It is not uncommon now for geophysical inverse problems to be parameterized by 10 to 105 unknowns associated with upwards of 106 to 107 data constraints. The matrix problem defining the linearization of such a system (e.g., ~m = b) is usually solved with a least-squares criterion (m = (~t~ -) ~ tb). The size of the matrix, however, discourages the direct solution of the system and researchers o...

Stationary phase solutions for the radiation patterns of borehole sources are commonly used to study the far-field seismic wavefields produced in crosshole or reverse VSP experiments, but they break down when the formation shear wave velocity is less than the tube wave velocity in the source borehole. This is because the tube wave, not the primary source, radiates the dominant shear wave signal...

An approximate theory for the scattering of an incident plane P wave into tube waves in a fluid-filled borehole drilled through two homogeneous half-spaces is proposed in this paper. This theory is in excellent agreement with the zero frequency formulation (White, 1983) for frequencies below hundreds of Hertz (in the range of conventional crosshole or VSP experiments) and flnite difference simu...

We consider lithological tomography in which the posterior distribution of (hydro)geological parameters interest is inferred from geophysical data by treating intermediate properties as latent variables. In such a variable model, one needs to estimate intractable likelihood given data. The pseudo-marginal method an adaptation Metropolis-Hastings algorithm unbiased approximation this obtained Mo...