Paul Docherty

Data repeatability for a new multi-component OBS node system

Summary Time-lapse seismic is an exacting experiment that targets subtle production related changes in the reservoir. With closely matched data acquisition emerging as a key component of time-lapse success, ocean bottom seismic (OBS) systems are one avenue currently being scrutinized for improved repeatability. During field trials of a new OBS node system in the deepwater Gulf of Mexico we measured the capability of the nodes for acquiring repeatable data. Rms differences in the neighborhood of 20% were observed for both hydrophone and vertical geophone, and a distinct correlation with source positioning error was evident. Horizontal geophone data were less repeatable, at around 40% rms difference, with a marked sensitivity to coupling with the ocean bottom.

Tomographic migration velocity analysis in 3-D

Large and complex velocity models, the prohibitive cost of depth imaging calculations, limited resources for interpreting velocity errors, and huge data sets: these are the obstacles that impede implementation of 3-D migration velocity analysis techniques. We have implemented a tomographic procedure that addresses these difficulties. It incorporates a flexible model parameterization, sparse ray tracing for traveltime approximations, automatic detection of residual moveout, parallel algorithm design, and a new feature: image computation in the direction normal to reflectors.

A Global Technique For Migration Velocity Analysis

Determination of the long wavelength, or background, velocity structure is a critical step in prestack imaging. We have developed an efficient procedure for the solution of this non-linear inverse problem using a genetic algorithm (GA). In our approach velocities are described by splines; velocity values at spline nodes are the parameters in the inversion. We distinguish between primary nodes, affecting very long wavelength variation, and secondary nodes, describing more rapid change. The GA evolves a population of trial solutions, seeking out the globally fittest velocity model. Key to the method is the evaluation of fitness, which is carried out in three steps: (i) map migration of zero-offset traveltimes through the trial velocity model to identify the approximate locations of reflectors; (ii) prestack Kirchhoff depth migration to generate image gathers in narrow depth windows centered on the predicted reflector locations; (iii) calculation of horizontal semblance within the image gathers. For the correct velocity model, reflection events appear flat in each of the gathers; thus, by calculating horizontal semblance we obtain a measure of fitness for the GA. Since the migration is performed over a narrow depth range in the neighborhood of a given reflector, rays need only be traced from a small number of depth points for each gather; additional ray information can be efficiently obtained using paraxial approximations.

Wide azimuth reflection response in 3-D angle gathers from OBS node data

Summary Wide azimuth seismic data illuminate the subsurface at a wide range of source-receiver azimuths. This valuable azimuthal information may be extracted from seismic data in the form of 3-D angle domain common image gathers (ADCIGs). Residual moveout (RMO) in 3-D ADCIGs generally varies with azimuth when the migration velocity is incorrect. However, to obtain accurate RMO in 3-D ADCIGs wide azimuth seismic data are necessary. Applications of 3-D ADCIGs include seismic interpretation and estimating velocity updates for wide-azimuth velocity tomography. We generate 3-D ADCIGs from wide azimuth OBS node data. OBS node data typically contain relatively fewer seafloor nodes compared to surface sources, but source coverage per node typically samples the full desired range of source-receiver offsets and azimuths. This makes OBS node data ideal for producing 3-D ADCIGs as long as the sampling of receiver nodes is sufficiently dense. Aliasing in ODCIGs caused by large node spacing is a potential problem that can degrade the quality of the ADCIGs. We address this in two ways. We image the downgoing wavefield, which offers wider subsurface illumination and overlap per node than can be obtained from the upgoing wavefield. We also perform anti-alias filtering of the ODCIGs by windowing them in the subsurface offset domain before conversion to 3-D ADCIGs. These steps allow us to obtain high quality 3-D ADCIGs from OBS node data. We demonstrate this using a deep-water OBS node field data set.

Finite difference 3D common-shot migration of data from the West Delta area of the Gulf of Mexico

The advent of the network, or “cluster,” of modern personal computers has enabled prestack 3D “wave equation” methods, such as common-shot migration, to become practical alternatives to standard Kirchhoff depth migration. Clusters have overcome hardware limitations (cost-effective memory and speed) that previously limited the widespread use of these wave equation algorithms. Prestack Kirchhoff migration is efficient and easily adapts to various data acquisition geometries, while its steep-dip and high-resolution imaging capabilities are unparalleled. Traveltime calculations, typically by ray tracing, are fundamental to conventional Kirchhoff migration. However, propagating wavefronts become complicated when traveling through complex geology; for example, a simple spherical wave propagating near its source eventually separates into several (or many) distinct “branches” as the wave encounters large lateral velocity variations. Computing 3D traveltime fields that faithfully represent such wave propagation and actually using these in 3D Kirchhoff migration is difficult and computationally expensive. Conventional Kirchhoff migration instead uses simplified, single-valued traveltime fields produced by criteria such as first arrival or maximum energy. Where several raypaths encounter a grid node, for example, the maximum-energy criterion selects the traveltime from the raypath with largest amplitude. The single-valued traveltime approximation may be poor in complex geology, where the traveltime fields really are multibranched or multivalued. Prestack wave equation imaging, on the other hand, such as finite difference common-shot migration, uses numerical modeling of the one-way wave equation instead of ray tracing. These wave equation methods can be more accurate than ray methods for modeling wave propagation in complex media. The result can be a superior image in areas of complex geology, such as beneath salt bodies. The most serious limitation of these one-way wave equation methods is that they are dip-limited relative to Kirchhoff methods, especially for strong lateral velocity variations. Most of todays prestack wave equation methods use accurate “dual-domain” techniques …

Long wavelength velocity determination using a genetic algorithm

Determination of the long wavelength, or background, velocity structure is a critical step in prestack imaging. We have developed an efficient procedure for the solution of this non-linear inverse problem using a genetic algorithm (GA). In our approach velocities are described by splines; velocity values at spline nodes are the parameters in the inversion. We distinguish between primary nodes, affecting very long wavelength variation, and secondary nodes, describing more rapid change. The GA evolves a population of trial solutions, seeking out the globally fittest velocity model. Key to the method is the evaluation of fitness, which is carried out in three steps: (1) map migration of zero-offset traveltimes through the trial velocity model to identify the approximation locations of primary reflectors; (2) prestack Kirchhoff depth migration to generate image gathers in narrow depth windows centered on the predicted reflector locations; (3) calculation of horizontal semblance within the image gathers. For the correct velocity model, reflection events appear flat in each of the gathers; thus, by calculating horizontal semblance we obtain a measure of fitness for the GA. Since the migration is performed over a narrow depth range in the neighborhood of a given reflector, rays need only be traced from a small number of depth points for each gather; additional ray information can be efficiently obtained using paraxial approximations.

A fast ray tracing routine for laterally inhomogeneous media

Abstract : This document describes the use of continuation or homotopy procedures in an efficient algorithm for the calculation of raypaths from points within a region at depth to receivers on the surface. Polynomials define the interfaces in a two-dimensional piecewise constant velocity medium. Starting with horizontal layering only, the interfaces are gradually deformed until the desired earth model is achieved. At each deformation step the ray equations determined by Fermats Principle are solved using Newtons method and the ray from the first source position to a receiver vertically above it is found. Next the author employs source continuation, moving the source on a grid within the region of interest. At each source position he finds the rays to all receivers using continuation in receiver location. Knowing the raypaths, it is straightforward to construct a table of traveltimes. These traveltimes alone serve to position reflectors in the subsurface. Two examples of migration and indicate possible applications to forward modeling are given. Additional keywords: Numerical methods and procedures, Fortran, Computer programs, Charts. (Author)