John C. Bancroft

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 appropri...

Reverse-time Migration For Tilted TI Media

Seismic anisotropy in dipping shales results in imaging and positioning problems for underlying structures. We develop a reverse-time anisotropic depth migration approach for Pwave and SV-wave seismic data in transversely isotropic (TI) media with a tilted axis of symmetry normal to bedding. Based on an accurate phase velocity formula, the wave equation of weak anisotropy for P-wave and SVwave in tilted transversely isotropic (TTI) media is derived from a P and SV dispersion relationship. The accuracy of the P-wave equation and the SV-wave equation are analyzed and compared with other acoustic wave equations for TTI media. The pseudo-spectral method is used to solve these equations implementing reverse-time migration. The resulting anisotropic depth-migration algorithm is applied to numerical seismic data and physical-model seismic data. According to the comparison between the isotropic and anisotropic migration results, the reverse-time anisotropic depth migration offers significant improvements in positioning and reflector continuity over those obtained using isotropic algorithms.

2-D wave equation modeling and migration by a new finite difference scheme based on the Galerkin method

Summary 2-D wave equation modeling and migration using a new finite difference scheme based on the Galerkin method are presented. Since it involves the semi-descretization of the finite element method (FEM), it is also called the finite element and finite difference method (FE-FDM). For a 2-D acoustic wave equation, by using the semi-discretization technique of the finite element method (FEM) in the z direction with linear elements, the original problem can be written as a coupled system of lower dimensional partial differential equations (PDEs) that depend continuously upon time and space in the x direction. The fourth-order finite difference method (FDM) is used to solve these PDEs. The concept and principle are introduced in this paper. Compared with the explicit finite-difference method of the same accuracy, the stability condition becomes looser and shows an advantage over the conventional FDM. An absorbing boundary condition of fourth-order accuracy is used to prevent boundary reflections. In numerical experiments, comparison is made between a FE-FDM numerical solution and an analytic solution of the quarterplane. Here, FE-FDM is shown to be accurate in numerical computation. In addition, a constant velocity model with two irregular interfaces is simulated to obtain a poststack seismic section, which is then successfully migrated. These examples show the potential of FE-FDM in modeling and reverse-time migration.

Single-well imaging using the full waveform of an acoustic sonic

Summary This work evaluates single-well imaging using the full waveform acquired by an acoustic well-logging tool. It begins by reviewing wave propagation in a fluid-filled borehole. Next we introduce a waveform processing flow using known seismic processing methods and apply it to a real field data set. The ultimate goal of this work is to image scattered energy beyond the borehole wall and thus gain a better picture of the reservoir characteristics around the borehole.

Converted wave migration and common conversion point binning by equivalent offset

A method for converted wave prestack time migration i s presented. This method splits the conventional prestack Kirchhoff time migration into two steps using equivalent offset binning. Migration gathers are first constructed instead of producing the migrated section directly. This step also completes the common reflection point binning. Conventional NMO and stacking applied on these gathers complete the imaging process.

Equivalent Offset CRP Gathers

Traditional seismic velocity analysis uses a gather of traces that have a common midpoint (CMP) between the source and receiver.A method is presented for creating a common reflection point (CRP) gather in which all input traces within the prestack migration aperture are used. The traces are sorted with an equivalent offset derived from the source to reflector and reflector to receiver distances. This equivalent offset CRP gather represents the traces that would prestack migrate to the output CRP location.

Microseismic hypocenter location using nonlinear optimization

Nonlinear optimization methods (or inversion) were investigated for analyzing synthetic microseismic arrival times. Two direct search techniques, the genetic algorithm and pattern search, were used to find the layered-earth velocity values from P-wave arrival times from a simulated perforation shot. For locating microseismic hypocenters, the gradient-based Levenberg-Marquardt algorithm was used to invert reduced arrival times from borehole and surface receiver arrays. Both categories of nonlinear optimization method, direct search and gradient-based, were effective for inverting arrival times to the required model parameters. Our experience suggests that the direct search methods, in particular pattern search, are simpler and faster in this application, i.e., inverting microseismic arrival time data to obtain layer either velocities or hypocenter coordinates.

A comparison of hydrocarbon indicators derived from AVO analysis

Numerous approaches have been published which derive fluid indicators (often called direct hydrocarbon indicators, or DHI) from AVO equations. The main idea behind these methods is to use the linearized Zoeppritz equations to extract petrophysical parameters such as P-impedance, S-impedance, bulk modulus, shear modulus, Lame’s parameters, Poisson’s ratio, etc. and, from cross-plots of these parameters, infer the fluid content. Often, these indicators provide a good tool to quickly identify hydrocarbon zones. But the question of whether there is a best approach and, if so, which one it is, is still under debate. The purpose of this study is to examine which indicator can most easily discriminate a gas/oil sand from its background geology, and which indicator is most sensitive to pore-fluid content estimation.

Estimation of anisotropy parameters in VTI media

Summary Anisotropy parameters in a VTI medium can be obtained by anisotropy velocity analysis performed on short-spread or long-spread reflection-seismic data, in combination with check-shot or well-log data. Analysis of three traveltime approximations to the actual reflection traveltime in weak anisotropy media shows that each traveltime approximation has its own requirements for spread length and subsurface anisotropic parameters. The accuracy of the estimated Thomsen’s anisotropic parameter δ (or e ) depends not only on the accuracy of the picked NMO velocity (or horizontal velocity) but also on the absolute value of ) ( δ e − . The smaller the absolute value of ) ( δ e − , the higher the accuracy of estimated anisotropy parameter δ or e . The results of the three traveltime inversions by semblance analysis for synthetic seismic examples demonstrate that nonhyperbolic estimation is better than the modified three-term Taylor series method, and the modified three-term Taylor series method better than hyperbolic estimation. None of these three approaches is suitable for estimating anisotropy parameters when the absolute value of ) ( δ e − is large (i.e. | δ e − | > 0.2 in this case).

Playing with fire: Noise alignment in trim and residual statics

It is well known the cross-correlation procedure in trim statics can produce spurious reproduction of signal. This phenomenon is quantified and is shown, in the limits of large fold, small correlation window, and large maximum allowable shift, to behave as a simple function of these variables for physically reasonable wavelet lengths. These results allow one to predict what choices of crosscorrelation parameters are likely to result in spurious alignment of noise. It is also shown that this function can help to indicate whether apparent signal is a result of the desired signal alignment, or simply constructed from random background noise. The effect of residual statics can also function as an indicator in this context.