We present a Finite Differences implementation of the 2D elastic wave equation. Our methodology makes use of both a staggered and a rotated grid, combining the stability and low phase dispersion of the two methods. The numerical simulation is done in the frequency domain, which allows us to easily implement an efficient boundary condition (PML) and enables the simulation of many sources simultaneously. We apply a compressed sparse matrix solver (LAPACK) and a vertical/horizontal displacement formulation in order to decrease the matrix demand for the implicit method. Results show the modeled snapshots in the time and frequency domains, which can be used as input for any seismic imaging process such as migration or Full Waveform Inversion.
Practical realization of the Wave Analogue of the Common Depth Point (WCDP) Method is described. It is a seismic processing data based on the strong mathematical solution of inverse scattering problem in linear approximation by multiple overlapping data. The WCDP method is tested on field data from numerous oil reservoirs. The results show high quality of WCDP profiles and stability for a wave velocity choice.
We propose an algorithm to compute the travel time matrix of the waves with the largest energy for prestack depth migration in an anisotropic medium with polar local symmetry or locally transversally isotropic (LTI). The algorithm is based in the phase shift concept to extrapolate the wave field. The irregularities that normally appear in the travel time matrix, computed by other methods, such as, ray tracing, when the medium has large velocity variations, do not appear with the same intensity in the proposed method. The algorithm is robust and its extension to the 3D case is straightforward.
We introduce a new scheme for depth migration in elastic vertical transverse isotropic media (VTI), using the concept of controlled illumination. In the proposed method the areal shots obtained from multicomponent records are extrapolated using phase‐shift techniques. Through the weighted addition of delayed shots we synthesize appropriate areal shots, which increases the accuracy of the seismic imaging in the area of interest. The computational cost of the present method is much lesser, when compared to the cost of migrating all the records, since only a few areal shots are necessary to image the area selected by the interpreters. The proposed method was tested on a typical numerical 2D model from the San Alberto field in Bolivia. It was possible to correct image an exploration target located underneath a thick highly tectonic deformed anisotropic shale layer, using only 3%of the computational time necessary to migrate all the shot records.
A successful prestack depth migration depends on a good depth interval velocity. The WCDP technique provides a reliable geological model after a composition based on interpretation of a series of time sections, which can be generated in a very short execution time when compared with the traditional prestack time migration. It will be discussed how this methodology works in order to obtain the geological model and the depth interval velocity field.
Summary We consider the elastic effects on an acoustic full waveform inversion generated by a synthetic pre-salt model of Santos basin, Brazil. We used P/S-velocity and density models to generate shot-gathers with acoustic, elastic (isotropic), constant and variable density modelling. The comparison of the amplitudes of the shot-gathers already provides a clue to the challenges acoustic FWI may face, as acoustic modelling is not able to provide the correct amplitude for the elastic data. This test is complemented with a constant-density acoustic FWI inversion, for all the different datasets, but with the same algorithm and parameterization. FWI with acoustic data was able to retrieve the correct information of high velocity sediments in the post/pre-salt environment and the stratification of the evaporitic sequence. On the other hand, the inversion of elastic data could not properly invert anything underneath the top of salt. The comparison of the inversion results indicates a direction in which algorithm and simplifications can be done to pursue an adequate property inversion.