The general solution of equations of saturated porous media with incompressible fluid for two dimensional axi-symmetric problem is obtained in the transformed domain. The Laplace and Hankel transforms have been used to investigate the problem. As an application of the approach concentrated source and source over circular region have been taken to show the utility of the approach. The transforme...

A three-dimensional (3-D) inversion scheme for fixedoffset ground penetrating radar (GPR) is derived that takes into account the loss in the soil and the planar air–soil interface. The forward model of this inversion scheme is based upon the first Born approximation and the dyadic Green function for a two-layer medium. The forward model is inverted using the Tikhonov-regularized pseudo-inverse ...

A description of the theory and numerical implementation of a 3-D linearized asymptotic anisotropic inversion method based on the generalized Radon transform is given. We discuss implementation aspects, including (1) the use of various coordinate systems, (2) regularization by both spectral and Bayesian statistical techniques, and (3) the effects of limited acquisition apertures on inversion. W...

This is the second paper in a two-part series that describes a massively parallel code that performs 2D full-waveform inversion of wide-aperture seismic data for imaging complex structures. We present several numerical validation of the full-waveform inversion code with both canonical and realistic synthetic examples. We illustrate how different multiscale strategies can be applied by either su...

We combine traction force data with Bayesian inversion to obtain an absolute estimate of the internal stress field of a cell monolayer. The method, Bayesian inversion stress microscopy, is validated using numerical simulations performed in a wide range of conditions. It is robust to changes in each ingredient of the underlying statistical model. Importantly, its accuracy does not depend on the ...

Scatterer detection in medical ultrasound imaging can be formulated as an inverse problem concerning a linear system model based on point scatterers. The applicability of different methods of regularized inversion is examined and a novel regularization scheme specifically adapted to ultrasound imaging is introduced. The results show that standard inversion methods fail in ultrasound imaging whi...

The analysis, design, and operation of high-voltage, transformer-coupled LC vector inversion generators are presented and discussed. The transformer-coupled LC inversion generator is easy to construct and, compared with Marx-type generators and conventional LC vector inversion generators, requires only one inversion switch, independent of the number of voltage multiplication stages. The transfo...

An adaptive multi-scale conjugate gradient method for distributed parameter estimations (or inverse problems) of wave equation is presented. The identification of the coefficients of wave equations in two dimensions is considered. First, the conjugate gradient method for optimization is adopted to solve the inverse problems. Second, the idea of multi-scale inversion and the necessary conditions...

The authors present an improvement on the FFf-based numerical inversion of Laplace transforms. Since inversions obtained by the FFT-based method contain large errors, especially for the latter half of the computed region, only the former half is acceptable. The truncation error, which is the greater part of the errors, is analysed and an acceleration method is proposed that uses a property of t...

Laplace transforms which admit a holomorphic extension to some sector strictly containing the right half plane and exhibiting a potential behavior are considered. A spectral order, parallelizable method for their numerical inversion is proposed. The method takes into account the available information about the errors arising in the evaluations. Several numerical illustrations are provided.