HR: 10:45h
AN: S32A-02    [Abstracts]
TI: Coherent-State Solutions of the Wave Equation
AU: * Foster, D J
EM: douglas.j.foster@conocophillips.com
AF: ConocoPhillips Co., PR2036 600 N. Dairy Ashford, Houston, TX 77252 United States
AU: Wu, R
AF: Ru-Shan Wu, University of California Santa Cruz, Santa Cruz, CA United States
AB: The coherent-state transform is used in obtaining a global, uniform asymptotic solution of the wave equation. This solution approximates high-frequency propagation of acoustic, optical and seismic waves in generally heterogeneous media. An understanding of the forward problem gives insight to how these type of propagators will perform as migration (imaging) operators. This insight can examine both the kinematics (travel time) and dynamic (amplitude) characteristics of the propagator. The coherent-state approximation has an advantage over more traditional methods (direct and Fourier transform), because it leads to a well-defined approximation independent of the complexity of the caustics. Two similarities of the coherent-state approximation and the Gaussian summation method are that phase functions are complex and both have a parametric dependence. A difference is that the Gaussian beam method is heuristic, whereas the coherent-state method has a theoretical basis. The ability of the coherent-state approximation to accurately model higher wave phenomena (i.e. diffractions, head waves, critical points, etc.) depends on this parameter. This parameter determines the shape of the coherent-state and controls the interpolation between ray theoretical phase and amplitude and Fourier domain (Maslov) phase and amplitude. As an illustration the edge diffraction problem is discussed. The diffracted wave has the correct asymptotic form but the accuracy depends on a parameter that controls the coherent-state. Also, an early test of a coherent-state migration is shown.
DE: 0689 Wave propagation (4275)
SC: Seismology [S]
MN: 2005 Joint Assembly