Open access peer-reviewed Edited Volume

III-Posed Inverse Problems - New Perspectives and Applications

Olga Hachay

Ural Branch of the Russian Academy of Sciences


Ill-Posed Inverse Problems Geophysics Seismic Electromagnetic Thermal Magnetic Medicine Mathematical Algorithms Hierarchical Nonlinear Historical Description Regularization

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About the book

To study complex dynamic processes and their monitoring, a synchronous technique for observing fields from various sources is already required. In this case, in contrast to previously solved problems related to the Geo-mapping of 3D layered - block media, when the unity of the complex interpretation model was achieved by superimposing separate models obtained by independent interpretation of data from various geophysical fields: gravitational, magnetic, seismic, electromagnetic, thermal, it is necessary take into account the thermodynamic relationship of the material parameters of the environment. Hence, the interpretation process no longer represents an independent solution of inverse problems for each field separately. The operator of the inverse problem in a complex interpretation is written out in the form of a system of equations for fields related by thermodynamic material relations. Examples include algorithms for determining convection mechanisms in the Earth’s mantle, interpretation of natural field anomalies associated with electrokinetic phenomena.

The theory of interpretation of geophysical fields is directly related to the solution of ill-posed problems and the theory of regularization created by the works of A.N. Tikhonov, V.K.Ivanov, M.M. Lavrentiev and their schools. As a result of its application, important results have been achieved in constructing models of local, regional, and global distributions of physical properties in the Earth and other celestial bodies, on which geophysical studies were carried out, in the framework of piecewise homogeneous models and linear approximation for describing the propagation of fields.
Further development of geophysical methods in the direction of constructing more and more adequate models of media and phenomena necessarily leads to more and more complex problems of mathematical geophysics, for which not only inverse, but also direct problems become significantly incorrect. In this regard, it is necessary to develop a new concept of regularization for simultaneously solving a system of heterogeneous operator equations.

Currently, the study of processes associated not only with geophysics and astrophysics but also with biology and medicine requires even more complication of interpretation models from non-linear and heterogeneous to hierarchical. This book will be devoted to the creation of new mathematical theories for solving ill-posed problems for complicated models.

Publishing process

Book initiated and editor appointed

Date completed: October 7th 2019

Applications to edit the book are assessed and a suitable editor is selected, at which point the process begins.

Chapter proposals submitted and reviewed

Deadline Extended: Open for Submissions

Potential authors submit chapter proposals ready for review by the academic editor and our publishing review team.

Approved chapters written in full and submitted

Deadline for full chapters: May 26th 2020

Once approved by the academic editor and publishing review team, chapters are written and submitted according to pre-agreed parameters

Full chapters peer reviewed

Review results due: August 14th 2020

Full chapter manuscripts are screened for plagiarism and undergo a Main Editor Peer Review. Results are sent to authors within 30 days of submission, with suggestions for rounds of revisions.

Book compiled, published and promoted

Expected publication date: October 13th 2020

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About the editor

Olga Hachay

Ural Branch of the Russian Academy of Sciences

EDUCATION BACKGROUND: Astrophysics (1969) Ural State University Ph. D. «The inverse problem for electromagnetic research of one-dimensional medium » (1979) IZMIRAN, Russian Academy of Sciences, Moscow Prof: «Mathematical modeling and interpretation alternating electromagnetic fields in the heterogeneous crust and earth’s Mantle » (1994) Moscow State University Geological Faculty. Language: Fluent in Russian, English, German. EMPLOYMENT: HISTORY From 1969 scientific member of the Institute of Geophysics UB RAS 1995-2004 Chief of the group of seismic and electromagnetic research. Elaboration of new common methods for searching the structure and the state of the upper crust Elaboration new theory of interpretation of electromagnetic and seismic fields and realizing it in new programs. From 2002-main scientific researcher of the Institute of geophysics UB RAS From 2008 –leader scientific researcher of the Institute in the frame of the laboratory of borehole geophysics.

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Book chapters authored 4

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