Kirchhoff Prestack Time Migration Research Articles

The effects of migration velocity errors on traveltime accuracy in prestack Kirchhoff time migration and the image of PS converted waves

We analyze prestack PS migration images and their focusing sensitivity to errors in the computed PS traveltimes. The key analysis tool is a formula that defines PS traveltimes errors as explicit functions of velocity model errors. The most important factors in this formula are the PS velocity and the P-to-S velocity ratio. Analysis shows that the error in PS traveltime for shallow events is usually larger than that for deep events for a given error in the velocity model. Also the PS traveltime is affected more severely by errors in the PS-velocity model than in the P-to-S velocity ratio. The effect of traveltime errors increases with dip angle of reflectors. Numerical analysis shows that, for a fixed scatterpoint, the effect of the PS-wave velocity error is several times larger than the effect of the error in the P-to-S velocity ratio. Examples from field data show that the PS-wave velocity must be estimated accurately with errors less than 1% in order perfectly flatten the events in common-image-point (CIP) gathers. In contrast, an error in the PS-velocity ratio of up to several percent is allowed. This suggests that for acceptable PS-wave migration, only the PS-velocity model and a rough estimate of the P-to-S velocity ratio is needed. This finding is useful for processing PS-wave data because it is difficult and time consuming to estimate the velocity ratio accurately from the real data. This finding is also useful for our understanding of PS-wave behavior and for PS-wave imaging.

Kirchhoff time migration for transversely isotropic media: An application to Trinidad data

Using a newly developed nonhyperbolic offset-mid-point traveltime equation for prestack Kirchhoff time migration, instead of the conventional double-square-root (DSR) equation, results in overall better images from anisotropic data. Specifically, prestack Kirchhoff time migration for transversely isotropic media with a vertical symmetry axis (VTI media) is implemented using an analytical offset-midpoint traveltime equation that represents the equivalent of Cheop's pyramid for VTI media. It includes higher-order terms necessary to better handle anisotropy as well as vertical inhomogeneity. Application of this enhanced Kirchhoff time-migration method to the anisotropic Marmousi data set demonstrates the effectiveness of the approach. Further application of the method to field data from Trinidad results in sharper reflectivity images of the subsurface, with the faults better focused and positioned than with images obtained using isotropic methods. The superiority of the anisotropic time migration is evident in the flatness of the image gathers.

Parallel processing of Prestack Kirchhoff Time Migration on a PC Cluster

This paper discusses an approach that implements a parallel processing of 3-D Prestack Kirchhoff Time Migration (PKTM) on a low-cost PC Cluster by using the Message Passing Interface (MPI), and analyses its performance using a real seismic data as examples. The PC Cluster provides a significant acceleration of the migration processing with the exact same image quality. The ratio between the communication time and processing time is a critical indicator for determining the efficiency of the PC Cluster. If the processing time is longer than the communication time, using more CPUs can efficiently reduce the elapsed time. On the contrary, using more CPUs cannot reduce the elapsed time. Appling this approach to the Alba dataset on our PC Cluster up to 15 CPUs, the elapsed time of PKTM is inversely proportional to the number of CPUs used. The elapsed time for migrating a 2-D seismic line is reduced from 15 h using one CPU to 1 h using 15 CPUs. The elapsed time for migrating a 3-D image is reduced from 630 h using one CPU to 42 h using 15 CPUs. Further reduction can be achieved by using more CPUs. However, an optimal CPU number is expected for an application on large PC clusters with hundreds of nodes. Adapting existing algorithms to the cluster environment offers the potential to allow the application of more accurate algorithms for PKTM to construct a more accurate image. This work has proven that the PC Cluster is a powerful and scalable computing resource for oil and gas exploration organizations.

