Christof Stork

Reflection tomography in the postmigrated domain

Reflection tomography is an inversion method that adjusts a velocity and reflector depth model to be consistent with the prestack time data. This tomography approach minimizes the misfit of the data and model in the premigrated domain. Generally, the data are represented by the traveltimes of reflection events, which has made the technique problematic and unpopular. Techniques generally known as “migration velocity analysis” have a similar objective but use the postmigrated domain. For a variety of practical reasons, this postmigrated domain has advantages over the premigrated domain. With slight modifications, the reflection tomography approach can be implemented in the postmigrated domain. In this domain, a model is determined by optimizing the consistency of imaged reflection events on what has been called a common reflection point (CRP) gather. Extending reflection tomography to the postmigrated domain allows much of the knowledge developed for migration velocity analysis to be coupled with that of re...

Linear aspects of tomographic velocity analysis

Prestack velocity analysis in areas of complex structure is a coupled migration and transmission inversion problem that can be analyzed from a tomographic perspective. By making as few a priori assumptions about the solution as possible in parameterizing the inverse problem, generalized tomographic velocity analysis is applicable to a wide range of geologic cases. Constraints modify the method to the unique characteristics of each application. The ray trace/traveltime formulation for tomography, as proposed by Bishop et al. (1985), provides a conceptual tool for presenting features that are important to automated prestack velocity analysis in complex structure, such as (1) the coupling of the velocity field to the reflector positions, (2) the nonuniform coverage of the model by the data, (3) the ability to perform a controlled inversion of large matrices over a wide eigenvalue range, and (4) the implementation of constraints in the inversion. These features may impact other automated prestack velocity ana...

Using constraints to address the instabilities of automated prestack velocity analysis

Generalized prestack velocity analysis methods that use an automated approach to resolve laterally variable interval velocity fields are beset by a series of problems. The problem of resolving lateral velocity variations has inherent complications that prevent automated methods from being robust enough to be applied routinely to data from a variety of geologic provinces. The use of automated prestack velocity analysis methods will not eliminate the step of carefully producing an initial velocity model derived from regional geologic information and an interpretation of a conventionally processed section. For the methods to regularly produce useful additional information, the unique characteristics of each application must be input into the prestack velocity analysis with the use of inversion constraints. These constraints serve either to adapt the generalized prestack velocity analysis to a focused objective in a particular area or to provide iterative, interpretational tools that help the user produce a velocity model.

Predicting and removing complex 3D surface multiples with WEM modeling--an alternative to 3D SRME for wide azimuth surveys?

Summary Wave equation modeling of multiples predicts multiples by performing one way propagator modeling using only a previously produced velocity model and migrated seismic image. Test results show that wave equation modeling of multiples using a v(x,y,z) velocity and the complete seismic image is effective for predicting complex 3D multiples for subsequent removal. The results appear competitive with 3D SRME methods in certain situations where multiples have 3D complexity or the acquisition geometry provides a challenge for 3D SRME. One situation where this approach is promising is wide-azimuth surveys.

Singular value decomposition of the velocity‐reflector depth tradeoff, Part 1: Introduction using a two‐parameter model

A singular value decomposition (SVD) of a two-parameter model serves to introduce several characteristics of a raypath inversion of the standard reflection seismology recording geometry. Two important families of eigenvectors consist of constructive interference and destructive interference of velocity and reflector depth. The eigenvalue that corresponds to the velocity-reflector depth destructive interference is very sensitive to the maximum ray angle in the data. For a cable length equal to twice the reflector depth, the theoretical linear resolution is quite high. The relative weighting between velocity and reflector depth is not critical so long as the weight is near 1.0.

