Karl Schleicher

True-amplitude imaging and dip moveout

True‐amplitude seismic imaging produces a three dimensional (3-D) migrated section in which the peak amplitude of each migrated event is proportional to the reflectivity. For a constant‐velocity medium, the standard imaging sequence consisting of spherical‐divergence correction, normal moveout (NMO), dip moveout (DMO), and zero‐offset migration produces a true‐amplitude image if the DMO step is done correctly. There are two equivalent ways to derive the correct amplitude‐preserving DMO. The first is to improve upon Hale’s derivation of F-K DMO by taking the reflection‐point smear properly into account. This yields a new Jacobian that simply replaces the Jacobian in Hale’s method. The second way is to calibrate the filter that appears in integral DMO so as to preserve the amplitude of an arbitrary 3-D dipping reflector. This latter method is based upon the 3-D acoustic wave equation with constant velocity. The resulting filter amounts to a simple modification of existing integral algorithms. The new F-K an...

3D beam prestack depth migration with examples from around the world

In 1999, we specialized in 2D seismic depth processing. It was necessary to progress into 3D depth migration, but it seemed unrealistic to utilize Kirchhoff or wave-equation methods and be able to compete with large companies, their compute resources, and their economies of scale. Consequently, it was decided to attempt the commercial development of an alternative approach that would hopefully provide similar or improved technical quality, but with capital outlay and economics that were more appropriate to a small company. A very straightforward approach referred to as beam prestack depth migration (BPSDM) was adopted; its origins dated to work performed in the 1930s by Frank Rieber. The anticipated merits of BPSDM were overall simplicity, economy, flexibility, and future development possibilities. The unknowns were the migration accuracy and quality achievable. BPSDM was essentially developed independently, but aspects of it obviously are related to much recently published work on other beam migrations a...

3-D time‐variant dip moveout by the f-k method

The standard seismic imaging sequence consists of normal moveout (NMO), dip moveout (DMO), stack, and zero‐offset migration. Conventional NMO and DMO processes remove much of the effect of offset from prestack data, but the constant velocity assumption in most DMO algorithms can compromise the ultimate results. Time‐variant DMO avoids the constant velocity assumption to create better stacks, especially for steeply dipping events. Time‐variant DMO can be implemented as a 3-D, f-k domain process using the dip decomposition method. Prestack data are moved out with a set of NMO velocities corresponding to discrete values of in‐line and crossline dips. The dip‐dependent NMO velocity is computed to remove the trace offset and azimuth dependence of event times for an arbitrary velocity function of depth. After stacking the moved out CMP gathers, a three‐dimensional (3-D) dip filter is applied to select the particular in‐line and crossline dip. The final zero‐offset image is obtained by summing all the dip‐filter...

Effect of Irregular Sampling On Prestack DMO

The theoretical derivation of most DMO algorithms assumes a uniform midpoint distribution for each common-offset, common-azimuth set of traces, Deviation from uniformity leads to artifacts similar to those caused by missing traces in post-stack migration. Despite the fact that many 3-D geometries do not satisfy these assumptions, good stacked sections are often produced by DMO because of the attenuation of artifacts that takes place in the stacking process. Applying DMO in a full prestack mode offers the advantage of improved velocity analysis, but artifacts caused by irregularities in the offset, midpoint, and source-receiver azimuth distributions can cause problems. A practical extension of the DMO algorithm can be used to approximately correct these artifacts and to predict the reliability of the output traces prior to stacking them.

Model Building for Tilted Transverse Anisotropic Depth Migration of the Crystal, Gulf of Mexico Wide Azimuth Survey

The method used to build an anisotropic model for TTI migration is described. The method includes calibrating seismic depth to well depths, estimation of the tilted axis of symmetry of the anisotropy, iterative depth migration and tomography, and salt horizon interpretation. Cycle time is reduced by using a fast 3D, wide azimuth, beam, prestack depth migration. Results are shown on a wide azimuth marine survey in the deep water Gulf of Mexico.

Migration velocity analysis: A comparison of two approaches

Wave equation processing algorithms are available to image very complex structures. In most cases these processes are limited by our ability to estimate the correct velocity field. There are two types of migration Velocity Analysis (MVA) that use migration as a tooI to estimate velocity. The first type, velocity scanning MVA, prestack migates the data with a suite of velocities.

Model Building for Tilted Transverse Anisotropic Depth Migration of the Crystal Gulf of Mexico – Wide Azimuth Survey

The method used to build an anisotropic model for TTI migration is described. The method includes calibrating seismic depth to well depths, estimation of the tilted axis of symmetry of the anisotropy, iterative depth migration and tomography, and salt horizon interpretation. Cycle time is reduced by using a fast 3D, wide azimuth, beam, prestack depth migration. Results are shown on a wide azimuth marine survey in the deep water Gulf of Mexico.

WKBJ Phase shift migration

Recent success in imaging overturned structures has renewed interest in phase shift migration. Claerbout (1985) described an extension of phase shift migration to image dips greater than 90 degrees, but the practical significance of this algorithm was not widely appreciated before the 1991 SEG (Hale et al, Radcliff et al). Phase shift migration is widely regarded as a reference migration. Most migration experts are surprised to discover the algorithm is not true amplitude when velocity increases with depth.

Parallel 3D migration on mainframe attached workstations

High performance workstations are becoming widely used for seismic processing and the significant cost advantage of these computers for computationally intensive technologies is expected to continue to increase. Clusters of workstations can be parallel programmed to provide the floating point performance required for solving large problems such as one pass 3-D post stack depth migration.

FK DMO for depth variable velocity

We have implemented a practical DMO algorithm by incorporating Hubral s stacking velocity theory into the Jakubowicz approach. This methodology allows for arbitrary velocity variations in depth and producer DMO impulse responses with triplications. We have analyzed the operator response for a constant velocity gradient. The resulting DMO impulse response adequately matches the ray-theoretical response. The method may also be extended to 3-D.