MULTIPLE REMOVAL SUCCESS IN THE CARNARVON BASIN WITH SRME

In 2003, Santos Ltd revisited a poor data quality area in the northern Carnarvon Basin, offshore Western Australia, where both short and long period multiple energy prohibits imaging of the underlying geology. Previous reprocessing efforts had failed to satisfactorily improve data quality, or reduce the level of multiple contamination. A two-dimensional (2D) reprocessing project was initiated to establish whether any modern variant of Surface-Related Multiple Elimination (SRME) could have success. Consequently, several versions of SRME were tested, with all output diagnostics being imaged with anisotropic Kirchhoff pre-stack time migration (PSTM). The new SRME results are a significant improvement over previous reprocessing efforts, and provide a much better platform for the picking of anisotropic velocity functions, and the application of PSTM imaging. Most of the multiple energy in this location is actually surface-related, with only a small component of internal multiple reverberations. Both long and short period multiple energy was successfully removed, and interpretation can now be pursued with more confidence in a difficult data location. Many outof- the-plane events still appear to contaminate the final 2D result, so a full three-dimensional (3D) production project was then pursued using standard (2D) SRME processing applied to 3D data gathers.Despite many noise challenges existing within the 3D field data, the final data images shed new light on a challenging geological environment, and prove the merits of SRME processing. A new generation of 3D acquisition and processing technology is now required to improve upon existing results, so a brief consideration is also given to the potential applications of 3D SRME processing to 3D seismic data from the North West Shelf. A brief example from offshore Brazil is used to illustrate the potential benefits of 3D SRME.

The Boris Oil Field in the Gulf of Mexico – a Geophysical Case Study

The Boris oil field was discovered in 2001 in Green Canyon block 282 in the deep water mini-basin area of the Gulf of Mexico. The Boris discovery was followed by the drilling of the Boris North appraisal well in 2002. First oil from the Boris field was produced in early 2003 with recoverable reserves estimated at 10 to 35 million barrels of oil equivalent. The Boris reservoir shows up as a bright seismic amplitude anomaly in Pliocene-age sand. Seismic reprocessing for robust amplitude fidelity and the use of Kirchhoff prestack time migration were the main geophysical tools that led to the discovery of the field. The Boris reservoir is steeply dipping at a depth of approximately 4500m. The original seismic data across the Boris field consisted of post-stack time migrated data that showed a broad, poorly defined amplitude with poor conformance to structure. After careful amplitude processing was input to prestack time migration, a bright well-defined amplitude ?appeared? on the seismic data with an excellent down-dip fit to structure. Concurrent with the reprocessing, a lithology and fluid prediction project was undertaken. Nearby well control was used to define rock property trends such as Vp versus depth, Vp versus Vs, and Vp versus density. The rock property trends were used to stochastically model the AVO response and the results were compared to the measured AVO response on the reprocessed seismic data. The results of the modelling showed that the fluid type at Boris was consistent with hydrocarbons. The Boris discovery well was drilled within three months of completing this reprocessing.

Imaging deepwater salt bodies in West Africa

The deep offshore of the Gulf of Guinea is a major challenge to seismic processing and imaging techniques, due to the complexity of the salt body structures (Figure 1). Even though Kirchhoff prestack time migration (preSTM) can image the top of salt and the wider, simple sedimentary basin reflections, it fails elsewhere.

The impact of common‐offset migration on porosity estimation by AVO inversion

The impact of prestack time migration on porosity estimation has been tested on a 2-D seismic line from the Valhall/Hod area in the North Sea. Porosity is estimated in the Cretaceous chalk section in a two‐step procedure. First, P-wave and S-wave velocity and density are estimated by amplitude variation with offset (AVO) inversion. These parameters are then linked to porosity through a petrophysical rock data base based on core plug analysis. The porosity is estimated both from unmigrated and prestack migrated seismic data. For the migrated data set, a standard prestack Kirchhoff time migration is used, followed by simple angle and amplitude corrections. Compared to modern high‐cost, true amplitude migration methods, this approach is faster and more practical. The test line is structurally fairly simple, with a maximum dip of 5°; but the results differ significantly, depending on whether migration is applied prior to the inversion. The maximum difference in estimated porosity is of the order of 10% (about 50% relative change). High‐porosity zones estimated from the unmigrated data were not present on the porosity section estimated from the migrated data.

The offset‐midpoint traveltime pyramid in transversely isotropic media

Prestack Kirchhoff time migration for transversely isotropic media with a vertical symmetry axis (VTI media) is implemented using an offset‐midpoint traveltime equation, Cheop’s pyramid equivalent equation for VTI media. The derivation of such an equation for VTI media requires approximations that pertain to high frequency and weak anisotropy. Yet the resultant offset‐midpoint traveltime equation for VTI media is highly accurate for even strong anisotropy. It is also strictly dependent on two parameters: NMO velocity and the anisotropy parameter, η. It reduces to the exact offset‐midpoint traveltime equation for isotropic media when η = 0. In vertically inhomogeneous media, the NMO velocity and η parameters in the offset‐midpoint traveltime equation are replaced by their effective values: the velocity is replaced by the rms velocity and η is given by a more complicated equation that includes summation of the fourth power of velocity.

