Inverse Theory Studies

Lead PI: Dr. William H Menke

Unit Affiliation: Seismology, Geology and Tectonophysics, Lamont-Doherty Earth Observatory (LDEO)

January 1986 - December 2022
Inactive
Project Type: Research

DESCRIPTION: I have a long term interest in "geophysical inverse theory", the process of taking data (such as observations of seismic waves) and turning them into images of the interior of the earth. I am interested in all aspects of the subject, including theory and applications. I am the author of a well-cited textbook, on the subject, now in its fourth edition.

OUTCOMES: Various theoretical results and improvements to data processing algorithms. An example is the "cross-convolution" technique that Vadim Levin and I invented, which has gained inportance in the interpretation of receiver functiona nd shear wave splitting data.

RESEARCH TEAM:

Zachary Eilon, Daniel Blatter, Ge Jin, Vadim Levin

COLUMBIA UNIVERSITY COLLABORATORS:

Department of Earth and Environmental Sciences (DEES)

EXTERNAL COLLABORATORS:

Rutgers University

WEBSITE:

https://www.ldeo.columbia.edu/users/menke/research_notes/index.html

PUBLICATIONS:

Menke, W. and D. Blatter, Trade-off of resolution and variance computed from ensebles of solutions, with application to Markov Chain Monte Carlo Methods, Geophys. J. Int. 218, 1522-1536, 2019.

Menke, W., Construction of Equivalent Functions in Anisotropic Radon Tomography, Applied Mathematics 10, 1, 2019.

Menke, W., Geophysical Data Analysis: Discrete Inverse Theory, Fourth Edition (Textbook), Elsevier, pp 350, 2018, ISBN: 9780128135556.

Menke, W., Sensitivity Kernels for the Cross-Convolution Measure, Bull. Seism. Soc. Am. 107, 2213-2224, doi: 10.1785/0120170045, 2017.

Menke, W., The uniqueness of single data function, multiple model functions, inverse problems including the Rayleigh wave dispersion problem, PAGEOPH 174, 1699-1710, 2017.

KEYWORDS

adjoint methods time series analysis inverse theory monte carlo methods cross-convolution method tomography geotomography uniqueness variance

THEMES

Earth fundamentals