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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:
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