Multi-scale Reverse-time-migration Based Inverse Scattering Using the Dyadic Parabolic Decomposition of Phase Space
نویسندگان
چکیده
We develop a representation of reverse time migration in terms of Fourier integral operators the canonical relations of which are graphs. Through the dyadic parabolic decomposition of phase space, we obtain the solution of the wave equation with a boundary source and homogeneous initial conditions using wave packets. On this basis, we develop a numerical procedure for the reverse time continuation from the boundary of scattering data and for RTM migration. The algorithms are derived from those we recently developed for the discrete approximate evaluation of the action of Fourier integral operators and inherit from their conceptual and numerical properties.
منابع مشابه
Multiscale Reverse-Time-Migration-Type Imaging Using the Dyadic Parabolic Decomposition of Phase Space
We develop a representation of reverse-time migration (RTM) in terms of Fourier integral operators, the canonical relations of which are graphs. Through the dyadic parabolic decomposition of phase space, we obtain the solution of the wave equation with a boundary source and homogeneous initial conditions using wave packets. On this basis, we develop a numerical procedure for the reverse-time co...
متن کاملMultiscale Discrete Approximation of Fourier Integral Operators
Abstract. We develop a discretization and computational procedures for the approximation of the action of Fourier integral operators whose canonical relations are graphs. Such operators appear in many physical contexts and computational problems, for instance in the formulation of imaging and inverse scattering of seismic reflection data. Our discretization and algorithms are based on a multi-s...
متن کاملDiscrete almost symmetric wave packets and multi - scale geometrical representation of ( seismic ) waves . Anton
We discuss a multi-scale geometrical representation of (seismic) waves via a decomposition into wave packets. Wave packets can be thought of as certain localized “fat” plane waves. As a starting point we take the frame of continuous “curvelets” and associated transform. Different discretizations, and approximations, of this transform lead to different discrete wave packets. One such discretizat...
متن کاملHigher - Dimensional Discrete Smith Curvelet Transform : a Parallel Algorithm
We revisit Smith’s frame of curvelets and discretize it making use of the USFFT as developed by Dutt and Roklin, and Beylkin. In the discretization, we directly approximate the underlying dyadic parabolic decomposition, its (rotational) symmetry, and approximate all the necessary decay estimates in phase space with arbitrary accuracy. Numerically, our transform is unitary. Moreover, if we apply...
متن کاملParameter determination in a parabolic inverse problem in general dimensions
It is well known that the parabolic partial differential equations in two or more space dimensions with overspecified boundary data, feature in the mathematical modeling of many phenomena. In this article, an inverse problem of determining an unknown time-dependent source term of a parabolic equation in general dimensions is considered. Employing some transformations, we change the inverse prob...
متن کامل