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Lecture Notes in Geosystems Mathematics and Computing

Numerical Simulation in Applied Geophysics

Authors: Santos, Juan Enrique, Gauzellino, Patricia Mercedes

  • 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 
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  • ISBN 978-3-319-48457-0
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About this Textbook

This book presents the theory of waves propagation in a fluid-saturated porous medium (a Biot medium) and its application in Applied Geophysics. In particular, a derivation of absorbing boundary conditions in viscoelastic and poroelastic media is presented, which later is employed in the applications.
 
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 with sufficient detail as to be easily implemented assuming the knowledge of scientific programming techniques.

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


Table of contents (12 chapters)

  • Waves in poroelastic solid saturated by a single-phase fluid

    Santos, Juan Enrique (et al.)

    Pages 1-31

  • A poroelastic solid saturated by two immiscible fluids

    Santos, Juan Enrique (et al.)

    Pages 33-53

  • A poroelastic solid saturated by a three-phase fluid

    Santos, Juan Enrique (et al.)

    Pages 55-77

  • Waves in a fluid-saturated poroelastic matrix composed of two weakly coupled solids

    Santos, Juan Enrique (et al.)

    Pages 79-95

  • Absorbing boundary conditions in elastic and poroelastic media

    Santos, Juan Enrique (et al.)

    Pages 97-119

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-3-319-48457-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.99
price for USA
  • ISBN 978-3-319-48456-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Numerical Simulation in Applied Geophysics
Authors
Series Title
Lecture Notes in Geosystems Mathematics and Computing
Copyright
2016
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-48457-0
DOI
10.1007/978-3-319-48457-0
Softcover ISBN
978-3-319-48456-3
Edition Number
1
Number of Pages
XV, 309
Topics