Nero Zero Frequency Sounding in Layered Media

POSTER

Abstract

We consider the mathematical model of frequency sounding of a continuously layered media. By the means of frequency asymptotic expansion of the wave field, this problem is equivalent to an inverse boundary value problem for the Ricatti equation. We solve the inverse Ricatti problem via a Cauchy problem for a first order quadratic equation for sequence-valued maps. The quadratic equation contains no unknown coefficients. The information of the medium is encoded in the initial value. For specific data, the Cauchy problem has a unique solution. Based on the contraction mapping principle the method of proof provides a stable reconstruction algorithm. The computational feasibility of the proposed approach is demonstrated in a numerical experiment.

Authors

  • Milind Purohit

    Univ of South Carolina, Benedict College, Sc 29204, Univ. South Carolina, Benedict College, Univ South Carolina, GA Tech, Central Microscopy Research Facility, University of Iowa, Iowa City, Iowa 52242, USA, Department of Chemistry, University of Sri Jayewardenepura, Nugegoda, Sri Lanka, Department of Physics and Astronomy, Georgia State University, Atlanta, Georgia 30303, USA, Department of Chemistry, University of Alabama at Birmingham, Birmingham, AL 35294, Department of Physics, University of Alabama at Birmingham, Birmingham, AL 35294, College of William \& Mary, Harvard University, Benedict College, SC 29204, Massachusetts Institute of Technology, University of Applied Science, Bielefeld, Germany, Francis Marion University, Physics Dept., Emory University, Emory University, Formerly Emory University, currently UCLA, Physics Department, Georgia State University, Univ. of Georgia, Dept. of Chemistry, Universidad Nacional de Quilmes, Argentina, Pr, Dr, Derpartment of Physics, Florida A\&M University, Tallahassee, FL-32307, Department of Physics, Emory University, Georgia Institute of Technology, Naval Research Laboratory, University of Alabama, Tsinghua University, Lawrence Berkeley National Laboratory, Vanderbilt University, Jagellonian Univ., Univ. of Bonn, North Carolina A\&T State Univ., North Carolina Central Univ., Duke Univ. and TUNL, Georgia State University, Dept of Physics, Emory University, Cell Biology Department, Emory University, Physics Department, Emory University, University of South Carolina

  • Alexandru Tamasan

    Mathematics Department, University of Central Florida

  • Johann Veras

    Mathematics Department, University of Central Florida