Inverse Problems of Seismology (Structural Review)

Summary The inverse problem of seismology is formulated as the determination of the set of cross-sections fitting all given observations. The schemes of solution of this problem by the trial-and-error method and the inversion method are described. Mathematical and computational problems involved in the solution are outlined. Not all these problems are solved at the present time. Among them optimal parametrization of cross-section and the determination of a probability distribution function for cross-section are the most urgent problems. But with certain limitations the described scheme of a trial-and-error method for joint interpretation of surface and body waves is in routine operation now. Results obtained are described in papers [2, 4, 6, 15, 22, 23]. Usually it is the non-uniqueness that strikes us when we see the solution of the inverse problem. But there is another side to the matter: if we do not look for an excessively detailed cross-section we may obtain quite definite conclusions even from very rough observations which are commonly regarded as useless.

[1]  A. Levshin,et al.  Joint Interpretation of Body and Surface Waves Data for a District in Middle Asia , 1966 .

[2]  D. Anderson,et al.  ATTENUATION IN THE MANTLE AND RIGIDITY OF THE CORE FROM MULTIPLY REFLECTED CORE PHASES. , 1964, Proceedings of the National Academy of Sciences of the United States of America.

[3]  L. Knopoff,et al.  The Crust and Upper Mantle of the Pacific Area , 1968 .

[4]  H. Turner.  On the Arrival of Earthquake Waves at the Antipodes, and on the Measurement of the Focal Depth of an Earthquake , 1922 .

[5]  B. Gutenberg.  Travel Times of Longitudinal Waves From Surface Foci. , 1953, Proceedings of the National Academy of Sciences of the United States of America.

[6]  V. Keilis-Borok,et al.  A Technique of a Joint Interpretation of Travel—Time and Ampitude—Distance Curves in the Upper Mantle Studies , 1966 .

[7]  F. Press,et al.  Inferences on crustal velocities and densities from P wave delays and gravity anomalies , 1964 .

[8]  M. Gerver,et al.  On the Characteristic Properties of Travel-Time Curves , 1967 .

[9]  Leon Knopoff,et al.  Density-Velocity Relations for Rocks , 1967 .

[10]  K. Okuda,et al.  [The fine structure of the retina]. , 1965, Nihon ganka kiyo.

[11]  G. Backus,et al.  The Resolving Power of Gross Earth Data , 1968 .

[12]  Robert A. Phinney,et al.  P wave diffraction theory and the structure of the core‐mantle boundary , 1966 .

[13]  M. A. Tuve,et al.  Crustal structure from seismic exploration , 1954 .

[14]  M. Gerver,et al.  Determination of a Seismic Wave Velocity from the Travel-Time Curve , 1966 .

[15]  W. J. Hannon,et al.  Velocity filtering of seismic core phases , 1966 .

[16]  M. Randall,et al.  The fine structure of the Earth's core , 1964 .

[17]  L. Knopoff,et al.  Analytical calculation of the seismic travel‐time problem , 1965 .

[18]  Frank Press,et al.  Earth models obtained by Monte Carlo inversion. , 1968 .

[19]  R. Phinney,et al.  A study of the core-mantle boundary using P waves diffracted by the Earth's core , 1966 .