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tivcly involved, during the last two dccadcs, in the devclapment and use of seismic modeling. Numerical solution of the elastic wave equaLon has Forward mndeling has proven ta be very useful for the proven to In a very valuable tool for gcnphys’cists in forward mdeling and migration. Among the techniques cnnstruction nfsynthctic data which can then be used to cheek the accuracy of a given interpretation. Modgenerally used in modeg Cent& Diflirreaces (exp!icit and implicit), A’ewmarR, Wilson and ffouhlt. The occulting large sparse system of linear cquatinns is no1t.d using both dbaet and iterative methods. For the direr. method the matrix is represented using the skyline stnragc scheme, Hhile for iterative methods the row-:.ire and the cewssed diqoaal schemes have been cr.&. The numerical methods have been implemented on mn IBM 3090 vector multiprocessor. Performance data for the different implementa:ions arc presented and compared with data previously obtained using pseudo-spectral and fiite difirences mcthodr on the same architecture. From nur results it is c ncludcd that Newmark and E*pltit Central DflJereacts are the most adeq;rate integration methods and Cor&,rte Cradient with compressed diugunul storage scher..c is the most cCAcient solver for vectnr cnmputers. cling is also used in seismic inversion, and in testing new algnrithms and prnccsning techniques. For there applicatinns, the use of accurate full elastic modeling is becoming mnre interesting with the recent trend tn extract more information from seismic surveys (i.e. shear-wave cxplnration ond ampliludr-vs-omsct annlysis). Evaluating varinus elastic forward mndcling prnccdurcs, it hecnmcr clear that analytical methods mny be nnt Hectivc, hccauac they nrc restricted to simple genmetrier with homngcncnus structures. Instead, numerical mcthnds (/ine in pnrticulnr, it allows the USE of non-unifnrm grids, having clcmcnts with varying characteristic sir.e, gcnmetry and order nf apprnximatinn. In this way it is possible tn achieve the dcsircd accuracy in the dill?rcnt rcginnr of the intcgration domain and simultancnusly tn incorporate, in o simple manner, hoondory conditinns defined on complex Introduction gcomctrics. Seismic prospectinn basically consists in grnerating wave flcld.~ at the surface of the earth, and mcaquring. the time it takes them to travel from the sc..rcc lo a series of recording geophnncs. The resulting seismic record represents the superposition of the wa:cs which have been reflected and rebacted t+om t1.s earth’s inhomogeneities back to the recording geopl..me. The objective of seismic work is the interpretatind of these seismic records in order to extract geological information. For this task, several data prncessing t chniques are used to ease the dinicult job of the ihterpreter. In fact, seismic records contain sueh a large bmnount of infnrmation that its interpretation is rather r:rbjcctivc. For this teason, the geophysical industry ha* been acOther hcnrfits prnvidctl by FEM arc the pnssihility nf using moving meshes 10 follow in detail ccrtnin areas of interest [4], hcllcr accuracy rnnr Pnis~nn coclScicnh hetwccn .21 and .45 [S], adcquntc treatment nf nonlincnr terms [6] nnd incorporation nfdiscnntinuitirs on the ma(rrial properties within the elements [7]. Ilowevct, FEM exhihits several drawhacks, spccinlly when the mesh in space or in time nre nnt properly gcnetatcd, such ns numerical attenuation or amplification [S], numcrical nnisotropy [RI, wave polarization [S], errors in phosc nnd group velocity [9] and sputinus wnves [ IO]. FEM lcods to a system ofordinary dimrential equatinns in time which can be intrgraicd with dit%rcnt methods. Depending on the method used explicit or implicit fnr |
