Biondo Biondi

Angle‐domain common‐image gathers for migration velocity analysis by wavefield‐continuation imaging

We analyze the kinematic properties of offset‐domain common image gathers (CIGs) and angle‐domain CIGs (ADCIGs) computed by wavefield‐continuation migration. Our results are valid regardless of whether the CIGs were obtained by using the correct migration velocity. They thus can be used as a theoretical basis for developing migration velocity analysis (MVA) methods that exploit the velocity information contained in ADCIGs.We demonstrate that in an ADCIG cube, the image point lies on the normal to the apparent reflector dip that passes through the point where the source ray intersects the receiver ray. The image‐point position on the normal depends on the velocity error; when the velocity is correct, the image point coincides with the point where the source ray intersects the receiver ray. Starting from this geometric result, we derive an analytical expression for the expected movements of the image points in ADCIGs as functions of the traveltime perturbation caused by velocity errors. By applying this ana...

Wave-Equation Migration Velocity Analysis

We overcome the limitations of conventional MVA in regions of high wavefield complexity (subsalt) using a wave-equation migration velocity analysis technique (Sava and Biondi, 2004a,a), and illustrate it on a realistic synthetic salt-dome dataset.

Angle-domain common image gathers by wave-equation migration

Shot- and offset-domain common image gathers encounter problems in complex media. They can place events that come from different points in the subsurface at one subsurface location based on identical arrival times and horizontal slownesses. Angle-domain common image gathers uniquely defineray couples for each point in the subsurface, therefore each event in the data will be associated with only one subsurface location. It is possible to generate angle-domain common image gathers with wave-equation migration methods and these angle-domain common image gathers may be used for velocity analysis and amplitude-versus-angle analysis. Applications of these methods to the Marmousi model are promising.

3-D prestack migration of common‐azimuth data

In principle, downward continuation of 3-D prestack data should be carried out in the 5-D space of full 3-D prestack geometry (recording time, source surface location, and receiver surface location), even when the data sets to be migrated have fewer dimensions, as in the case of common‐azimuth data sets that are only four dimensional. This increase in dimensionality of the computational space causes a severe increase in the amount of computations required for migrating the data. Unless this computational efficiency issue is solved, 3-D prestack migration methods based on downward continuation cannot compete with Kirchhoff methods. We address this problem by presenting a method for downward continuing common‐azimuth data in the original 4-D space of the common‐azimuth data geometry. The method is based on a new common‐azimuth downward‐continuation operator derived by a stationary‐phase approximation of the full 3-D prestack downward‐continuation operator expressed in the frequency‐wavenumber domain. Althou...

Least-squares attenuation of reverse-time-migration artifacts

Reverse-time-migration artifacts occur when diving waves, head waves or backscattered waves crosscorrelate. These events are particularly strong where high velocity contrasts exist. Simple filtering of the final image can lead to good results but might compromise the integrity of the signal of interest. We demonstrate that a better technique is to apply least-squares filtering with prediction-error filters, a method traditionally used for S/N separation.

Azimuth moveout for 3-D prestack imaging

We introduce a new partial prestack‐migration operator called “azimuth moveout” (AMO) that rotates the azimuth and modifies the offset of 3-D prestack data. Followed by partial stacking, AMO can reduce the computational cost of 3-D prestack imaging. We have successfully applied AMO to the partial stacking of a 3-D marine data set over a range of offsets and azimuths. When AMO is included in the partial‐stacking procedure, high‐frequency steeply dipping energy is better preserved than when conventional partial‐stacking methodologies are used. Because the test data set requires 3-D prestack depth migration to handle strong lateral variations in velocity, the results of our tests support the applicability of AMO to prestack depth‐imaging problems. AMO is a partial prestack‐migration operator defined by chaining a 3-D prestack imaging operator with a 3-D prestack modeling operator. The analytical expression for the AMO impulse response is derived by chaining constant‐velocity DMO with its inverse. Equivalentl...

