The decades following SEG's 1990 volume on numerical modeling showed a step change in the application and use of full wave equation modeling methods enabled by the increase in computational power. Full waveform inversion, reverse time migration, and 3D elastic finite-difference synthetic data generation are examples. A searchable CD is included.

The importance of seismic wave research lies not only in our ability to understand and predict earthquakes and tsunamis, but it also reveals information on the Earth's composition and features in much the same way as it led to the discovery of Mohorovicic's discontinuity. As our theoretical understanding of the physics behind seismic waves has grown, physical and numerical modeling have greatly advanced and now augment applied seismology for better prediction and engineering practices. This book demonstrates the latest techniques and advances in seismic wave analysis from a theoretical approach, data acquisition and interpretation, to analyses and numerical simulations, as well as research applications. The major topics in this book cover aspects on seismic wave propagation, characteristics of their velocities and attenuation, deformation process of the Earth's medium, seismic source process and tectonic dynamics with relating observations, as well as propagation modeling of seismic waves.

Fundamentals of Seismic Wave Propagation, published in 2004, presents a comprehensive introduction to the propagation of high-frequency body-waves in elastodynamics. The theory of seismic wave propagation in acoustic, elastic and anisotropic media is developed to allow seismic waves to be modelled in complex, realistic three-dimensional Earth models. This book provides a consistent and thorough development of modelling methods widely used in elastic wave propagation ranging from the whole Earth, through regional and crustal seismology, exploration seismics to borehole seismics, sonics and ultrasonics. Particular emphasis is placed on developing a consistent notation and approach throughout, which highlights similarities and allows more complicated methods and extensions to be developed without difficulty. This book is intended as a text for graduate courses in theoretical seismology, and as a reference for all academic and industrial seismologists using numerical modelling methods. Exercises and suggestions for further reading are included in each chapter.

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.

The phenomenon of rockburst damage localization, which is not well understood, has been observed in deep underground mines. Analysis of seismic wave propagation in underground mines is of great interest for improved understanding of the dynamic rock failure problem. This thesis aims at making a contribution for improving understanding of the seismic wave propagation in deep underground mines. Advanced numerical modeling tools are used and new modeling techniques are developed to attain this goal. In this thesis, research is emphasized on the ground motion around excavations due to seismic wave propagation that results from a fault-slip seismic event in the far-field and the near-field. It is found that moment tensor point source model seems to be suitable for the source representation in the far-field and the non-point source model (such as kinematic rupture source model) seems to be suitable for the source representation in the near-field. The modeling results confirm that ground motion is influenced by many factors such as target-source distance, slip direction, spatial location, and geometrical and geological conditions. Influence of wavelength-to-excavation span (/D) ratio on the wavefield is investigated to gain insights of ground motion behavior under both quasi-static and dynamic loading conditions. It is revealed that PPV (peak particle velocity) values increase as the /D ratio increases and the amplification effect increases as the /D ratio decreases. The loading condition maybe changed from the dynamic loading to the quasi-static condition when the /D is larger than 30. Strong dynamic loading should be considered when the /D ratio is small (less than 10, with a shear wavelength less than 50 m and an excavation span greater than 5 m) for most underground excavations. A method is proposed to estimate the quality factor (a measure of energy loss per oscillation cycle) for shear waves propagating in underground hard rocks so as to gain insight into the influence of internal attenuation on seismic wave propagation. A proper shear wave quality factor can be obtained by comparing modeling results with that from a scaling law, even if there are no high quality data for quality factor back analysis. Furthermore, the influence of different geological structures on seismic wave propagation is studied. It is shown that wave propagation patterns around an excavation can be altered and PPV amplification and shielding effect can occur near the excavation boundaries amongst other reasons due to heterogeneities such as tunnels, open and backfilled stopes, and dykes in underground mines. Finally, a coupled numerical procedure, which couples FLAC and SPECFEM2D, is developed to consider the excavation effect on ground motion. The FLAC model considers the excavationinduced stress change and rock mass failure, and passes the input data to SPECFEM2D by invoking FISH scripts. In addition, a new nonlinear velocity model that considers the influence of confinement and rock mass failure on wave velocity is presented. This nonlinear velocity model and the coupled numerical technique are used to model a simple stope excavation problem. It is found that there is a large difference in the wavefields and ground motions between the results from the uniform and non-uniform velocity models. A relatively stronger amplification is observed in the low confinement zones and on the excavation surface in the non-uniform velocity models. Because stress redistribution and rock mass failure around an excavation are considered, a realistic non-uniform velocity field can be obtained. The proposed coupled numerical procedure offers a method to improve the understanding of the site amplification effect and ground motion near excavation boundaries. This thesis presents some insights with regard to seismic wave propagation due to fault-slip seismic events in underground mines. If seismic wave propagation in underground mines can be modeled properly using techniques such as these presented in this thesis, then it is possible to conduct forensic analysis after a large seismic event so as to explain one of many factors that caused rockburst damage localization. Alternatively, the modeling approach may provide valuable inputs for decision-making with regard to strengthening high risk areas to prevent rockburst, thus improving mine safety.