A method for inverse scattering based on the generalized Bremmer coupling series
نویسندگان
چکیده
Imaging with seismic data is typically done under the assumption of single scattering. Here we formulate a theory that includes multiply scattered waves in the imaging process. We develop both a forward and an inverse scattering series derived from the Lippmann–Schwinger equation and the Bremmer coupling series. We estimate leading-order internal multiples explicitly using the third term of the forward series. From the inverse series, two images are constructed, one formed with all the data, the other with the estimated leading-order internal multiples; the final image is formed from the difference of these two images. We combine the modelling of the leading-order internal multiples with the construction of the second image resulting in one two-part imaging procedure. (Some figures in this article are in colour only in the electronic version)
منابع مشابه
Inverse scattering problem for the Impulsive Schrodinger equation with a polynomial spectral dependence in the potential
In the present work, under some di¤erentiability conditions on the potential functions , we rst reduce the inverse scattering problem (ISP) for the polynomial pencil of the Scroedinger equation to the corresponding ISP for the generalized matrix Scrödinger equation . Then ISP will be solved in analogy of the Marchenko method. We aim to establish an e¤ective algorithm for uniquely reconstructin...
متن کاملUniform Asymptotic Expansion of the Generalized Bremmer Series
The Bremmer coupling series solution of the wave equation, in generally inhomogeneous media, requires the introduction of pseudo-differential operators. In this paper, in two dimensions, uniform asymptotic expansions of the Schwartz kernels of these operators are derived. Also, we derive a uniform asymptotic expansion of the one-way propagator appearing in the series. We focus on designing clos...
متن کاملInverse scattering theory: renormalization of the Lippmann-Schwinger equation for acoustic scattering in one dimension.
The most robust treatment of the inverse acoustic scattering problem is based on the reversion of the Born-Neumann series solution of the Lippmann-Schwinger equation. An important issue for this approach to inversion is the radius of convergence of the Born-Neumann series for Fredholm integral kernels, and especially for acoustic scattering for which the interaction depends on the square of the...
متن کاملA numerical Algorithm Based on Chebyshev Polynomials for Solving some Inverse Source Problems
In this paper, two inverse problems of determining an unknown source term in a parabolic equation are considered. First, the unknown source term is estimated in the form of a combination of Chebyshev functions. Then, a numerical algorithm based on Chebyshev polynomials is presented for obtaining the solution of the problem. For solving the problem, the operational matrices of int...
متن کاملThermo-Viscoelastic Interaction Subjected to Fractional Fourier law with Three-Phase-Lag Effects
In this paper, a new mathematical model of a Kelvin-Voigt type thermo-visco-elastic, infinite thermally conducting medium has been considered in the context of a new consideration of heat conduction having a non-local fractional order due to the presence of periodically varying heat sources. Three-phase-lag thermoelastic model, Green Naghdi models II and III (i.e., the models which predicts the...
متن کامل