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.

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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, Lamé'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.

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A B S T R A C TSeismic anisotropy in dipping shales results in imaging and positioning problems for underlying structures. We develop an anisotropic reverse-time depth migration approach for P-wave 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 and dispersion relationships for weak anisotropy, we derive the wave equation for P-wave and SV-wave propagation in tilted transversely isotropic (TTI) media. The accuracy of the P-wave equation and the SV-wave equation is analyzed and compared with other acoustic wave equations for TTI media. Using this analysis and the pseudospectral method, we apply reverse-time migration to numerical and physical-model data. According to the comparison between the isotropic and anisotropic migration results, the anisotropic reverse-time depth migration offers significant improvements in positioning and reflector continuity over those obtained using isotropic algorithms. I N T R O D U C T I O NSome hydrocarbon resource exploration and development projects are in areas containing dipping anisotropic sequences. Specifically, thick anisotropic sequences of dipping sandstones and shales often overlie a reservoir in fold and thrust belts, such as in the Canadian Foothills (Isaac and Lawton 1999). In these cases, depth migrations with either an isotropic migration algorithm or a transversely isotropic (TI) with vertical axis of symmetry (VTI) assumption will have imaging problems and positioning errors. Anisotropic depth migration is required to correctly locate images when dipping transversely isotropic strata are present.Imaging in the presence of anisotropy has been investigated in a number of studies. Alkhalifah (1995) proposed Gaussian beam depth migration for VTI media. Tong et al. (1998) applied the Kirchhoff true amplitude migration technique to anisotropic media. Vestrum, Lawton and Schmid (1999) adopted a ray-tracing algorithm to image structures below dipping TI media. Several methods have been proposed that are based on wavefield extrapolation in laterally varying VTI * E-mail: xdu@ucalgary.ca media. Ferguson and Margrave (1999) addressed nonstationary phase-shift for TI media. Zhang, Verschuur and Wapenaar (2001) proposed short spatial convolution operators to extrapolate the wavefields recursively in space-frequency domain for both quasi-P and quasi-SV waves in tilted TI media. Baumstein and Andersonet (2003) combined the phase-shift and explicit correction operators to reduce the cost by using a shorter explicit correction operator. A reverse-time migration (McMechan 1983;Wu, Lines and Lu 1996;Yoon et al. 2003) using a two-way hyperbolic wave equation could handle multi-arrivals, steep dips and overturned reflections. It propagates the measured wavefield backward in time using a hyperbolic wave equation and does not suffer from the dip limitations of one-way downward continuation algorithms.Although numerical computations of the wave equation are expensive, the rapid de...