Theory and practice of geophysical data inversion

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This volume presents a diverse range of recent advancements in geophysical data inversion, encompassing fundamental mathematics, general theory, numerical methods, and algorithm implementation. The papers are driven by challenges in geophysical research and applications, highlighting the growing significance of exploration methods across various fields, including structural geology, mineral and energy resource prospecting, hydrogeology, geotechnology, environmental protection, and archaeology. The first section focuses on foundational mathematics and theory related to geophysical data inversion, addressing topics such as stabilization algorithms for ill-posed inverse problems, the sensitivity of kernel function estimations to random data errors, and techniques to reduce errors in inverse modeling through linear constraints. Additionally, it covers numerical procedures for boundary value problems, accuracy and stability in inverse ill-posed problems related to moments, and fast Fourier transforms for potential field issues. The second section explores gravity and magnetics, examining the solvability of inverse gravimetric problems involving point masses and other elementary sources, as well as solutions for nonuniformly distributed data from paleomagnetic studies, satellite observations, and surface projections of buried archaeological targets through inverse filtering of geomagnetic data.