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This volume collects state-of-the-art contributions on the numerical simulation of fractured porous media, focusing on flow and geomechanics. This book is ideal for computational scientists and numerical analysts interested in recent developments of numerical discretization techniques for underground flow and geomechanics.

The authors introduce geomathematics as an active research area to a wider audience. In the second chapter geomathematics is introduced as a new scientific area which nevertheless has its roots in antiquity. The Appendix (Chapter 5) is devoted to the GEM - International Journal on Geomathematics founded ten years ago.

This monograph presents a rigorous mathematical framework for a linear elastic model arising from volcanology that explains deformation effects generated by inflating or deflating magma chambers in the Earth's interior.

This book presents the theory of waves propagation in a fluid-saturated porous medium (a Biot medium) and its application in Applied Geophysics.

This monograph presents cutting-edge research on dispersive wave modelling, and the numerical methods used to simulate the propagation and generation of long surface water waves.

Readers will be well-prepared for the final chapters that present regularized solutions of inverse problems in finite-dimensional spaces, with Chapter Three covering linear problems and Chapter Four studying nonlinear problems.

Introduction.- Part I: Forward Modelling of the Gravity Field.- The Vertical Gravitational Signal of Homogeneous Bodies, Bounded in the Horizon Plane.- Fourier Methods.- Part II: The Preprocessing and Processing of Gravity Data: From Observations to a Gravity Map on a Local Horizontal Plane.- The Gravity Field of Earth.- Gravity Surveying and Preprocessing.- Gravity Processing.- Part III: Inverse Theory and Applications.- Elementary Inverse Theory.- On the Mathematical Characterization of the Inverse Gravity Problem.- General Inversion Approaches.- Some Conclusions.- Part IV: Appendices.- Mathematical Auxillia.- The Theory of Random Fields and the Wiener-Kolmogorov Prediction Method.- The Tikhonov Regularization and Morozov''s Discrepancy Principle.