Edip Baysal

Reverse time migration

Migration of stacked or zero-offset sections is based on deriving the wave amplitude in space from wave field observations at the surface. Conventionally this calculation has been carried out through a depth extrapolation. We examine the alternative of carrying out the migration through a reverse time extrapolation. This approach may offer improvements over existing migration methods, especially in cases of steeply dipping structures with strong velocity contrasts. This migration method is tested using appropriate synthetic data sets.

Forward modeling by a Fourier method

A Fourier or pseudospectral forward-modeling algorithm for solving the two-dimensional acoustic wave equation is presented. The method utilizes a spatial numerical grid to calculate spatial derivatives by the fast Fourier transform. time derivatives which appear in the wave equation are calculated by second-order differcncing. The scheme requires fewer grid points than finite-diffcrcnce methods to achieve the same accuracy. It is therefore believed that the Fourier method will prove more efficient than finitedifference methods. especially when dealing with threedimensional models. The Fourier forward-modeling method was tested against two problems, a single-layer problem with a known analytic solution and a wedge problem which was also tested by physical modeling. The numerical results agreed with both the analytic and physical model results. Furthermore, the numerical model facilitates the explanation of certain events on the time section of the physical model which otherwise could not easily be taken into account.

A two-way nonreflecting wave equation

In seismic modeling and in migration it is often desirable to use a wave equation (with varying velocity but constant density) which does not produce interlayer reverberations. The conventional approach has been to use a one‐way wave equation which allows energy to propagate in one dominant direction only, typically this direction being either upward or downward (Claerbout, 1972). We introduce a two‐way wave equation which gives highly reduced reflection coefficients for transmission across material boundaries. For homogeneous regions of space, however, this wave equation becomes identical to the full acoustic wave equation. Possible applications of this wave equation for forward modeling and for migration are illustrated with simple models.

A unified method for 2-D and 3-D refraction statics

Most of the seismic data processing procedures are divided into 2-D, 2.5-D, crooked lines or 3-D versions dictated by the differences in the shot and receiver configurations. In this paper, we introduce a tomographic approach that overcomes these geometrical difficulties and provides stable statics solutions from picked first-break times. We also show that the first-break picks contain both the short and the long wavelength surface statics. The solutions are obtained by solving a set of generalized surface-consistent delay-time equations using the method of weighted least squares and conjugate gradient. While iterating, each first-break pick is evaluated to ensure its consistency with the least-squares solution. Based on consistency, we weight the traveltime picks and use them in the next iteration. These weights also serve as an indicator of anomalous picks to the user. We show that long wavelength solutions leave large residual errors in the least-squares solutions. We also use the expected length of the Fresnel zone to differentiate between short and long wavelength static solutions. After removing the influence of long wavelength statics, we apply short wavelength statics to reduce the residual errors further. We demonstrate the validity of our unified method by applying it to actual data examples. The removal of both long and short wavelength statics improves the initial data set that produces a more consistent set of velocities and leaves only the short wavelength residual reflection statics, which are generally less than quarter wavelet period delays. This removes the most probable cause of the leg jump contamination and poor velocity estimates from the residual statics computations, especially from the 3-D data.

Migration with the full acoustic wave equation

Conventional finite‐difference migration has relied on one‐way wave equations which allow energy to propagate only downward. Although generally reliable, such equations may not give accurate migration when the structures have strong lateral velocity variations or steep dips. The present study examined an alternative approach based on the full acoustic wave equation. The migration algorithm which developed from this equation was tested against synthetic data and against physical model data. The results indicated that such a scheme gives accurate migration for complicated structures.

Surface Related Multiple Attenuation on Sigsbee2B Dataset

Surface related multiple attenuation (SRMA) has become a viable method for multiple suppression especially in complex structure where conventional methods may fail. Wave-equation based SRMA approaches generally work in a two-step fashion. In a data driven approach, surface related multiples are first predicted through convolution and integration of seismic data without any prior information about subsurface structures. The predicted multiples are then used to attenuate surface multiples recorded in seismic data. There are several approaches to subtract multiples from the seismic data, such as minimum energy wavelet extraction (Verschuur, 1992; Berkhout 1997), 1D matching filter (Berkhout, 1997), 2D matching filters (Wang, 2003), pattern recognition (Spitz, 1999), prediction error filters (Guitton, 2003). Abma (2002) compared some of these subtraction methods.

Velocity analysis for depth migration

Time migration is by far the most commonly used imaging technique in seismic processing. Its popularity is not due to the economics . The time and the depth migrations takes essentially the same length of computer time. There are some differences, however, aside from the difference in their display dimensions of time and depth ; the time migrated sections appear similar in frequency content to the CDP sections and the migration process tolerate considerable errors in the velocity field . On the other hand, depth migrated sections while they show a more accurate picture of the subsurface, as demanded by todays complex exploration targets, they do require more precise velocity/depth models .