×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Ramm, A.G, Scattering by obstacles, (1986), Reidel Dordrecht · Zbl 0607.35006
[2] 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
[3] Ramm, A.G, A uniqueness theorem for two-parameter inversion, Inverse problems, 4, L7-L10, (1988) · Zbl 0699.35250
[4] Ramm, A.G, Multidimensional inverse problems and completeness of the products of solutions to homogeneous PDE, Z. angew. math. mech., 305, N4-N5, (1989)
[5] Ramm, A.G, Multidimensional inverse problems, J. math. anal. appl., 134, 211-253, (1988) · Zbl 0632.35076
[6] Ramm, A.G, Recovery of potential from the fixed energy scattering data, Inverse problems, 4, 877-886, (1988) · Zbl 0632.35075
[7] Ramm, A.G, Characterization of the scattering data in multidimensional inverse scattering problems, (), 153-167
[8] 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
[9] Ramm, A.G, A method for solving inverse diffraction problems, Inverse problems, 3, L23-L25, (1987) · Zbl 0619.35111
[10] Ramm, A.G, Numerical method for solving 3D inverse scattering problems, Appl. math. lett., 1, N4, (1988) · Zbl 0713.35097
[11] Ramm, A.G, Numerical method for solving 3D inverse problems with complete and incomplete data, () · Zbl 0721.35087
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.