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© 2016

Numerical Simulation in Applied Geophysics

  • 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

Textbook

Table of contents

  1. Front Matter
    Pages i-xv
  2. Juan Enrique Santos, Patricia Mercedes Gauzellino
    Pages 1-31
  3. Juan Enrique Santos, Patricia Mercedes Gauzellino
    Pages 33-53
  4. Juan Enrique Santos, Patricia Mercedes Gauzellino
    Pages 55-77
  5. Juan Enrique Santos, Patricia Mercedes Gauzellino
    Pages 79-95
  6. Juan Enrique Santos, Patricia Mercedes Gauzellino
    Pages 97-119
  7. Juan Enrique Santos, Patricia Mercedes Gauzellino
    Pages 121-153
  8. Juan Enrique Santos, Patricia Mercedes Gauzellino
    Pages 155-187
  9. Juan Enrique Santos, Patricia Mercedes Gauzellino
    Pages 189-211
  10. Juan Enrique Santos, Patricia Mercedes Gauzellino
    Pages 213-231
  11. Juan Enrique Santos, Patricia Mercedes Gauzellino
    Pages 233-268
  12. Juan Enrique Santos, Patricia Mercedes Gauzellino
    Pages 269-281
  13. Juan Enrique Santos, Patricia Mercedes Gauzellino
    Pages 283-299
  14. Back Matter
    Pages 301-309

About this book

Introduction

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.

Keywords

Poroelasticity anisotropy viscoelasticity seismic waves finite elements method mesoscale macroscale numerical upscaling effective media

Authors and affiliations

  1. 1.Facultad de Ingeniería, Instituto del Gas y del PetróleoUniversidad de Buenos AiresCiudad Autónoma de Buenos AiresArgentina
  2. 2.Departamento de Geofísica Aplicada, Facultad de Ciencias Astronómicas y GeofísicasUNLP Universidad Nacional de La PlataLa PlataArgentina

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

Industry Sectors
Finance, Business & Banking

Reviews

“Readers are provided not only with exhaustive descriptions of the underlying theory but also with abundant detail about the computations required to produce the book’s many illustrative examples. … book is illustrated with fine color figures, which effectively illustrate the mathematics used to produce them. … key reference for those actively working in this area as well as for those like myself, who on occasion should recall that our real earth is neither perfectly elastic, nor perfectly homogeneous and isotropic.” (Sven Treitel, The Leading Edge, October, 2017)

“The detailed illustrations and equally detailed descriptions of the examples are an effective way to guide the geophysical community to an understanding of the main features of the theory’s applications and of the noteworthy numerical results. Thus, while the book is a quite valuable reference work for specialists, it also turns out to be an excellent reference for those working in other areas of geophysical research.” (Oscar Lovera, The Leading Edge, October, 2018)

“This book is a great addition to the collection of 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)