Incorporating geologic information into reflection tomography

In areas of complex geology, prestack depth migration is often necessary if we are to produce an accurate image of the subsurface. Prestack depth migration requires an accurate interval velocity model. With few exceptions, the subsurface velocities are not known beforehand and should be estimated. When the velocity structure is complex, with significant lateral variations, reflection-tomography methods are often an effective tool for improving the velocity estimate. Unfortunately, reflection tomography often converges slowly, to a model that is geologically unreasonable, or it does not converge at all. The large null space of reflection-tomography problems often forces us to add a sparse parameterization of the model and/or regularization criteria to the estimation. Standard tomography schemes tend to create isotropic features in velocity models that are inconsistent with geology. These isotropic features result, in large part, from using symmetric regularization operators or from choosing a poor model parameterization. If we replace the symmetric operators with nonstationary operators that tend to spread information along structural dips, the tomography will produce velocity models that are geologically more reasonable. In addition, by forming the operators in helical 1D space and performing polynomial division, we apply the inverse of these space-varying anisotropic operators. The inverse operators can be used as a preconditioner to a standard tomography problem, thereby significantly improving the speed of convergence compared with the typical regularized inversion problem. Results from 2D synthetic and 2D field data are shown. In each case, the velocity obtained improves the focusing of the migrated image.

Wave-equation migration velocity analysis by focusing diffractions and reflections

We propose a method for estimating interval velocity using the kinematic information in defocused diffractions and reflections. We extract velocity information from defocused migrated events by analyzing their residual focusing in physical space (depth and midpoint) using prestack residual migration. The results of this residual-focusing analysis are fed to a linearized inversion procedure that produces interval velocity updates. Our inversion procedure uses a wavefield-continuation operator linking perturbations of interval velocities to perturbations of migrated images, based on the principles of wave-equation migration velocity analysis introduced in recent years. We measure the accuracy of the migration velocity using a diffraction-focusing criterion instead of the criterion of flatness of migrated common-image gathers that is commonly used in migration velocity analysis. This new criterion enables us to extract velocity information from events that would be challenging to use with conventional veloci...

Prestack imaging of overturned reflections by reverse time migration

SUMMARY We present a simple method for computing angle-domain Common Image Gathers (CIGs) using prestack reverse time migration. The proposed method is an extension of the method proposed by Rickett and Sava (2001) to compute CIGs by downward-continuation shot-profile migration. We demonstrate with a synthetic example the use of the CIG gathers for migration velocity updating. A challenge for imaging both overturned and prismatic reflections is the discrimination of the reflection generated on either side of interfaces. We show how the propagation direction of the reflections can be determined by evaluating the crosscorrelation of the source wavefield with the receiver wavefield at time lags different than zero. Reflections can be easily separated once their direction of propagation is determined. We demonstrate the method by imaging overturned events generated by a segment of dipping reflector immersed in a vertically layered medium. We also applied the method to a North Sea data set with overturned events. The results of reverse time prestack migration are superior to the one obtained by a downward-continuation migration, and the CIGs obtained by applying the proposed method provide useful information for velocity updating.

Stable wide-angle Fourier-finite difference downward extrapolation of 3-D wavefields

I present an unconditionally stable, implicit finite‐difference operator that corrects the constant‐velocity phase‐shift operator for lateral velocity variations. The method is based on the Fourier finite‐difference (FFD) method. Contrary to previous results, my correction operator is stable even when the medium velocity has sharp discontinuities, and the reference velocity is higher than the medium velocity. The stability of the new correction enables the definition of a new downward‐continuation method based on the interpolation of two wavefields: the first wavefield is obtained by applying the FFD correction starting from a reference velocity lower than the medium velocity; the second wavefield is obtained by applying the FFD correction starting from a reference velocity higher than the medium velocity. The proposed Fourier finite‐difference plus interpolation (FFDPI) method combines the advantages of the FFD technique with the advantages of interpolation.A simple and economical procedure for defining ...