{<span class="ff6">p</span></div><div class="t m0 x30 h11 y9a ff6 fs6 fc0 sc0 ls2d ws0">rr</div><div class="t m0 x45 h8 y96 ff2 fs4 fc0 sc0 ls2f ws0">)c<span class="_ _1a"></span>o<span class="_ _1a"></span>t<span class="ff6 ls2">h<span class="ff4">z<span class="ff2">3</span></span>p</span></div><div class="t m0 x2d ha y9a ff3 fs6 fc0 sc0 ls2 ws0">r<span class="ff6">h</span></div><div class="t m0 x46 h8 y96 ff2 fs4 fc0 sc0 ls2 ws0">]<span class="ff4">z<span class="ff3">f</span></span></div><div class="t m0 x47 h11 y9a ff6 fs6 fc0 sc0 ls2 ws0">h</div><div class="t m0 x48 h8 y96 ff2 fs4 fc0 sc0 ls2 ws0">,</div><div class="t m0 x1 hb y9b ff6 fs4 fc0 sc0 ls2 ws0">oL</div><div class="t m0 x3 hc y9c ff2 fs6 fc0 sc0 ls2 ws0">t</div><div class="t m0 xd hd y9d ff7 fs4 fc0 sc0 ls2 ws0">o</div><div class="t m0 xe h11 y9c ff6 fs6 fc0 sc0 ls2 ws0">r</div><div class="t m0 x49 hb y9d ff4 fs4 fc0 sc0 ls2 ws0">~<span class="ff6">L</span></div><div class="t m0 x9 ha y9c ff3 fs6 fc0 sc0 ls2 ws0">r</div><div class="t m0 x4a hb y9d ff6 fs4 fc0 sc0 ls2 ws0">p</div><div class="t m0 x1d ha y9c ff3 fs6 fc0 sc0 ls2 ws0">r<span class="ff6">r</span></div><div class="t m0 x1b h10 y9d ff4 fs4 fc0 sc0 ls2 ws0">z</div><div class="t m0 x4b h8 y9e ff2 fs4 fc0 sc0 ls2 ws0">1</div><div class="t m0 x4b he y9f ff3 fs4 fc0 sc0 ls2 ws0">r</div><div class="t m0 x4c hb ya0 ff6 fs4 fc0 sc0 ls2 ws0">L</div><div class="t m0 x26 h11 y9c ff6 fs6 fc0 sc0 ls2 ws0">h</div><div class="t m0 x4d hb y9d ff6 fs4 fc0 sc0 ls2 ws0">p</div><div class="t m0 x4e h11 y9c ff6 fs6 fc0 sc0 ls2d ws0">hr</div><div class="t m0 x4f h10 y9d ff4 fs4 fc0 sc0 ls2 ws0">z</div><div class="t m0 x32 h8 y9e ff2 fs4 fc0 sc0 ls2 ws0">1</div><div class="t m0 x31 h8 y9f ff3 fs4 fc0 sc0 ls2 ws0">r<span class="_ _11"> </span><span class="ff2 ls30">sin<span class="_ _19"> </span></span><span class="ff6">h</span></div><div class="t m0 x50 hb ya0 ff6 fs4 fc0 sc0 ls2 ws0">L</div><div class="t m0 x2d h11 y9c ff6 fs6 fc0 sc0 ls2 ws0">r</div><div class="t m0 x51 hb y9d ff6 fs4 fc0 sc0 ls2 ws0">p</div><div class="t m0 x52 h11 y9c ff6 fs6 fc0 sc0 ls2d ws0">rr</div><div class="t m0 x18 h10 ya1 ff4 fs4 fc0 sc0 ls2 ws0">z</div><div class="t m0 x44 h8 ya2 ff2 fs4 fc0 sc0 ls2 ws0">1</div><div class="t m0 xa he ya3 ff3 fs4 fc0 sc0 ls2 ws0">r</div><div class="t m0 x12 h8 ya4 ff2 fs4 fc0 sc0 ls2 ws0">(3<span class="ff6">p</span></div><div class="t m0 x4b ha ya5 ff3 fs6 fc0 sc0 ls2 ws0">r<span class="ff6">r</span></div><div class="t m0 x4c h8 ya1 ff4 fs4 fc0 sc0 ls2 ws0">z<span class="ff2">2<span class="ff6">p</span></span></div><div class="t m0 x14 h11 ya5 ff6 fs6 fc0 sc0 ls2d ws0">hr</div><div class="t m0 x3e h8 ya1 ff2 fs4 fc0 sc0 ls2 ws0">cot<span class="_ _11"> </span><span class="ff6">h</span>)<span class="ff4">z<span class="ff3">f</span></span></div><div class="t m0 x2d h11 ya5 ff6 fs6 fc0 sc0 ls2 ws0">r</div><div class="t m0 x46 h8 ya1 ff2 fs4 fc0 sc0 ls2 ws0">,<span class="_ _1b"> </span>(2)</div><div