[1] The Global Positioning System (GPS) system now makes it possible to monitor deformation of the Earth’s surface along plate boundaries with unprecedented accuracy. In theory, the spatiotemporal evolution of slip on the plate boundary at depth, associated with either seismic or aseismic slip, can be inferred from these measurements through some inversion procedure based on the theory of dislo...

In this paper we discuss some aspects of sparse reconstruction techniques for inverse problems, which recently became popular due to several superior properties compared to linear reconstructions. We briefly review the standard sparse reconstructions based on `-minimization of coefficients with respect to an orthonormal basis, and also some recently proposed improvements based on Bregman iterat...

1. Abstract In order to predict strong earthquake ground motion, it is inevitable to construct a relevant subsurface structure model, especially S-wave velocity structure of the site of consideration. Inversion analysis with micro-tremor observation is frequently used to acquire S-wave velocity structure due to its convenience and inexpensiveness. Usually inversion analysis is carried out for e...

We study the effect of additive noise to inversion FIOs associated a diffeomorphic canonical relation. use microlocal defect measures measure power spectrum in phase space and analyze how that is transformed under inversion. In general, white noise, for example, mapped depending on position direction. particular, we compute standard deviation, locally, added as function deviation data. As an Ra...

Inverse elastic-wave scattering problems are shown to be ill-posed in general. Standard simplifying assumptions--the first Born approximation, the physical optics approximation, and the stopping power approximation of tomography--are shown to reduce to the same ill-posed mathematical problem, that of inverting a Fourier transform. Practical implications of this fact are illustrated with examples.