Demonstration of MVA tomography with controls and constraints for determining an accurate velocity model for prestack depth migration

I demonstrate an approach called MVA (Migration Velocity Analysis) tomography for determining an accurate velocity model for pre-stack depth migration. As a direct inversion method, this approach may produce an accurate velocity model in significantly less time than iterative migration approaches. Moreover, as a tomographic technique that uses ray paths, this approach may resolve complex velocity models that cause problems for focusing analysis methods. A key component of MVA tomography approach is interactive inversion controls and geologic constraints that enable an interpreter to “steer” the inversion to find a range of possible velocity models that are consistent with his seismic data and geologic knowledge.

Hybrid genetic autostatics: New approach for large‐amplitude statics with noisy data

Large amplitude statics or noisy data cause probms in residual statics methods that use a master trace or ck correlation peaks. A solution may not be found that eoduces coherent reflectors in the stacked section or the jlution may suffer from cycle skips. A combination of vo new complimentary approaches, genetic algorithms Id waveform steepest ascent, into a hybrid method can vercome these pitfalls and produce more optimal soluons. The danger of traces undergoing cycle skips in atic solutions correspond to a local maxima in the stack awer objective function. The problem of avoiding local linirna requires the use of a global search mechanism Ich as a genetic algorithm. However, global search mechanisms suffer from excessive computation cost rhen they start with a collection of random models. qaveform based steepest ascent is an efficient and stable pproach for finding the local maxima near a random tarting model, This steepest ascent approach is used here I provide an initial high-graded population for the enetic algorithm and to speed the genetic algorithm with ccasional steepest ascent iterations in the population volution. Waveform steepest ascent “climbs” the objective unction rather than picking correlation peaks. Repeated pplication of the hill climbing allows one to find the leak without a pre-determined bias. In addition, we use he cross-correlation of every trace in a CDP with every Ither CDP trace to avoid algorithmic problems related to he use of a master trace. This large set of correlations jrovides a vastly over-determined system of equations which helps stabilize the inversion, which is particularly lseful with noisy data. To efficiently determine a statics solution from the slopes of the massive crosscorrelations, we use an accelerated iterative matrix inver. sion borrowed from tomographic inversion. The statics problem serves as an efficient model fol testing new inverse methods that could be useful in othel applications of seismology.

Predicting subsalt dip-dependent illumination variations using density bubbles with RTM migration

Summary Variable illumination cause significant problems when imaging subsalt or other geologic regions with velocity variations. Much effort is taken to identify and improve the artifacts from these illumination variations, with limited success. A key challenge is that the illumination variations are a strong function of dip angle. Methods based on a single illumination value at each depth location or based on predefined reflector dip will be incomplete. We propose using “density bubbles” to identify the illumination variations as a function of dip, as seen in figure 1. These density bubbles are spheres of moderate density increase inserted in a model used to produce synthetic data. After the synthetic data is processed and migrated, a human can easily see illumination variations as a function of dip. This can be an essential QC mechanism to evaluate different acquisition approaches and imaging approaches. And after imaging, these density bubbles can be an effective interpretation tool for the interpreter to guide him on the imperfections of the seismic image produced with the real data that corresponds to the synthetic data.

On “Delayed-shot 3D depth migration” (Yu Zhang, James Sun, Carl Notfors, Samuel H. Gray, Leon Chernis, and Jerry Young, 2005, GEOPHYSICS, 71, E21–E28)

We present an alternative perspective on a key equation in the paper “Delayed-shot 3D depth migration” by Zhang et al. (2005). An alternative perspective indicates that a greater number of P-values are needed for a complete delayed-shot migration of typical marine-streamer data than those presented by Zhang et al. With the alternative equation, delayed-shot WEM migration is mathematically no more efficient than shot-WEM migration for typical marine streamer data.

On “Delayed-shot 3D depth migration” ()

We present an alternative perspective on a key equation in the paper “Delayed-shot 3D depth migration” by Zhang et al. (2005). An alternative perspective indicates that a greater number of P-values are needed for a complete delayed-shot migration of typical marine-streamer data than those presented by Zhang et al. With the alternative equation, delayed-shot WEM migration is mathematically no more efficient than shot-WEM migration for typical marine streamer data.