class="t m0 x4 hf ya6 ff2 fs4 fc0 sc0 ls29 ws0">where<span class="_ _4"> </span>the<span class="_ _4"> </span>elements<span class="_ _4"> </span><span class="ff8 ls2"></span></div><div class="t m0 x53 ha ya7 ff3 fs6 fc0 sc0 ls21 ws0">ij</div><div class="t m0 x54 h8 y4f ff2 fs4 fc0 sc0 ls2 ws0">of<span class="_ _4"> </span>t<span class="_ _5"></span>he<span class="_ _4"> </span>s<span class="_ _5"></span>train<span class="_ _b"> </span>te<span class="_ _5"></span>nsor<span class="_ _b"> </span>are<span class="_ _b"> </span>given<span class="_ _b"> </span>by</div><div class="t m0 x4 hb ya8 ff6 fs4 fc0 sc0 ls2 ws0">L</div><div class="t m0 x55 hc ya9 ff2 fs6 fc0 sc0 ls2 ws0">t</div><div class="t m0 x56 hf yaa ff8 fs4 fc0 sc0 ls2 ws0"></div><div class="t m0 x57 ha ya9 ff3 fs6 fc0 sc0 ls2a ws0">rr</div><div class="t m0 x58 hb yaa ff4 fs4 fc0 sc0 ls2 ws0">~<span class="ff6">L</span></div><div class="t m0 x59 ha ya9 ff3 fs6 fc0 sc0 ls2 ws0">r</div><div class="t m0 x5a hd yaa ff7 fs4 fc0 sc0 ls2 ws0">o</div><div class="t m0 x5b ha ya9 ff3 fs6 fc0 sc0 ls2 ws0">r</div><div class="t m0 x5c h8 yaa ff2 fs4 fc0 sc0 ls2 ws0">,</div><div class="t m0 x4 hb yab ff6 fs4 fc0 sc0 ls2 ws0">L</div><div class="t m0 x55 hc yac ff2 fs6 fc0 sc0 ls2 ws0">t</div><div class="t m0 x56 hf yad ff8 fs4 fc0 sc0 ls2 ws0"></div><div class="t m0 x57 h11 yac ff6 fs6 fc0 sc0 ls2d ws0">hh</div><div class="t m0 x5d h10 yad ff4 fs4 fc0 sc0 ls2 ws0">~</div><div class="t m0 x5e h8 yae ff2 fs4 fc0 sc0 ls2 ws0">1</div><div class="t m0 x5e he yaf ff3 fs4 fc0 sc0 ls2 ws0">r</div><div class="t m0 x5f hb yb0 ff6 fs4 fc0 sc0 ls2 ws0">L</div><div class="t m0 x60 h11 yac ff6 fs6 fc0 sc0 ls2 ws0">h</div><div class="t m0 x61 hd yad ff7 fs4 fc0 sc0 ls2 ws0">o</div><div class="t m0 x62 h11 yac ff6 fs6 fc0 sc0 ls2 ws0">h</div><div class="t m0 x63 h10 yad ff4 fs4 fc0 sc0 ls2 ws0">z</div><div class="t m0 x64 h8 yae ff2 fs4 fc0 sc0 ls2 ws0">1</div><div class="t m0 x64 he yaf ff3 fs4 fc0 sc0 ls2 ws0">r</div><div class="t m0 x65 hd yb0 ff7 fs4 fc0 sc0 ls2 ws0">o</div><div class="t m0 x66 ha yac ff3 fs6 fc0 sc0 ls2 ws0">r</div><div class="t m0 x67 h8 yad ff2 fs4 fc0 sc0 ls2 ws0">,</div><div class="t m0 x4 hb yb1 ff6 fs4 fc0 sc0 ls2 ws0">L</div><div class="t m0 x55 hc yb2 ff2 fs6 fc0 sc0 ls2 ws0">t</div><div class="t m0 x56 hf yb3 ff8 fs4 fc0 sc0 ls2 ws0"></div><div class="t m0 x57 h11 yb2 ff6 fs6 fc0 sc0 ls2d ws0">rr</div><div class="t m0 x68 h10 yb3 ff4 fs4 fc0 sc0 ls2 ws0">~</div><div class="t m0 x69 h8 yb4 ff2 fs4 fc0 sc0 ls2 ws0">1</div><div class="t m0 x59 h8 yb5 ff3 fs4 fc0 sc0 ls2 ws0">r<span class="_ _11"> </span><span class="ff2 ls2b">sin<span class="_ _19"> </span></span><span class="ff6">h</span></div><div class="t m0 x6a hb yb6 ff6 fs4 fc0 sc0 ls2 ws0">L</div><div class="t m0 x6b h11 yb2 ff6 fs6 fc0 sc0 ls2 ws0">r</div><div class="t m0 x6c hd yb3 ff7 fs4 fc0 sc0 ls2 ws0">o</div><div class="t m0 x6d h11 yb2 ff6 fs6 fc0 sc0 ls2 ws0">r</div><div class="t m0 x66 h10 