Seismic imaging with generalized Radon transforms.

Abstract: Generalized Radon transforms are Fourier integral operators which are used, for instance, as imaging models in geophysical exploration. They appear naturally when linearizing about a known background compression wave speed. In this work we consider seismic operators with two scanning geometries: zero-offset (the source and receiver are at the same point and translated over the surface of the earth) and common-offset (the source and receiver are offset a fixed distance from each other and translated together). We first analyze the model with a linearly increasing background velocity in two spatial dimensions. We verify the Bolker condition for the zero-offset scanning geometry and provide meaningful arguments for it to hold even if the common-offset is positive. The Bolker condition allows us to infer that the normal operator is a pseudodifferential operator. We calculate its top order symbol in the zero-offset case to study how it maps singularities. Second, to support the usage of background models obtained from linear regression, we prove that the Bolker condition is stable under sufficiently small perturbations of the background velocity or of the offset.

Authors: Peer Christian Kunstmann and Andreas Rieder, Department of Mathematics, Karlsruhe Institute of Technology (KIT), D-76128, Karlsruhe, Germany, Eric Todd Quinto, Department of Mathematics, Tufts University, Medford, MA 02155, USA.

Mathematics

Audience: researchers in the topic

International Zoom Inverse Problems Seminar, UC Irvine