P. van Riel

Resolution in seismic trace inversion by parameter estimation

An alternative to the conventional time series approach to single‐trace modeling and inversion by convolution and inverse filtering is a parametric approach. To obtain insight into the potential of the parametric approach, the solution of the single‐trace forward problem is formulated in matrix terms. For the nonlinear reflector lag time parameters this is achieved by linearization, which is shown to be a valid approximation over a sufficiently large region. The matrix forward operators are analyzed by means of the singular value decomposition (SVD). The SVD can be considered a generalization of the Fourier transform of convolution operators. On the basis of the SVD analysis, inverse operators are designed which combine stability with high resolving power. A method to determine the resolving power of the parametric inverse operators is presented. Several examples show how wavelet bandwidth, data noise level, and model complexity influence the resolving power of the data for the reflection coefficient and ...

Resolution Limits in Inversion by Parameter Estimation

In the inversion of echo acoustical data by deconvolution no deterministic assumptions about the reflectivity function are made; it is a function unknown everywhere. With deconvolution, reflectivity information outside the data bandwidth cannot be retrieved. In deconvolution the best one can do to improve resolution is to use a wavelet deconvolution filter to dephase the propagating wavelet and weight it such that a flat amplitude spectrum is obtained within the data bandwidth, (Berkhout, 1985)

Synthetic Focussing in Medical Ultrasound

Presently, puls-echo techniques present the main activity in the acoustics group of the Delft University of Technology.