yb3 ff4 fs4 fc0 sc0 ls2 ws0">z</div><div class="t m0 x6e h8 yb4 ff2 fs4 fc0 sc0 ls2 ws0">1</div><div class="t m0 x6e he yb5 ff3 fs4 fc0 sc0 ls2 ws0">r</div><div class="t m0 x6f hd yb6 ff7 fs4 fc0 sc0 ls2 ws0">o</div><div class="t m0 x70 ha yb2 ff3 fs6 fc0 sc0 ls2 ws0">r</div><div class="t m0 x71 h10 yb3 ff4 fs4 fc0 sc0 ls2 ws0">z</div><div class="t m0 x72 h8 yb4 ff2 fs4 fc0 sc0 ls2 ws0">cot<span class="_ _11"> </span><span class="ff6">h</span></div><div class="t m0 x73 he yb5 ff3 fs4 fc0 sc0 ls2 ws0">r</div><div class="t m0 x74 hd yb6 ff7 fs4 fc0 sc0 ls2 ws0">o</div><div class="t m0 x75 h11 yb2 ff6 fs6 fc0 sc0 ls2 ws0">h</div><div class="t m0 x76 h8 yb3 ff2 fs4 fc0 sc0 ls2 ws0">,</div><div class="t m0 x4 hb yb7 ff6 fs4 fc0 sc0 ls2 ws0">L</div><div class="t m0 x55 hc yb8 ff2 fs6 fc0 sc0 ls2 ws0">t</div><div class="t m0 x56 hf yb9 ff8 fs4 fc0 sc0 ls2 ws0"></div><div class="t m0 x57 ha yb8 ff3 fs6 fc0 sc0 ls2 ws0">r<span class="ff6">h</span></div><div class="t m0 x77 h10 yb9 ff4 fs4 fc0 sc0 ls2 ws0">~</div><div class="t m0 x78 h8 yba ff2 fs4 fc0 sc0 ls2 ws0">1</div><div class="t m0 x78 h8 ybb ff2 fs4 fc0 sc0 ls2 ws0">2</div><div class="t m0 x60 h8 yba ff2 fs4 fc0 sc0 ls2 ws0">1</div><div class="t m0 x60 he ybb ff3 fs4 fc0 sc0 ls2 ws0">r</div><div class="t m0 x62 hb ybc ff6 fs4 fc0 sc0 ls2 ws0">L</div><div class="t m0 x79 h11 yb8 ff6 fs6 fc0 sc0 ls2 ws0">h</div><div class="t m0 x6a hd yb9 ff7 fs4 fc0 sc0 ls2 ws0">o</div><div class="t m0 x6b ha yb8 ff3 fs6 fc0 sc0 ls2 ws0">r</div><div class="t m0 x7a hb yb9 ff4 fs4 fc0 sc0 ls2 ws0">z<span class="ff6">L</span></div><div class="t m0 x7b ha yb8 ff3 fs6 fc0 sc0 ls2 ws0">r</div><div class="t m0 x7c hd yb9 ff7 fs4 fc0 sc0 ls2 ws0">o</div><div class="t m0 x7d h11 yb8 ff6 fs6 fc0 sc0 ls2 ws0">h</div><div class="t m0 x54 h10 yb9 ff4 fs4 fc0 sc0 ls2 ws0">{</div><div class="t m0 x7e h8 yba ff2 fs4 fc0 sc0 ls2 ws0">1</div><div class="t m0 x7e he ybb ff3 fs4 fc0 sc0 ls2 ws0">r</div><div class="t m0 x7f hd ybc ff7 fs4 fc0 sc0 ls2 ws0">o</div><div class="t m0 x72 h11 yb8 ff6 fs6 fc0 sc0 ls2 ws0">h</div><div class="t m0 x80 h12 ybd ff9 fs4 fc0 sc0 ls31 ws0"></div><div class="t m0 x81 h8 ybe ff2 fs4 fc0 sc0 ls2 ws0">,</div><div class="t m0 x4 hb ybf ff6 fs4 fc0 sc0 ls2 ws0">L</div><div class="t m0 x55 hc yc0 ff2 fs6 fc0 sc0 ls2 ws0">t</div><div class="t m0 x56 hf yc1 ff8 fs4 fc0 sc0 ls2 ws0"></div><div class="t m0 x57 h11 yc0 ff6 fs6 fc0 sc0 ls2d ws0">hr</div><div class="t m0 x82 h10 yc1 ff4 fs4 fc0 sc0 ls2 ws0">~</div><div class="t m0 x83 h8 yc2 ff2 fs4 fc0 sc0 ls2 ws0">1</div><div class="t m0 x83 h8 yc3 ff2 fs4 fc0 sc0 ls2 ws0">2</div><div class="t m0 x84 h8 yc2 ff2 fs4 fc0 sc0 ls2 ws0">1</div><div class="t m0 x85 h8 yc3 ff3 fs4 fc0 sc0 ls2 ws0">r<span class="_ _11"> </span><span class="ff2 ls2b">sin<span class="_ _19"> </span></span><span class="ff6">h</span></div><div class="t m0 x86 hb yc4 ff6 fs4 fc0 sc0 ls2 ws0">L</div><div class="t m0 x87 h11 yc0 ff6 fs6 fc0 sc0 ls2 