Echo-reconstruction techniques for non-intrusive imaging have wide application, from subsurface and underwater imaging to medical and industrial diagnostics. The techniques are based on experiments in which a collection of short acoustic or electromagnetic impulses, emitted at the surface, illuminate a certain volume and are backscattered by inhomogeneities of the medium. The inhomogeneities ac...

We address the problem of estimating sound speeds (seismic velocities) inside the earth which is necessary for obtaining seismic images in regular Cartesian coordinates. The main goals are to develop algorithms to convert time migration velocities to true seismic velocities, and to convert time-migrated images to depth images in regular Cartesian coordinates. Our main results are three-fold. Fi...

Claerbout’s daylight imaging concept is generalized to the general theory of interferometric seismic imaging (II). Interferometric seismic imaging is defined to be any algorithm that inverts crosscorrelated seismic data for the reflectivity or source distribution. As examples, we show that II can be used to image reflectivity distributions by migrating ghost reflections in passive seismic data,...

Wave-equation, finite-frequency imaging and inversion still faces considerable challenges in addressing the inversion of highly complex velocity models as well as in dealing with nonlinear imaging (e.g., migration of multiples, amplitudepreserving migration). Extended images (EI’s), as we present here, are particularly important for designing image-domain objective functions aimed at addressing...

We address the problem of estimating seismic velocities inside the earth which is necessary for obtaining seismic images in regular Cartesian coordinates. We derive a relation between the true seismic velocities and the routinely obtained so called ”time migration velocities”, which are some kind of mean velocities. We formulate an inverse problem and show that it is ill-posed. We suggest three...

An angle-dependent reflection coefficient is recovered by seismic migration in the angle-domain. We propose a post-migration technique for computing scattering and dip angle common-image gathers (CIGs) from seismic images, extended by the subsurface offset, in relation with wave-equation migration methods. Our methodology suggests a system of Radon transform operators by introducing local trans...

Seismic images and the geologic information they provide contribute significantly to our understanding of the earth’s subsurface. In this thesis, I focus on methods relevant for constructing and interpreting seismic images, including methods for velocity estimation, seismic imaging, and interpretation, which together address key aspects of reflection seismic data processing. Specifically, I pro...

We present results of the application of the wavelet transform method to seismic imaging. The objective of this research is to develop 3D seismic Kirchhoff imaging in the wavelet-transform domain, making use of the time-frequency property of wavelets. We propose to migrate the wavelets as units rather than single samples as in conventional Kirchhoff migration implementation. In practice, the wa...