Douglas W. Hanson

Toward a unified analysis for source plane-wave migration

In complex areas with large lateral velocity variations, wave-equation-based source plane-wave migration can produce images comparable to those from shot-profile migration, with less computational cost. Image quality can be better than in ray-theory-based Kirchhoff-type methods. This method requires the composition of plane-wave sections from all shot gathers. We provide a general framework to evaluate plane-wave composition in prestack source plane-wave migration. Our analysis shows that a plane-wave section can be treated as encoded shot gathers. This study provides the theoretical justification for applying plane-wave migration algorithms to sparsely sampled shot gathers with irregularly distributed receivers and limited offset. In addition, we discuss cylindrical-wave migration, which is 3D migration of 2D-constructed plane waves along the inline direction. We mathematically prove the equivalence of shot and plane-wave migration, and their equivalence to cylindrical wave migration in 3D cases when the sail lines are straight. Examples (including the Sigsbee 2A model) demonstrate the theory.

Plane Wave Source Composition: An Accurate Phase Encoding Scheme For Prestack Migration

Wave equation based shot profile migration can produce higher quality images than Kirchhoff type methods. However, the high costs largely limit their production use. The cost of a complete wave equation shot profile migration equals the cost of migrating a single shot times the number of shots migrated. Thus, methods to reduce the number of migrations required for a complete experiment while preserving the image quality are as significant as those that increase the efficiency for each migration. One way to increase the efficiency of shot migration is to extrapolate the linearly combined wavefields from multiple shots together. However, special treatment is needed to take care of the cross-term artifacts, which are generated in applying the imaging condition. This technique is generally called phase encoding. Plane-wave source migration is one such method to reduce the number of migrations. In this paper, we demonstrate the concept of plane-wave source composition from the phase encoding point of view. We will show that plane wave source composition is a specific phase encoding technique in shot profile migration. This study demonstrates a systematic error analysis for the plane wave source approximation in migration. This offers the possibility of applying different composing schemes in each migration. We can show that this approach can generate results nearly equivalent to those of shot profile migration. Numerical tests on the Marmousi model and others prove the efficiency and accuracy of this method.

Common‐offset depth migrations and traveltime tomography

Many methods of depth migration velocity analysis emphasize Well-focused images. Others linearize and invert the effect of perturbed velocities on migrated images. We prefer to use developed methods of reflection traveltime tomography by converting picked migrated reflections into equivalent multi-offset traveltimes. Migration benefits prestack picking by simplifying reflections and diminishing noise. Depth migration does not add information to reflections, however. In fact, the bias of a poor velocity model should be removed. Conventional dynamic ray methods, or extrapolated traveltime tables suffice for the estimation of prestack traveltimes (geometric modeling). We need only find the midpoint hat reflects from a migrated point at the correct angle and offset. Constant-offset sections of a North Sea line were independently migrated in depth and viewed on a 3D interpretive workstation. One reflection at the base of chalk imaged at inconsistent depths over offset. This and ather reflections were picked over a range of offsets. Equivalent prestack traveltimes were modeled through the migration velocity model. The chosen method of traveltime tomography implicitly encouraged consistency in commonreflection points for raypaths at various offsets. The final estimated velocity model showed an increase in velocities near the base of the chalk, then a decrease in velocities below. Remigration of the data with the revised velocities greatly increased the visibility of the reflection at the base of the chalk.

3D Interval Velocity/Depth Model Building In the Southern Gas Basin UK, 3D Versus 2D Model Building

Summary Prestack depth imaging can be used to obtain a more accurate image of the earth’s subsurface in complex geologic areas. Prestack depth imaging relies on a correct interval velocity/depth model. We show two methods of obtaining a 3D velocity model in the Southern Gas Basin of the North Sea. In the first method a 3D velocity model is created by interpolating a series of 2D velocity models derived from iterative 2D tomography and prestack depth migration. In the second method an initial model is created using 3D coherency inversion. 3D tomography is then used to update the velocity model with a sparse set of CIP gathers. The 3D model building procedure is faster and yields a more accurate 3D velocity model than the 2D method.

Advances in prestack depth migration

Abstract Prestack depth migration is a useful tool for understanding complex structures in the North Sea and elsewhere around the world. Advances in computer speed and algorithm design have made depth migration of most 2-D data sets practical with current technology. Depth migrations greatest limitation is its sensitivity to the background velocity field. Currently, the most active research is on techniques for determining this velocity field, such as layer stripping, focusing analysis and tomography. These tools involve a degree of interpretation not normally seen in conventional seismic processing. If a good prestack depth migration is to be obtained, it is now well accepted that this interpretation component must form an integral part of the velocity model determination process. We present examples from the North Sea illustrating the strengths, and weaknesses, of various depth migration velocity analysis methods, and the interpretive steps they involve.

Traveltime tomography with multioffset common‐reflection points

Reflection traveltime tomography has evolved away from layered models toward independent parameters for velocities and reflectors. We introduce a simple method of optimizing interval velocities and common-reflection points simultaneously. Interval velocities are parametrized as a smooth function of spatial coordinates, independently of common-reflection points. Dynamic ray methods and explicit traveltime extrapolations identify common-reflection points that best model prestack traveltimes. The error between a modeled and measured traveltime is scaled by the cosine of a raypath’s angle of reflection. This scaled traveltime error is equivalent to the error of a reflection at normalincidence, or zero-offset. Velocities are revised to minimize the variance of these equivalent errors for all offsets of a common-reflection point. A North Sea seismic line was particularly unsuitable for a layered velocity model. Salt interrupted reflections, and chalk velocities increased rapidly with depth. The tomographically estimated velocities showed strong lateral changes. Prestack depth migration confumed that the velocity model accurately explained traveltimes.