ws0">r</div><div class="t m0 x7b hd yc1 ff7 fs4 fc0 sc0 ls2 ws0">o</div><div class="t m0 x53 h11 yc0 ff6 fs6 fc0 sc0 ls2 ws0">h</div><div class="t m0 x6e h10 yc1 ff4 fs4 fc0 sc0 ls2 ws0">z</div><div class="t m0 x88 h8 yc2 ff2 fs4 fc0 sc0 ls2 ws0">1</div><div class="t m0 x88 he yc3 ff3 fs4 fc0 sc0 ls2 ws0">r</div><div class="t m0 x89 hb yc4 ff6 fs4 fc0 sc0 ls2 ws0">L</div><div class="t m0 x8a h11 yc0 ff6 fs6 fc0 sc0 ls2 ws0">h</div><div class="t m0 x8b hd yc1 ff7 fs4 fc0 sc0 ls2 ws0">o</div><div class="t m0 x8c h11 yc0 ff6 fs6 fc0 sc0 ls2 ws0">r</div><div class="t m0 x8d h10 yc1 ff4 fs4 fc0 sc0 ls2 ws0">{</div><div class="t m0 x8e h8 yc2 ff2 fs4 fc0 sc0 ls29 ws0">cot<span class="_ _19"> </span><span class="ff6 ls2">h</span></div><div class="t m0 x8f he yc3 ff3 fs4 fc0 sc0 ls2 ws0">r</div><div class="t m0 x90 hd yc4 ff7 fs4 fc0 sc0 ls2 ws0">o</div><div class="t m0 x91 h11 yc0 ff6 fs6 fc0 sc0 ls2 ws0">r</div><div class="t m0 x5f h12 yc5 ff9 fs4 fc0 sc0 ls32 ws0"></div><div class="t m0 x92 h8 yc6 ff2 fs4 fc0 sc0 ls2 ws0">,</div><div class="t m0 x4 hb yc7 ff6 fs4 fc0 sc0 ls2 ws0">L</div><div class="t m0 x55 hc yc8 ff2 fs6 fc0 sc0 ls2 ws0">t</div><div class="t m0 x56 hf yc9 ff8 fs4 fc0 sc0 ls2 ws0"></div><div class="t m0 x57 ha yc8 ff3 fs6 fc0 sc0 ls2 ws0">r<span class="ff6">r</span></div><div class="t m0 x5d h10 yc9 ff4 fs4 fc0 sc0 ls2 ws0">~</div><div class="t m0 x5e h8 yca ff2 fs4 fc0 sc0 ls2 ws0">1</div><div class="t m0 x5e h8 ycb ff2 fs4 fc0 sc0 ls2 ws0">2</div><div class="t m0 x93 h8 yca ff2 fs4 fc0 sc0 ls2 ws0">1</div><div class="t m0 x5c h8 ycb ff3 fs4 fc0 sc0 ls2 ws0">r<span class="_ _11"> </span><span class="ff2 ls30">sin<span class="_ _19"> </span></span><span class="ff6">h</span></div><div class="t m0 x94 hb ycc ff6 fs4 fc0 sc0 ls2 ws0">L</div><div class="t m0 x95 h11 yc8 ff6 fs6 fc0 sc0 ls2 ws0">r</div><div class="t m0 x96 hd yc9 ff7 fs4 fc0 sc0 ls2 ws0">o</div><div class="t m0 x7c ha yc8 ff3 fs6 fc0 sc0 ls2 ws0">r</div><div class="t m0 x97 hb yc9 ff4 fs4 fc0 sc0 ls2 ws0">z<span class="ff6">L</span></div><div class="t m0 x70 ha yc8 ff3 fs6 fc0 sc0 ls2 ws0">r</div><div class="t m0 x71 hd yc9 ff7 fs4 fc0 sc0 ls2 ws0">o</div><div class="t m0 x98 h11 yc8 ff6 fs6 fc0 sc0 ls2 ws0">r</div><div class="t m0 x99 h10 yc9 ff4 fs4 fc0 sc0 ls2 ws0">{</div><div class="t m0 x9a h8 yca ff2 fs4 fc0 sc0 ls2 ws0">1</div><div class="t m0 x9a he ycb ff3 fs4 fc0 sc0 ls2 ws0">r</div><div class="t m0 x9b hd ycc ff7 fs4 fc0 sc0 ls2 ws0">o</div><div class="t m0 x8e h11 yc8 ff6 fs6 fc0 sc0 ls2 ws0">r</div><div class="t m0 x9c h12 ycd ff9 fs4 fc0 sc0 ls33 ws0"></div><div class="t m0 x9d h8 yce ff2 fs4 fc0 sc0 ls2 ws0">.