Inverse geophysical and potential scattering on a small body

Alexander I. Katsevich; Alexander G. Ramm

doi:10.1117/12.224181

9 October 1995 Inverse geophysical and potential scattering on a small body

Alexander I. Katsevich, Alexander G. Ramm

Proceedings Volume 2570, Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications; (1995) https://doi.org/10.1117/12.224181
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

Abstract

Simple and numerically stable approaches to approximate solution of inverse geophysical and potential scattering problems are described. The method we propose consists of two steps. Let v(z) be the inhomogeneity (potential), and let D be its support. First, we find approximations to the zeroth moment (total intensity) v(z)dz and the first moment (center of gravity) zv(z)dz/ v(z)dz of the function v(z). We call this step 'inhomogeneity localization', because in many cases the center of gravity lies inside D or is located close to it. Second, we refine the above moments and find the tensor of the second central moments of v(z). Using this information, we find an ellipsoid D and a real constant v, such that the inhomogeneity (potential) v(z) equals v,z an element of D, and v(z) equals 0,z not an element of D, fits best the scattering data and has the same zeroth, first, and second moments. We call this step 'approximate inversion'. The proposed method does not require any intensive computations, it is very simple to implement and it is relatively stable towards noise in the data.

Citation Download Citation

Alexander I. Katsevich and Alexander G. Ramm "Inverse geophysical and potential scattering on a small body", Proc. SPIE 2570, Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications, (9 October 1995); https://doi.org/10.1117/12.224181

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available