BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Todd Quinto (Tufts University) DTSTART:20220609T160000Z DTEND:20220609T170000Z DTSTAMP:20260423T021310Z UID:Inverse/91 DESCRIPTION:Title: Seismic imaging with generalized Radon transforms.\nby Todd Quinto (T ufts University) as part of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nGeneralized Radon transforms are Fourier integral operators which are used\, for instance\, as imaging models in geophysica l exploration. They appear naturally when linearizing about a known backgr ound compression wave speed. In this work we consider seismic operators wi th two scanning geometries: zero-offset (the source and receiver are at th e same point and translated over the surface of the earth) and common-offs et (the source and receiver are offset a fixed distance from each other an d translated together). We first analyze the model with a linearly increas ing background velocity in two spatial dimensions. We verify the Bolker co ndition for the zero-offset scanning geometry and provide meaningful argum ents for it to hold even if the common-offset is positive. The Bolker cond ition allows us to infer that the normal operator is a pseudodifferential operator. We calculate its top order symbol in the zero-offset case to stu dy how it maps singularities. Second\, to support the usage of background models obtained from linear regression\, we prove that the Bolker conditio n is stable under sufficiently small perturbations of the background veloc ity or of the offset.\n\nAuthors: Peer Christian Kunstmann and Andreas Rie der\, Department of Mathematics\, Karlsruhe Institute of Technology (KIT)\ , D-76128\, Karlsruhe\, Germany\, Eric Todd Quinto\, Department of Mathema tics\, Tufts University\, Medford\, MA 02155\, USA.\n LOCATION:https://researchseminars.org/talk/Inverse/91/ END:VEVENT END:VCALENDAR