<span class="_ _1c"> </span>(3)</div><div class="t m0 x5 h8 ycf ff2 fs4 fc0 sc0 ls2 ws0">In<span class="_ _4"> </span>t<span class="_ _5"></span>he<span class="_ _b"> </span>iso<span class="_ _5"></span>tropic<span class="_ _b"> </span>ca<span class="_ _5"></span>se,<span class="_ _4"> </span>th<span class="_ _5"></span>e<span class="_ _4"> </span>st<span class="_ _5"></span>ress<span class="_ _5"></span>^<span class="_ _5"></span>s<span class="_ _5"></span>trai<span class="_"> </span>n<span class="_ _b"> </span>r<span class="_ _5"></span>elati<span class="_ _5"></span>on<span class="_ _4"> </span>i<span class="_ _5"></span>s</div><div class="t m0 x4 hb yd0 ff6 fs4 fc0 sc0 ls2 ws0">p</div><div class="t m0 x55 ha yd1 ff3 fs6 fc0 sc0 ls2a ws0">rr</div><div class="t m0 x57 hf yd2 ff4 fs4 fc0 sc0 ls2 ws0">~<span class="ff6">j*</span>z<span class="ff2">2<span class="ff6">k<span class="ff8"></span></span></span></div><div class="t m0 x79 ha yd1 ff3 fs6 fc0 sc0 ls2c ws0">rr</div><div class="t m0 x9e he yd2 ff4 fs4 fc0 sc0 ls2 ws0">z<span class="ff3">M</span></div><div class="t m0 x96 ha yd1 ff3 fs6 fc0 sc0 ls2a ws0">rr</div><div class="t m0 x97 h8 yd2 ff2 fs4 fc0 sc0 ls2 ws0">,</div><div class="t m0 x4 hb yd3 ff6 fs4 fc0 sc0 ls2 ws0">p</div><div class="t m0 x55 h11 yd4 ff6 fs6 fc0 sc0 ls2d ws0">hh</div><div class="t m0 x9f hf yd5 ff4 fs4 fc0 sc0 ls2 ws0">~<span class="ff6">j*</span>z<span class="ff2">2<span class="ff6">k<span class="ff8"></span></span></span></div><div class="t m0 xa0 h11 yd4 ff6 fs6 fc0 sc0 ls2d ws0">hh</div><div class="t m0 xa1 he yd5 ff4 fs4 fc0 sc0 ls2 ws0">z<span class="ff3">M</span></div><div class="t m0 x67 h11 yd4 ff6 fs6 fc0 sc0 ls2d ws0">hh</div><div class="t m0 x54 h8 yd5 ff2 fs4 fc0 sc0 ls2 ws0">,</div><div class="t m0 x4 hb yd6 ff6 fs4 fc0 sc0 ls2 ws0">p</div><div class="t m0 x55 h11 yd7 ff6 fs6 fc0 sc0 ls2d ws0">rr</div><div class="t m0 xa2 hf yd8 ff4 fs4 fc0 sc0 ls2 ws0">~<span class="ff6">j*</span>z<span class="ff2">2<span class="ff6">k<span class="ff8"></span></span></span></div><div class="t m0 x6a h11 yd7 ff6 fs6 fc0 sc0 ls2d ws0">rr</div><div class="t m0 x6c he yd8 ff4 fs4 fc0 sc0 ls2 ws0">z<span class="ff3">M</span></div><div class="t m0 x97 h11 yd7 ff6 fs6 fc0 sc0 ls2d ws0">rr</div><div class="t m0 xa3 h8 yd8 ff2 fs4 fc0 sc0 ls2 ws0">,</div><div class="t m0 x4 hb yd9 ff6 fs4 fc0 sc0 ls2 ws0">p</div><div class="t m0 x55 ha yda ff3 fs6 fc0 sc0 ls2 ws0">r<span class="ff6">h</span></div><div class="t m0 x57 hf ydb ff4 fs4 fc0 sc0 ls2 ws0">~<span class="ff2">2<span class="ff6">k<span class="ff8"></span></span></span></div><div class="t m0 x5a ha yda ff3 fs6 fc0 sc0 ls2 ws0">r<span class="ff6">h</span></div><div class="t m0 x69 he ydb ff4 fs4 fc0 sc0 ls2 ws0">z<span class="ff3">M</span></div><div class="t m0 x9e ha yda ff3 fs6 fc0 sc0 ls2 ws0">r<span class="ff6">h</span></div><div class="t m0 x6c h8 ydb ff2 fs4 fc0 sc0 ls2 ws0">,</div><div class="t m0 x4 hb ydc ff6 fs4 fc0 sc0 ls2 ws0">p</div><div class="t m0 x55 h11 ydd ff6 fs6 fc0 sc0 ls2d ws0">hr</div><div class="t m0 xa4 hf yde ff4 fs4 fc0 sc0 ls2 ws0">~<span class="ff2">2<span class="ff6">k<span class="ff8"></span></span></span></div><div class="t m0 x9c h11 ydd ff6 fs6 fc0 sc0 ls2d ws0">hr</div><div class="t m0 xa5 he yde ff4 fs4 fc0 sc0 ls2 