BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Sabre//Sabre VObject 4.5.8//EN CALSCALE:GREGORIAN BEGIN:VTIMEZONE TZID:Europe/Zurich X-LIC-LOCATION:Europe/Zurich TZURL:http://tzurl.org/zoneinfo/Europe/Zurich BEGIN:DAYLIGHT TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST DTSTART:19810329T020000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:+0200 TZOFFSETTO:+0100 TZNAME:CET DTSTART:19961027T030000 RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU END:STANDARD END:VTIMEZONE BEGIN:VEVENT UID:news887@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190514T111137 DTSTART;TZID=Europe/Zurich:20190525T110000 SUMMARY:Seminar in Numerical Analysis: Florian Faucher (Université de Pau) DESCRIPTION:We study the inverse problem associated with the propagation of time-harmonic waves. In the seismic context\, the available measurements correspond with partial reflection data\, obtained from one side illuminat ion (only from the Earth surface). The inverse problem aims at recovering the subsurface Earth medium parameters and we employ the Full Waveform Inv ersion (FWI) method\, which relies on an iterative minimization algorithm of the difference between the measurement and simulation. \\r\\nWe investi gate the deployment of new devices developed in the acoustic setting: the dual-sensors\, which are able to capture both the pressure field and the v ertical velocity of the waves. For solving the inverse problem\, we define a new cost function\, adapted to these two types of data and based upon t he reciprocity. We first note that the stability of the problem can be sho wn to be Lipschitz\, assuming piecewise linear parameters. In addition\, r eciprocity waveform inversion allows a separation between the observationa l and numerical acquisitions. In fact\, the numerical sources do not have to coincide with the observational ones\, offering new possibilities to cr eate adapted computational acquisitions\, consequently reducing the numeri cal cost. We illustrate our approach with three-dimensional medium reconst ructions\, where we start with minimal information on the target models. W e also extend the methodology for elasticity. \\r\\nEventually\, if time a llows\, we shall explore the model representation in numerical seismic inv ersion\, where the adaptive eigenspace method appears as a promising appro ach to have a compromise between number of unknowns and resolution. \\r\\nReferences \\r\\n[1]  G. Alessandrini\, M. V. de Hoop\, F. Faucher\, R. Gaburro and E. Sincich\, Inverse problem for the Helmholtz e quation with Cauchy data: reconstruction with conditional well-posedness d riven iterative regularization\, ESAIM: M2AN (2019). \\r\\n[2]  E. Berett a\, M. V. De Hoop\, F. Faucher\, and O. Scherzer\, Inverse boundary value problem for the Helmholtz equation: quantitative conditional Lipschitz sta bility estimates. SIAM Journal on Mathematical Analysis\, 48(6)\, pp.3962- 3983 (2016).\\r\\n[3]  M. J. Grote\, M. Kray\, and U. Nahum\, Adaptive ei genspace method for inverse scattering problems in the frequency domain. I nverse Problems\, 33(2)\, 025006 (2017). \\r\\n[4]  H. Barucq\, F. Fauche r\, and O. Scherzer\, Eigenvector Model Descriptors for Solving an Inverse Problem of Helmholtz Equation. arXiv preprint arXiv:1903.08991 (2019).For further information about the seminar\, please visit this webpage. X-ALT-DESC:We study the inverse problem associated with the propagation of time-harmonic waves. In the seismic context\, the available measurements c orrespond with partial reflection data\, obtained from one side illuminati on (only from the Earth surface). The inverse problem aims at recovering t he subsurface Earth medium parameters and we employ the Full Waveform Inve rsion (FWI) method\, which relies on an iterative minimization algorithm o f the difference between the measurement and simulation. \nWe investigate the deployment of new devices developed in the acoustic setting: the dual- sensors\, which are able to capture both the pressure field and the vertic al velocity of the waves. For solving the inverse problem\, we define a ne w cost function\, adapted to these two types of data and based upon the re ciprocity. We first note that the stability of the problem can be shown to be Lipschitz\, assuming piecewise linear parameters. In addition\, recipr ocity waveform inversion allows a separation between the observational and numerical acquisitions. In fact\, the numerical sources do not have to co incide with the observational ones\, offering new possibilities to create adapted computational acquisitions\, consequently reducing the numerical c ost. We illustrate our approach with three-dimensional medium reconstructi ons\, where we start with minimal information on the target models. We als o extend the methodology for elasticity. \nEventually\, if time allows\, w e shall explore the model representation in numerical seismic inversion\, where the adaptive eigenspace method appears as a promising approach to ha ve a compromise between number of unknowns and resolution.

\nReferences \n[1]  \;G. Alessandrini\, M. V. de Hoop\, F. Faucher\, R. Gaburro and E. Sincich\, Inverse problem for the Helmholtz e quation with Cauchy data: reconstruction with conditional well-posedness d riven iterative regularization\, ESAIM: M2AN (2019). \n[2]  \;E. Beret ta\, M. V. De Hoop\, F. Faucher\, and O. Scherzer\, Inverse boundary value problem for the Helmholtz equation: quantitative conditional Lipschitz st ability estimates. SIAM Journal on Mathematical Analysis\, 48(6)\, pp.3962 -3983 (2016).\n[3]  \;M. J. Grote\, M. Kray\, and U. Nahum\, Adaptive eigenspace method for inverse scattering problems in the frequency domain. Inverse Problems\, 33(2)\, 025006 (2017). \n[4]  \;H. Barucq\, F. Fau cher\, and O. Scherzer\, Eigenvector Model Descriptors for Solving an Inve rse Problem of Helmholtz Equation. arXiv preprint arXiv:1903.08991 (2019).

For further information about the seminar\, please visit this webpage. DTEND;TZID=Europe/Zurich:20190524T120000 END:VEVENT END:VCALENDAR