Alejandro A. Valenciano

Flattening without picking

We present an efficient full-volume automatic dense-picking method for flattening seismic data. First local dips (stepouts) are calculated over the entire seismic volume. The dips are then resolved into time shifts (or depth shifts) using a nonlinear Gauss-Newton iterative approach that exploits fast Fourier transforms to minimize computation time. To handle faults (discontinuous reflections), we apply a weighted inversion scheme. The weight identifies locations of faults, allowing dips to be summed around the faults to reduce the influence of erroneous dip estimates near the fault. If a fault model is not provided, we can estimate a suitable weight (essentially a fault indicator) within our inversion using an iteratively reweighted least squares (IRLS) method. The method is tested successfully on both synthetic and field data sets of varying degrees of complexity, including salt piercements, angular unconformities, and laterally limited faults.

Target-oriented wave-equation inversion

A target-oriented strategy can be applied to estimate a wave-equation least-squares inverse (LSI) image. By explicitly computing the wave-equation Hessian, the LSI image is obtained as the solution of a nonstationary least-squares inverse filtering problem. The rows of the Hessian are the nonstationary filters containing information about the acquisition geometry, the velocity model, and the band-limited characteristics of the seismic data. By exploiting the sparsity and the structure of the Hessian matrix, a large number of iterations, necessary to achieve convergence, can be computed cheaply. The results on a structurally complex model show the improvements of the LSI image versus the migrated image.

2-D Deconvolution Imaging Condition For Shot-profile Migration

To implement a better imaging condition that is feasible in p ractice it is important to understand the 3-D prestack data and wavefi elds dimensionality. 3-D prestack seismic data is defined in a 5-D continuum (t,xs , ys ,xg , yg) (Biondi, 1998), wheret is time, xs is the sourcex position,ys is the sourcey position,xg is the geophonex position, andyg is the geophoney position. After applying the first step of shot-profile migration (source and receiver wavefiel ds construction) we have for each shot position ( xs , ys ) the source and the receiver wavefieldsu(x , y,z,t) and d(x , y,z,t). After wavefields propagation a new dimension is added ( z). Then the wavefields have 6-D dimensions.

Smoothing imaging condition for shot-profile migration

Amplitudes in shot-profile migration can be improved if the imaging condition incorporates a division deconvolution in the time domain of the upgoing wavefield by the downgoing wavefield. This division can be enhanced by introducing an optimal Wienerfilterwhichassumesthatthenoisepresentinthedatahas a white spectrum. This assumption requires a damping parameter, related to the signal-to-noise ratio, often chosen by trial and error. In practice, the damping parameter replaces the small valuesofthespectrumofthedowngoingwavefieldandavoidsdivision by zero. The migration results can be quite sensitive to the damping parameter, and in most applications, the upgoing and downgoing wavefields are simply multiplied. Alternatively, the division can be made stable by filling the small values of the spectrumwithanaverageoftheneighboringpoints.Thisaveraging is obtained by running a smoothing operator on the spectrum ofthedowngoingwavefield.Thisoperationcalledthesmoothing imaging condition. Our results show that where the spectrum of the downgoing wavefield is high, the imaging condition with dampingandsmoothingyieldssimilarresults,thuscorrectingfor illumination effects. Where the spectrum is low, the smoothing imaging condition tends to be more robust to the noise level present in the data, thus giving better images than the imaging condition with damping. In addition, our experiments indicate that the parameterization of the smoothing imaging condition, i.e., choice of window size for the smoothing operator, is easy and repeatable from one data set to another, making it a valuable additiontoourimagingtoolbox.

Imaging by target-oriented wave-equation inversion

Wave-equation inversion is a powerful technique able to build higher-resolution images with balanced amplitudes in complex subsurface areas relative to migration alone. Wave-equation inversion can be performed in image space without making velocity-model or acquisition-geometry approximations. Our method explicitly computes the least-squares Hessian matrix, defined from the modeling/migration operators, and uses a linear solver to find the solution of the resulting system of equations. One important advantage of the explicit computation of the Hessian, compared to iterative modeling/migration operations schemes, is that most of the work (precomputing the Hessian) is done up front; afterward, different inversion parameters or schemes can be tried at lower cost. Another advantage is that the method canhandle 3D data in a target-oriented fashion. The inversion in the presence of a complex overburden leads to an ill-conditioned system of equations that must be regularized to obtain a stable numerical solution...

Interval velocity estimation using edge-preserving regularization

Interval velocity estimation is a central problem in reflection seismology (Claerbout, 1999). Without an estimate of seismic velocities, we would be unable to transform prestack seismic data into an interpretable image. Advanced velocity estimation techniques (Clapp, 2001; Biondi and Sava, 1999) have been developed to estimate interval velocity in complex geological environments, though the cost of these methods is often considerable.

Robust Imaging Condition For Shot-Profile Migration

For shot-profile migration, illumination compensation can be achieved if the imaging condition incorporates a deconvolution (division in the frequency domain) of the upgoing wavefield by the down-going wavefield. To avoid division by zero, the deconvolution requires the selection of a damping parameter that turns out to be quite difficult to select. Consequently, a cross-correlation of the two wavefields is often selected. Alternatively, the zeros in the spectrum of the down-going wavefield can be filled with an average of the neighboring points. Therefore, instead of dividing by the wavefield, we can divide by a smoothed version of it. Smoothing is robust and easy to parameterize. It also corrects illumination problems in the migrated images.

Robust Illumination Compensation for Shot-Profile Migration

For shot-profile migration, illumination compensation can be achieved if the imaging condition incorporates a deconvolution (division in the frequency domain) of the up-going wavefield by the down-going wavefield. To avoid division by zero, the deconvolution requires the selection of a damping parameter that turns out to be quite difficult to select. Consequently, a cross-correlation of the two wavefields is often selected. Alternatively, the zeros in the spectrum of the down-going wavefield can be filled with an average of the neighboring points. Therefore, instead of dividing by the wavefield, we can divide by a smoothed version of it. Smoothing is robust and easy to parameterize. It also corrects illumination problems in the migrated images.

Wave-Equation Angle-Domain Hessian

A regularization in the reflection angle dimension (and, more generally in the reflection and azimuth angles) is necessary to stabilize the wave-equation inversion problem. The angle-domain Hessian can be computed from the subsurface-offset Hessian by an offset-to-angle transformation. This transformation can be done in the image space following the Sava and Fomel (2003) approach.

Imaging by target‐oriented wave‐equation inversion: 3‐D field data results

Wave-equation inversion is a powerful technique able to build clean images with balanced amplitudes in complex subsurface areas relative to migration alone. This paper illustrates how to perform wave-equation inversion in image space without making any velocity model or acquisition geometry approximations. The method explicitly computes the least-squares Hessian matrix, defined from the modeling/migration operators, and uses an iterative solver to find the solution of the resulting system of equations. This technique can handle 3-D data in a target-oriented fashion. The inversion in the presence of a complex overburden leads to an ill-conditioned system of equations that needs to be regularized to obtain a stable numerical solution. Regularization can be implemented in the poststack image-domain (zero subsurface offset), where the options for a regularization operator are limited to a customary damping, or in the prestack image-domain (subsurface offset), where a physically-inspired regularization operator (differential semblance) can be applied. Though the prestack imagedomain inversion is more expensive than the poststack imagedomain inversion, it can improve the reflectors continuity into the shadow zones with an enhanced signal-to-noise ratio. We demonstrate the utility of both these methods by improving the subsalt-sediment images of a 3-D Gulf of Mexico field data set.