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Numerical method for solving 3D inverse problems of geophysics. (English) Zbl 0663.65133
A numerical method is presented to invert surface data for the refraction coefficient. This is an inverse problem of the form: find $$v\in L_ 2(D)$$, given $$u=u(x,y)$$, $$x,y\in R^ 3$$, $$y_ 3=0$$, $$k>0$$ satisfying $$(\Delta +k+kv)u=-\partial (x-y)$$ in $$R^ 3$$. Here D is a finite region in $$R^ 3| x_ 3<0$$, and v vanishes outside D.

##### MSC:
 65Z05 Applications to the sciences 35R30 Inverse problems for PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems 65N99 Numerical methods for partial differential equations, boundary value problems 86A25 Geo-electricity and geomagnetism
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##### References:
  Ramm, A.G, Scattering by obstacles, (1986), Reidel Dordrecht · Zbl 0607.35006  Ramm, A.G, Completeness of the products of solutions to PDE and uniqueness theorems in inverse scattering, Inverse problems, 3, L77-L82, (1987) · Zbl 0636.35066  Ramm, A.G, A uniqueness theorem for two-parameter inversion, Inverse problems, 4, L7-L10, (1988) · Zbl 0699.35250  Ramm, A.G, Multidimensional inverse problems and completeness of the products of solutions to homogeneous PDE, Z. angew. math. mech., 305, N4-N5, (1989)  Ramm, A.G, Multidimensional inverse problems, J. math. anal. appl., 134, 211-253, (1988) · Zbl 0632.35076  Ramm, A.G, Recovery of potential from the fixed energy scattering data, Inverse problems, 4, 877-886, (1988) · Zbl 0632.35075  Ramm, A.G, Characterization of the scattering data in multidimensional inverse scattering problems, (), 153-167  Ramm, A.G, A characterization of the scattering data in 3D inverse scattering problem (with O. weaver), Inverse problems, 3, L49-L52, (1987) · Zbl 0657.35103  Ramm, A.G, A method for solving inverse diffraction problems, Inverse problems, 3, L23-L25, (1987) · Zbl 0619.35111  Ramm, A.G, Numerical method for solving 3D inverse scattering problems, Appl. math. lett., 1, N4, (1988) · Zbl 0713.35097  Ramm, A.G, Numerical method for solving 3D inverse problems with complete and incomplete data, () · Zbl 0721.35087
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