Rock physics in four dimensions

Abstract

The measurement of the seismic velocity of a medium is fundamental to many applications in geoscience and engineering. Examples include the monitoring of: ice sheet melting, the health of concrete structures, temperature in volcanic regions, and sub-surface fluid pressure due to hydrocarbon extraction or the injection of CO2 to mitigate climate change. Velocities are also used to infer elastic properties, such as bulk and shear moduli and density, which can then be used to develop a wide range of rock physics models. This thesis addresses two key areas of research related to the seismic velocity: first, the improvement in the methodology of measuring changes in velocity in the time-lapse or four dimensional mode; and second, the interpretation of changing velocity measurements in terms of underlying processes, using various rock physics models. First, I investigate the use of coda wave interferometry (CWI) for measuring temporal changes in bulk velocity, particularly in an experimental rock physics setting. CWI uses the diffuse, multiply-scattered waves that arrive in the tail of the seismogram, sampling the entire medium and sampling the same sub-volumes many times, thus coda waves are far more sensitive to changes in a medium compared to the first arriving ballistic waves. Compared to conventional methods of phase picking of first arriving waves, CWI provides significant improvements in the accuracy and precision of estimates of velocity changes and is far more robust in the presence of background noise. CWI is also capable of jointly estimating changing source locations, allowing the estimation of the relative locations of a cluster of acoustic emissions with simultaneous velocity perturbations, all with a single receiver. Previously, the estimate of velocity change made by CWI has been an average of changes in compressional (P) and shear (S) wave velocities, which has previously been a major limitation to the application of the CWI method. I present a new method to use CWI for estimating changes in both P and S wave velocities individually. I then validate this method using numerical simulations on a range of media and the results of triaxial rock deformation experiments. The second part of this thesis is based on understanding the relationship between seismic velocity and time-dependent variables, including the evolving differential stress during deformation and changes in porosity during cementation. I investigate the seismic velocity-differential stress relationship during the experimental deformation of two finely laminated carbonate samples, using CWI to measure the temporal changes in both P and S wave velocity, allowing the inversion of crack density to interpret the mechanical behaviour of these carbonate samples. I then investigate the velocity-porosity relationship with an entirely digital method, using digital rocks where deposition and cementation are computationally simulated. I then simulate wavefield propagation through the digital rocks using a 3D finite-difference method to estimate the velocity of the medium. I statistically test two competing inclusion models for modelling elastic moduli-porosity data and find one that allows variable inclusion aspect ratio to be the most appropriate for fitting the data. I find CWI to be an effective method characterising changes in a medium in a rock physics environment. By providing a method for estimating separate changes in P and S wave velocity, I greatly improve the relevance and applicability of CWI for experimental rock physics. The method can be extended for the characterisation of media for a variety of applications in geoscience and engineering