ws0">z<span class="ff3">M</span></div><div class="t m0 xa1 h11 ydd ff6 fs6 fc0 sc0 ls2d ws0">hr</div><div class="t m0 x95 h8 yde ff2 fs4 fc0 sc0 ls2 ws0">,</div><div class="t m0 x4 hb ydf ff6 fs4 fc0 sc0 ls2 ws0">p</div><div class="t m0 x55 ha ye0 ff3 fs6 fc0 sc0 ls2 ws0">r<span class="ff6">r</span></div><div class="t m0 x9f hf ye1 ff4 fs4 fc0 sc0 ls2 ws0">~<span class="ff2">2<span class="ff6">k<span class="ff8"></span></span></span></div><div class="t m0 x9c ha ye0 ff3 fs6 fc0 sc0 ls2 ws0">r<span class="ff6">r</span></div><div class="t m0 x5c he ye1 ff4 fs4 fc0 sc0 ls2 ws0">z<span class="ff3">M</span></div><div class="t m0 x6b ha ye0 ff3 fs6 fc0 sc0 ls2 ws0">r<span class="ff6">r</span></div><div class="t m0 x6d h8 ye1 ff2 fs4 fc0 sc0 ls2 ws0">,<span class="_ _1d"> </span>(4)</div><div class="t m0 x4 h8 ye2 ff2 fs4 fc0 sc0 ls2 ws0">wher<span class="_ _5"></span>e<span class="_ _4"> </span><span class="ff6">j<span class="_ _4"> </span></span>an<span class="_ _5"></span>d<span class="_ _4"> </span><span class="ff6">k<span class="_ _4"> </span></span><span class="ls34">are<span class="_ _b"> </span>the<span class="_ _4"> </span>Lame</span></div><div class="t m0 x8a h8 ye3 ff2 fs4 fc0 sc0 ls2 ws0">¨</div><div class="t m0 xa6 hf ye2 ff2 fs4 fc0 sc0 ls35 ws0">parameters<span class="_ _4"> </span>and<span class="_ _4"> </span><span class="ff6 ls2">*<span class="ff4">~<span class="ff8"></span></span></span></div><div class="t m0 xa7 ha ye4 ff3 fs6 fc0 sc0 ls2c ws0">rr</div><div class="t m0 xa8 hf ye5 ff4 fs4 fc0 sc0 ls2 ws0">z<span class="ff8"></span></div><div class="t m0 xa9 h11 ye6 ff6 fs6 fc0 sc0 ls2d ws0">hh</div><div class="t m0 xaa hf ye5 ff4 fs4 fc0 sc0 ls2 ws0">z<span class="ff8"></span></div><div class="t m0 xab h11 ye4 ff6 fs6 fc0 sc0 ls2d ws0">rr</div><div class="t m0 xac h8 ye5 ff2 fs4 fc0 sc0 ls2 ws0">.</div><div class="t m0 x5 h8 ye7 ff2 fs4 fc0 sc0 ls2 ws0">In<span class="_ _1"> </span>the<span class="_ _1"> </span>foll<span class="_ _5"></span>owing<span class="_ _1"> </span>se<span class="_ _5"></span>ctio<span class="_ _5"></span>n<span class="_ _b"> </span>w<span class="_ _5"></span>e<span class="_ _b"> </span>d<span class="_ _5"></span>escr<span class="_ _5"></span>ibe<span class="_ _1"> </span>the<span class="_ _1"> </span>nu<span class="_ _5"></span>meri<span class="_ _5"></span>cal<span class="_ _1"> </span>sol<span class="_ _5"></span>utio<span class="_ _5"></span>n</div><div class="t m0 x4 h8 ye8 ff2 fs4 fc0 sc0 ls2 ws0">to<span class="_ _4"> </span>t<span class="_"> </span>h<span class="_ _5"></span>ese<span class="_ _b"> </span>equ<span class="_ _5"></span>ation<span class="_ _5"></span>s.</div><div class="t m0 x4 h7 ye9 ff1 fs4 fc0 sc0 ls36 ws0">3<span class="_ _c"> </span>THE<span class="_ _1"> </span>NUMERIC<span class="_ _0"></span>AL<span class="_ _b"> </span>ALGORITHM</div><div class="t m0 x4 h7 yea ff1 fs4 fc0 sc0 ls37 ws0">3.