Paul J. Fowler

Reverse time migration in tilted transversely isotropic "TTI… media

Reverse time migration (RTM) exhibits great advantages over other imaging methods because it is based on computing numerical solutions to a two-way wave equation. It does not suffer from dip limitation like one-way downward continuation techniques do, thus enabling overturned reflections to be imaged. As well as correctly handling multipathing, RTM has the potential to image internal multiples when the boundaries responsible for generating the multiples are present in the model. In isotropic media, one can use a scalar acoustic wave equation for RTM of pressure data. In anisotropic media, P- and SV-waves are coupled together so, formally, elastic wave equations must be used for RTM. A new wave equation for P-waves is proposed in tilted transversely isotropic (TTI) media that can be solved as part of an acoustic anisotropic RTM algorithm, using standard explicit finite differencing. If the shear velocity along the axis of symmetry is set to zero, stable numerical solutions can be computed for media with a ...

Coupled equations for reverse time migration in transversely isotropic media

Reverse time migration (RTM) images reflectors by using time-extrapolation modeling codes to synthesize source and receiver wavefields in the subsurface. Asymptotic analysis of wave propagation in transversely isotropic (TI) media yields a dispersion relation describing coupled P- and SV-wave modes. This dispersion relation can be converted into a fourth-order scalar partial differential equation (PDE). Increased computational efficiency can be achieved using equivalent coupled second-order PDEs. Analysis of the corresponding dispersion relations as matrix eigenvalue systems allows one to characterize all possible coupled linear second-order systems equivalent to a given linear fourth-order PDE and to determine which ones yield optimally efficient finite-difference implementations. Setting the shear velocity along the axis of symmetry to zero yields a simpler approximate TI wave equation that is more efficient to implement. This simpler approximation, however, can become unstable for some plausible combinations of anisotropic parameters. The same eigensystem analysis can be applied using finite vertical shear velocity to obtain solutions that avoid these instability problems.

Suppressing unwanted internal reflections in prestack reverse-time migration

Prestack reverse-time migration, a wave-equation technique using two-way propagation, correctly handles multiarrivals and enables imaging of overturned reflections. However, image artifacts occur when backscattered waves cross-correlate. These artifacts are particularly strong where high-velocity contrasts occur. A method for removing unwanted internal reflections during propagation of both the source and receiver wavefields is presented. This method applies a directional damping term to the wave equation in areas of the velocity model where unwanted reflections occur. Tests on synthetic data show good suppression of image artifacts.

Suppressing Artifacts In Prestack Reverse Time Migration

Two-way migration methods require significantly greater computational resources than one-way migration methods. However, their advantage is that they can not only handle multiarrivals, but have virtually no dip limitation, enabling imaging of overturned reflections. Reverse time migration, a wave equation technique using two-way propagation, correctly handles both multiarrivals and the phase changes due to caustics, but by using two-way propagation, does not suffer from dip limitation like one-way downward continuation techniques. Although one-way wave equation techniques can be implemented and classified as true-amplitude migrations, reverse time migration makes no approximations that must be corrected to control amplitude.

Recursive integral time extrapolation methods for scalar waves

We derive and compare a variety of algorithms for recursive time extrapolation of scalar waves using approximate operators derived from integral solutions of a wave equation. These methods fall into two categories: those based on combining or interpolating homogeneous solutions, and those based on series expansions of heterogeneous operators. The former suffer from oscillatory noise at large velocity discontinuities unless the time step is small, whereas the latter allow accurate extrapolation at large time steps, but are more costly.

Modeling And Reverse Time Migration of Orthorhombic Pseudo-acoustic P-waves

Current commercial seismic imaging techniques routinely handle wave propagation in transversely isotropic media with vertical symmetry axis (VTI). VTI anisotropy is ubiquitous in sedimentary basins because lithification generally occurs in a stress environment dominated by the vertically oriented gravitational gradient. Tectonic stresses can rotate the symmetry axis away from vertical, requiring compensation for tilted transverse isotropy (TTI) effects as well. Tectonic stresses can also induce fracturing in rocks, which can further lower the symmetry class describing wave propagation. The next lower symmetry class of importance for describing seismic waves is orthorhombic, which incorporates not just layering effects but also perpendicular fracturing.

Anisotropic Kirchhoff prestack time migration for enhanced multicomponent imaging

Kirchhoff prestack time migration is routinely used with good results in conventional data processing and has also recently become popular in the processing of multicomponent data. We have seen that accurate raytracing methods and inclusion of anisotropy are giving further improvement in imaging and are particularly important for handling the converted waves in multicomponent data sets. In this paper, we will present the anisotropic velocity model building for multicomponent data and the results from applying Kirchhoff prestack time migration on several data sets.