Velocity Analysis of Converted Waves Based on the Hyperbolic Moveout Equation: The RTM Method
Vladimir Grechka, Ilya Tsvankin, 2001. "Velocity Analysis of Converted Waves Based on the Hyperbolic Moveout Equation: The RTM Method", Anisotropy 2000: Fractures, Converted Waves, and Case Studies, L. Ikelle, A. Gangi
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Conventional velocity analysis, developed for pure reflection modes recorded on common-midpoint (CMP) gathers, usually cannot be directly applied to converted (PS ) waves. The problems are caused by such inherent features of PS-data as the asymmetry of PS-wave moveout in CMP geometry, polarity reversal at small offsets associated with the vanishing PS-wave reflection coefficient, and reflection-point dispersal. Whereas the moveout asymmetry precludes application of the conventional hyperbolic moveout equation, the polarity reversal reduces the accuracy of velocity-analysis methods based on coherency measures. Here, we propose a velocity-analysis technique for converted waves that overcomes some of those problems. The key idea of our method is to re-sort PS-wave data in such a way that the reflection traveltime becomes symmetric al in the vicinity of a chosen source-receiver offset. Since the traveltime at this offset typically has a minimum, we call our procedure "re-sorting to the traveltime minimum" (RTM) and the corresponding gather - the RTM gather. An important advantage of this approach is that the re-sorting algorithm operates only with the slopes of a selected reflection event and is fully independent of the velocity model. Moreover, RTM gathers can be built just for source-receiver pairs sufficiently removed from the area of polarity reversal and low reflection amplitude.
Since the PS-wave moveout of RTM gathers is locally symmetric, it can be flattened by the conventional hyperbolic moveout equation. The normal-moveout (NMO) velocity on RTM gathers depends on the velocity structure of the subsurface and therefore can be used to estimate the medium parameters. Then the subsurface model can be reconstructed by migrating -data, which solves the problem of reflection point dispersal. As an example of inverting PS -wave NMO velocities in RTM geometry, we perform parameter estimation for a homogeneous VTI (transversely isotropic with a vertical symmetry axis) layer above a dipping reflector. The results show that the traveltimes of the P-, PSV-, and PSH -waves reflected from the dipping interface can be inverted for all five medium parameters (including the P and S wave vertical velocities) and the dip and depth of the reflector.
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“This volume contains 25 papers that represent most of the best work in seismic anisotropy in 1998 and 1999. Fracture characterizations and processing of converted waves are the two main topics covered in this volume. They are addressed from both theoretical and practical viewpoints. Also included are papers describing the historical roots of seismic anisotropy.”