Geophysical data inversion methods and applications

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The book covers a range of topics in mathematical theory and geophysics, beginning with regularization and cross-validation methods for nonlinear, ill-posed inverse problems, and exploring active constraint strategies in optimization. It discusses robust prediction techniques and methods for recovering orientation distribution functions using maximum entropy. Theoretical aspects of cooperative approaches to solving inverse problems in integral geophysics are examined, alongside applications of spherical spline approximation in physical geodesy and impedance scattering theory. In the gravity and magnetics section, the text addresses optimization of magnetic anomalies, depth determination from gravity gradients, and iterative inversion techniques applied to geological structures. It delves into the influence of core-mantle boundary irregularities and stochastic modeling of potential fields. The section also includes studies on geomagnetic field reversals and the potential of geophysical maps over buried ancient sites. The electrics and electromagnetics segment discusses resistivity sounding data and borehole measurement inversions, while the seismics section covers automated static corrections, fast Radon transform applications, and optimization methods for dynamic problems in wave equations. Finally, the joint inversion of geophysical data and geothermics is explored, with case studies on subsurface models and thermal anomaly