We present a novel methodology for exploring 4D seismic data in the context of monitoring subsurface resources. Data-space exploration is a key activity in scientific research, but it has long been overlooked in favour of model-space investigations. Our methodology performs a data-space exploration that aims to define structures in the covariance matrix of the observational errors. It is based on Bayesian inferences, where the posterior probability distribution is reconstructed through trans-dimensional (trans-D) Markov chain Monte Carlo sampling. The trans-D approach applied to data-structures (termed ”partitions’) of the covariance matrix allows the number of partitions to freely vary in a fixed range during the McMC sampling. Due to the trans-D approach, our methodology retrieves data-structures that are fully data-driven and not imposed by the user. We applied our methodology to 4D seismic data, generally used to extract information about the variations in the subsurface. In our study, we make use of real data that we collected in the laboratory, which allows us to simulate different acquisition geometries and different reservoir conditions. Our approach is able to define and discriminate different sources of noise in 4D seismic data, enabling a data-driven evaluation of the quality (so-called ”repeatability’) of the 4D seismic survey. We find that: (1) trans-D sampling can be effective in defining data-driven data-space structures; (2) our methodology can be used to discriminate between different families of data-structures created from different noise sources. Coupling our methodology to standard model-space investigations, we can validate physical hypothesis on the monitored geo-resources.

It is now well-established that earthquakes change the seismic velocity of the near surface. There is certainly some understanding of what mechanisms are responsible for these changes, but there remain many questions. Here we attempt to answer the question of the relative importance of different connection mechanisms between cracks and how these change with applied load. To study this, we first perform nonlinear wave-mixing experiments in two sandstone samples at a variety of applied uniaxial stresses. The two samples differ in the relative orientation of their microstructures. We find that although the samples show velocity anisotropy we do not see aligned structures in scanning electron microscope images. By measuring the changes in velocities with applied stress we find that most cracks close during our experiments independent of crack orientation. By contrast, we find that the nonlinear wave interactions vary strongly with applied load and with crack orientation. We analyze these differences and relate them to an emerging model of nonlinear wave interactions with microstructures.

It is now well-established that earthquakes change the seismic velocity of the near surface. There is certainly some understanding of what mechanisms are responsible for these changes, but there remain many questions. One of these open questions is how cracks and other microstructures within the rock control these changing velocities. Here we look at the nonlinear interaction of two waves, one of which (the PUMP) simulates the effect of an earthquake and the other (the probe) senses the changes in the travel time caused by the passage of the PUMP wave. We use a sandstone sample that is established to have a nonlinear response that depends on the orientation of the sample layering. We study two samples with different orientations of this layering, which we infer to be different orientations of the micro-structure. We show that the dependence of these changes on applied load are exponential, with a characteristic load of 11.4-12.5~MPa that is independent of sample orientation and probe wavetype (P or S); this value agrees with results from the literature.