<span class="_ _f"></span>1<span class="_ _c"> </span>Physical<span class="_ _b"> </span>and<span class="_ _1"> </span>computa<span class="_ _0"></span>tional<span class="_ _b"> </span>domain</div><div class="t m0 x4 h8 yeb ff2 fs4 fc0 sc0 ls2 ws0">T<span class="_ _f"></span>o<span class="_ _d"> </span>solve<span class="_ _d"> </span>t<span class="_ _5"></span>he<span class="_ _d"> </span>equat<span class="_ _5"></span>ions<span class="_ _d"> </span>d<span class="_ _5"></span>escr<span class="_ _5"></span>ibed<span class="_ _d"> </span>in<span class="_ _d"> </span>th<span class="_ _5"></span>e<span class="_ _a"> </span>p<span class="_ _5"></span>reviou<span class="_ _5"></span>s<span class="_ _d"> </span>sect<span class="_ _5"></span>ion,</div><div class="t m0 x4 h8 yec ff2 fs4 fc0 sc0 lsd ws0">all<span class="_ _9"> </span>space-dependen<span class="_"> </span>t<span class="_ _9"> </span>¢elds<span class="_ _9"> </span>are<span class="_ _9"> </span>de¢ned<span class="_ _9"> </span>on<span class="_ _9"> </span>a<span class="_ _9"> </span>curved<span class="_ _9"> </span>grid,<span class="_ _9"> </span>a</div><div class="t m0 x4 h8 yed ff2 fs4 fc0 sc0 ls2 ws0">sph<span class="_ _5"></span>erica<span class="_ _5"></span>l<span class="_ _e"> </span>sec<span class="_ _5"></span>tion<span class="_ _5"></span>,<span class="_ _d"> </span>as<span class="_ _e"> </span>i<span class="_ _5"></span>llus<span class="_ _5"></span>trate<span class="_ _5"></span>d<span class="_ _d"> </span>in<span class="_ _e"> </span>Fig<span class="_ _5"></span>.<span class="_ _19"> </span>1<span class="_ _0"></span>.<span class="_ _e"> </span>In<span class="_ _e"> </span>each<span class="_ _e"> </span>d<span class="_ _5"></span>imen<span class="_ _5"></span>-</div><div class="t m0 x4 h8 yee ff2 fs4 fc0 sc0 ls38 ws0">sion<span class="_ _7"> </span><span class="ff3 ls2">j<span class="_ _5"></span><span class="ff2">,<span class="_ _9"> </span>the<span class="_ _7"> </span>¢<span class="_ _5"></span>elds<span class="_ _9"> </span>are<span class="_ _9"> </span>de¢n<span class="_ _5"></span>ed<span class="_ _7"> </span>o<span class="_ _5"></span>n<span class="_ _7"> </span>the<span class="_ _9"> </span>Chebys<span class="_ _5"></span>hev<span class="_ _7"> </span>co<span class="_ _5"></span>lloc<span class="_ _5"></span>atio<span class="_ _5"></span>n</span></span></div><div class="t m0 x4 h4 yef ff1 fs2 fc0 sc0 ls2 ws0">Fig<span class="_ _5"></span>ur<span class="_ _5"></span>e<span class="_ _4"> </span>1.<span class="_ _7"> </span><span class="ff2">Physica<span class="_ _5"></span>l<span class="_ _4"> </span>domai<span class="_ _5"></span>n<span class="_ _3"> </span>for<span class="_ _4"> </span>3<span class="_ _5"></span>-D<span class="_ _4"> </span>simulati<span class="_ _5"></span>ons.