Report to Landmark Graphics Corporation, University Partnership Program

Seismic processing requires accurate knowledge of the earth's velocity structure to properly image and interpret multi-fold seismic data. Conventional analysis methods are based on determining the best fit hyperbolas to seismic travel-times, T, as a function of source-receiver offset, X, in CMP gathers. The results of this analysis are the two-way normal-time, and the stacking velocity for each event analyzed. If the source-receiver offsets are not too large compared to the reflector depth, the stacking velocities can be equated to the RMS velocity. From knowledge of the RMS velocity and two-way normal times above and below a zone of interest, the interval velocity can be determined. Even if the earth is truly one-dimensional, i.e., velocity varies only as a function of depth, errors arise from the departure of the actual travel-times trajectories from the assumed T(X) hyperbola and the departure of the stacking velocity from the RMS velocity. These errors are in addition to the uncertainties involved in determining both the stacking velocity and the two-way normal-times from limited offset, band limited data in the presence of coherent and random noise. An alternative interval velocity analysis method can be implemented if we first perform a plane wave decomposition of the seismic data. By transforming the data to the the domain of intercept time, t, and horizontal ray parameter, p, velocity analyses can be performed exactly for a one-dimensional earth model without the need for intermediate quantities such as the stacking and RMS velocities. Workstation technology, such as the LandmarkTM, can then be used to do this velocity analysis interactively. For example, the original seismic data are plane wave decomposed on a remote computer, e.g., a Cray, and are then transferred either via ethernet or tape to the Landmark for interpretation. The interpretation is done directly in the ?-p domain by interactively 3 defining ?-p travel time curves and superimposing these curves on the ? -p data. Once reasonable agreement is achieved, the plane wave data are NMO corrected in the ?-p domain and then redisplayed. (The NMO corrections can be to two-way time or to depth.) The interpretation procedure is now repeated in the NMO domain to refine the velocity depth structure. The data can be windowed in time and ray parameter prior to analysis and the window changed during the interpretation process. The parameters determined directly by the interpreter are the interval velocity and the thickness and/or two-way normal-time of each layer. No approximations are required and all source receiver offsets are implicitly included in the analysis.Landmark Graphics CorporationInstitute for Geophysic

Journal of Geophysics and Engineering

Texto completo. Acesso restrito. p. 1-9The pure P-wave equation for modelling and migration in tilted transversely isotropic (TTI) media has attracted more and more attention in imaging seismic data with anisotropy. The desirable feature is that it is absolutely free of shear-wave artefacts and the consequent alleviation of numerical instabilities generally suffered by some systems of coupled equations. However, due to several forward–backward Fourier transforms in wavefield updating at each time step, the computational cost is significant, and thereby hampers its prevalence. We propose to use a hybrid pseudospectral (PS) and finite-difference (FD) scheme to solve the pure P-wave equation. In the hybrid solution, most of the cost-consuming wavenumber terms in the equation are replaced by inexpensive FD operators, which in turn accelerates the computation and reduces the computational cost. To demonstrate the benefit in cost saving of the new scheme, 2D and 3D reverse-time migration (RTM) examples using the hybrid solution to the pure P-wave equation are carried out, and respective runtimes are listed and compared. Numerical results show that the hybrid strategy demands less computation time and is faster than using the PS method alone. Furthermore, this new TTI RTM algorithm with the hybrid method is computationally less expensive than that with the FD solution to conventional TTI coupled equationsSalvado

Journal of Geophysics and Engineering

Texto completo: acesso restrito. p. 291-301In isotropic media, we use the scalar acoustic wave equation to perform reverse time migration (RTM) of the recorded pressure wavefield data. In anisotropic media, P- and SV-waves are coupled, and the elastic wave equation should be used for RTM. For computational efficiency, a pseudo-acoustic wave equation is often used. This may be solved using a coupled system of second-order partial differential equations. We solve these using a pseudo spectral method and the rapid expansion method (REM) for the explicit time marching. This method generates a degenerate SV-wave in addition to the P-wave arrivals of interest. To avoid this problem, the elastic wave equation for vertical transversely isotropic (VTI) media can be split into separate wave equations for P- and SV-waves. These separate wave equations are stable, and they can be effectively used to model and migrate seismic data in VTI media where |epsilon − δ| is small. The artifact for the SV-wave has also been removed. The independent pseudo-differential wave equations can be solved one for each mode using the pseudo spectral method for the spatial derivatives and the REM for the explicit time advance of the wavefield. We show numerically stable and high-resolution modeling and RTM results for the pure P-wave mode in VTI media

Revista Brasileira de Geofísica

Três métodos de migração 2-D pré-empilhamento em profundidade usando operadores de extrapolação "split-step" foram desenvolvidos e testados em dados sísmicos ordenados em famílias de tiro comum. No primeiro método, chamado de migração "split-step" simultâneo (SS-S), a migração é realizada simultaneamente para as fontes e receptores usando-se operadores de extrapolação do tipo "split-step". Os dados registrados nos receptores são depropagados em profundidade e a propagação da fonte é simulada utilizando-se operadores "split-step" em ambos os procedimentos. A imagem final, ou seção migrada em profundidade, é obtida somando-se todas as freqüências de interesse durante o processo de correlação dos campos propagados e depropagados, para cada nível de profundidade e somando-se todos os tiros migrados. Visando diminuir o tempo computacional do método de migração SS-S, implementamos um segundo método, cujo cálculo dos tempos da fonte é realizado através da solução por diferencias finitas da equação iconal. Este segundo método é referido como método híbrido (SS-H). O terceiro método de migração desenvolvido e implementado é o resultado da combinação dos métodos SS-S e "Phase-shift Plus Interpolation" (PSPI). Neste caso, os campos de ondas são depropagados para diferentes velocidades e interpolados, como no método PSPI convencional. Ele é aqui denominado de método PSPI-SS. Quanto à escolha do operador de extrapolação "split-step" se deve, principalmente, à sua facilidade de implementação computacional e por apresentar imagens migradas de boa precisão e, também, pela sua robustez, mesmo em situações de forte contraste lateral de velocidade. Os resultados apresentados neste trabalho foram obtidos usando-se dados sintéticos, gerados a partir dos modelos Marmousi e EAGE/SEG, modelos em profundidade que apresentam uma alta complexidade geológica. Os resultados foram comparados entre si e os três métodos apresentaram imagens migradas bastante satisfatórias.São Paul

3-D Traveltime Calculations

This report presents a series of traveltime calculations for a 3-D scheme.Institute for Geophysic