Numerical Simulation in Applied Geophysics

1. Front Matter

   Pages i-xv

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2. Waves in poroelastic solid saturated by a single-phase fluid

   • Juan Enrique Santos, Patricia Mercedes Gauzellino

   Pages 1-31

3. A poroelastic solid saturated by two immiscible fluids

   • Juan Enrique Santos, Patricia Mercedes Gauzellino

   Pages 33-53

4. A poroelastic solid saturated by a three-phase fluid

   • Juan Enrique Santos, Patricia Mercedes Gauzellino

   Pages 55-77

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

   • Juan Enrique Santos, Patricia Mercedes Gauzellino

   Pages 79-95

6. Absorbing boundary conditions in elastic and poroelastic media

   • Juan Enrique Santos, Patricia Mercedes Gauzellino

   Pages 97-119

7. Solution of differential equations using the finite element method

   • Juan Enrique Santos, Patricia Mercedes Gauzellino

   Pages 121-153

8. Modeling Biot media at the meso-scale using a finite element approach

   • Juan Enrique Santos, Patricia Mercedes Gauzellino

   Pages 155-187

9. The meso-scale. Fractures as thin layers in Biot media and induced anisotropy

   • Juan Enrique Santos, Patricia Mercedes Gauzellino

   Pages 189-211

10. Fractures modeled as boundary conditions in Biot media and induced anisotropy

    • Juan Enrique Santos, Patricia Mercedes Gauzellino

    Pages 213-231

11. The macro-scale. Seismic monitoring of CO2 sequestration

    • Juan Enrique Santos, Patricia Mercedes Gauzellino

    Pages 233-268

12. Wave propagation in partially frozen porous media

    • Juan Enrique Santos, Patricia Mercedes Gauzellino

    Pages 269-281

13. The macro-scale. Wave propagation in transversely isotropic media

    • Juan Enrique Santos, Patricia Mercedes Gauzellino

    Pages 283-299

14. Back Matter

    Pages 301-309

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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 withsufficient detail as to be easily implemented assuming the knowledge of scientific programming techniques.

• Poroelasticity
• anisotropy
• viscoelasticity
• seismic waves
• finite elements method
• mesoscale
• macroscale
• numerical upscaling
• effective media
• partial differential equations

“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 understandingof 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 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)

• Facultad de Ingeniería, Instituto del Gas y del Petróleo, Universidad de Buenos Aires, Ciudad Autónoma de Buenos Aires, Argentina

  Juan Enrique Santos

• Departamento de Geofísica Aplicada, Facultad de Ciencias Astronómicas y Geofísicas, UNLP Universidad Nacional de La Plata, La Plata, Argentina

  Patricia Mercedes Gauzellino

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

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