Diffraction stacking with stacking velocity analysis - Its application to a surface seismic survey in an active fault area

A new type of prestack time migration method is presented. This method is a kind of prestack Kirchhoff time migration. One of the biggest advantages of this method is that data processing can be performed without a priori information about the velocity structure. The optimum constant stacking velocity can be determined at each image point from a stacking velocity analysis based on primary diffraction patterns. This proposed data processing method does not require multiples iterations for achieving the velocity structure in the case of prestack migration.Both the conventional CDP stacking method and the conventional stacking velocity analysis are modified as follows.In the case of the CDP stacking method, the amplitudes of observed data are stacked along the reflection pattern in a CDP gather. On the other hand, in the case of diffraction stacking method with stacking velocity analysis, the amplitudes of observed data are stacked along the diffraction pattern in a common source gather or common receiver gather.Stacking velocity analysis can be a useful tool for detecting characteristic patterns. Conventional stacking velocity analysis is modified to detect patterns caused by diffraction events. Final stacked records can be obtained based on results of stacking velocity analysis.The proposed data processing procedure was applied to surface seismic field data obtained in an active fault area and it was found that the active fault was imaged more adequately by application of diffraction stacking than CDP stacking. The reason was discussed from the viewpoint of S/N ratio. Our numerical experiments revealed that diffraction stacking generally has the ability to produce a seismic reflection image with higher S/N ratio than CDP stacking even for a flat and horizontal reflector. This can be explained by Huygens’ principle. And also, stacking coverage, defined as an angle range of collecting seismic traces, is an important factor in obtaining the highest S/N ratio. This can be explained in terms of Fresnel zones.

The equivalent offset method of prestack time migration

A prestack time migration is presented that is simple, efficient, and provides detailed velocity information. It is based on Kirchhoff prestack time migration and can be applied to both 2-D and 3-D data. The method is divided into two steps: the first is a gathering process that forms common scatterpoint (CSP) gathers; the second is a focusing process that applies a simplified Kirchhoff migration on the CSP gathers, and consists of scaling, filtering, normal moveout (NMO) correction, and stacking. A key concept of the method is a reformulation of the double square‐root equation (of source‐scatterpoint‐receiver traveltimes) into a single square root. The single square root uses an equivalent offset that is the surface distance from the scatterpoint to a colocated source and receiver. Input samples are mapped into offset bins of a CSP gather, without time shifting, to an offset defined by the equivalent offset. The single square‐root reformulation gathers scattered energy to hyperbolic paths on the appropriate CSP gathers. A CSP gather is similar to a common midpoint (CMP) gather as both are focused by NMO and stacking. However, the CSP stack is a complete Kirchhoff prestack migrated section, whereas the CMP stack still requires poststack migration. In addition, the CSP gather has higher fold in the offset bins and a much larger offset range due to the gathering of all input traces within the migration aperture. The new method gains computational efficiency by delaying the Kirchhoff computations until after the CSP gather has been formed. The high fold and large offsets of the CSP gather enables precise focusing of the velocity semblance and accurate velocity analysis. Our algorithm is formulated in the space‐time domain, which enables prestack migration velocity analysis to be performed at selected locations and permits prestack migration of a 3-D volume into an arbitrarily located 2-D line.

On the relation between the stacking process and resolution of a stacked section in a crosswell seismic survey

This paper describes the effect of source/receiver geometrical arrangements on the lateral resolution when implementing the diffraction stacking process in a crosswell seismic survey. Diffraction stacking with a stacking velocity analysis is equivalent to the Kirchhoff prestack time migration except for performing stacking velocity analysis.The resolving power of seismic data primarily depends on the dominant frequency of the recorded wavelet and the average velocity of the subsurface. It is proposed that lateral resolving power is also controlled by source/receiver geometrical arrangements. To obtain a better understanding of the concept of the seismic lateral resolution, the problem of seismic imaging is approached from the viewpoint of interference of equi-traveltime planes. Suitable source/receiver geometrical arrangements in homogeneous media are discussed. These studies are illustrated on a numerical simulation model, in which a zero phase Ricker wavelet is used and homogeneous and isotropic media is assumed. As a result, we indicate that source/receiver geometrical arrangements can influence the lateral resolution.