<span class="_ _3"> </span>The<span class="_ _4"> </span>ang<span class="_ _5"></span>ular<span class="_ _4"> </span>rang<span class="_ _5"></span>e<span class="_ _4"> </span>in</span></div><div class="t m0 x4 h4 yf0 ff6 fs2 fc0 sc0 ls2 ws0">r<span class="_ _3"> </span><span class="ff2">and<span class="_ _4"> </span></span>h<span class="_ _3"> </span><span class="ff2">is<span class="_ _4"> </span>80</span></div><div class="t m0 x61 h13 yf1 ffa fs2 fc0 sc0 ls2 ws0">0</div><div class="t m0 xad h4 yf0 ff2 fs2 fc0 sc0 ls2 ws0">.<span class="_ _11"> </span>Th<span class="_"> </span>e<span class="_ _4"> </span>sect<span class="_ _5"></span>ion<span class="_ _3"> </span>i<span class="_ _5"></span>s<span class="_ _3"> </span>ce<span class="_ _5"></span>ntre<span class="_"> </span>d<span class="_ _4"> </span>around<span class="_ _4"> </span>the<span class="_ _3"> </span>e<span class="_ _5"></span>quator<span class="_ _3"> </span>(<span class="_ _5"></span><span class="ff6">h<span class="ff4">~</span></span><span class="ls3">90</span></div><div class="t m0 xae h13 yf1 ffa fs2 fc0 sc0 ls2 ws0">0</div><div class="t m0 xaf h4 yf0 ff2 fs2 fc0 sc0 ls2 ws0">).<span class="_ _11"> </span>The</div><div class="t m0 x4 h4 yf2 ff2 fs2 fc0 sc0 ls2 ws0">radia<span class="_ _5"></span>l<span class="_ _b"> </span>range<span class="_ _1"> </span>is<span class="_ _b"> </span>13<span class="_ _0"></span>71<span class="_ _4"> </span>km<span class="_ _1"> </span><span class="ffb">¦<span class="ff3">r</span>¦<span class="_"> </span></span>637<span class="_ _f"></span>1<span class="_ _b"> </span>km<span class="_ _5"></span>.<span class="_ _b"> </span>Note<span class="_ _1"> </span>the<span class="_ _b"> </span>d<span class="_ _5"></span>ensi¢<span class="_ _5"></span>catio<span class="_ _5"></span>n<span class="_ _b"> </span>of<span class="_ _b"> </span>t<span class="_ _5"></span>he</div><div class="t m0 x4 h4 yf3 ff2 fs2 fc0 sc0 ls2 ws0">grid<span class="_ _4"> </span>ne<span class="_"> </span>ar<span class="_ _4"> </span>t<span class="_"> </span>h<span class="_ _5"></span>e<span class="_ _3"> </span>b<span class="_ _5"></span>oundar<span class="_ _5"></span>ies<span class="_ _4"> </span>due<span class="_ _4"> </span>to<span class="_ _3"> </span>t<span class="_ _5"></span>he<span class="_ _4"> </span>Chebyshev<span class="_ _4"> </span>formulat<span class="_ _5"></span>ion.</div><div class="t m0 xb0 h4 yf4 ff2 fs2 fc0 sc0 ls2 ws0">ß<span class="_ _4"> </span>1<span class="_ _0"></span>999<span class="_ _4"> </span>RAS,<span class="_ _4"> </span><span class="ff3">GJI<span class="_ _6"> </span><span class="ff1">136,<span class="_ _4"> </span></span></span>559^5<span class="_ _5"></span>66</div><div class="t m0 x1 h6 yf5 ff2 fs3 fc0 sc0 ls39 ws0">560<span class="_ _1e"> </span><span class="ff3 ls2">H.<span class="_ _4"> </span>Ig<span class="_ _5"></span>el</span></div><div class="t m1 x8 h9 y4e ff5 fs5 fc0 sc0 ls2 ws0"> by guest on November 22, 2013<span class="_ _15"></span><span class="fc1">http://gji.oxfordjournals.org/<span class="_ _16"></span><span class="fc0">Downloaded from </span></span></div><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div>