Overview
- This book deals with theoretical models for wave propagation in porous media
- This volume presents finite element procedures developed to solve problems in Applied Geophysics
- This work shows detailed explanation of the implementation of the numerical simulation algorithms in serial and parallel computers
Part of the book series: Lecture Notes in Geosystems Mathematics and Computing (LNGMC)
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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
About this book
The partial differential equations describing the propagation of waves in Biot media are solved using the Finite Element Method (FEM).
Waves propagating in a Biot medium suffer attenuation and dispersion effects. In particular the fast compressional and shear waves are converted to slow diffusion-type waves at mesoscopic-scale heterogeneities (on the order of centimeters), effect usually occurring in the seismic range of frequencies.
In some cases, a Biot medium presents a dense set of fractures oriented in preference directions. When the average distance between fractures is much smaller than the wavelengths of the travelling fast compressional and shear waves, the medium behaves as an effective viscoelastic and anisotropic medium at the macroscale.
The book presents a procedure determine the coefficients of the effective medium employing a collection of time-harmonic compressibility and shear experiments, in the context of Numerical Rock Physics. Each experiment is associated with a boundary value problem, that is solved using the FEM.
This approach offers an alternative to laboratory observations with the advantages that they are inexpensive, repeatable and essentially free from experimental errors.
The different topics are followed by illustrative examples of application in Geophysical Exploration. In particular, the effects caused by mesoscopic-scale heterogeneities or the presence of aligned fractures are taking into account in the seismic wave propagation models at the macroscale.
The numerical simulations of wave propagation are presented withsufficient detail as to be easily implemented assuming the knowledge of scientific programming techniques.
Reviews
“This book is a great addition to the collectionof books on wave propagation and numerical simulations. … we find the book to be a very useful read and would recommend it to students and researchers actively working in the area. This book is certainly an important reference that provides a succinct description of numerical simulations of wave propagation in real media.” (Mrinal K. Sen and Janaki Vamaraju, The Leading Edge, October, 2018)
Authors and Affiliations
About the authors
Juan Enrique is professor at the Department of Mathematics, Purdue University, USA.
Patricia M. Gauzellino is professor at the Departamento de Geofísica Aplicada, Facultad de Ciencias Astronómicas y Geofísicas
Bibliographic Information
Book Title: Numerical Simulation in Applied Geophysics
Authors: Juan Enrique Santos, Patricia Mercedes Gauzellino
Series Title: Lecture Notes in Geosystems Mathematics and Computing
DOI: https://doi.org/10.1007/978-3-319-48457-0
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2016
Softcover ISBN: 978-3-319-48456-3Published: 14 January 2017
eBook ISBN: 978-3-319-48457-0Published: 13 January 2017
Series ISSN: 2730-5996
Series E-ISSN: 2512-3211
Edition Number: 1
Number of Pages: XV, 309
Topics: Mathematical Modeling and Industrial Mathematics, Geophysics/Geodesy, Partial Differential Equations, Geophysics and Environmental Physics, Mathematical Applications in the Physical Sciences