Cataclastic deformation bands, which are common in sandstone reservoirs and which may negatively affect fluid flow, are generally associated with notable thickness variations. It has been suggested previously that such thickness variations represent an important control on how deformation bands affect fluid flow. The effects of such thickness variations are tested in this study though statistical analysis and fluid flow simulation of an array of cataclastic deformation bands in Cretaceous sandstones in in the Bassin de Sud‐Est in Provence, France. Spatial outcrop data are statistically analyzed for incorporation in flow simulation models, and numerical simulations are used to investigate the effects of notable thickness variations on how the deformation bands influence effective permeability and flow dynamics. A suite of simulations is performed using a combination of fine‐scale and coarse‐scale grids, revealing that the effective permeability of the simulated reservoir is reduced by a factor of 15–25. More interestingly, the simulations further demonstrated that, as compared to the overall effect of the deformation band array on fluid flow, thickness variations along the bands proved to have negligible effects only. Thus, our simulations indicate that the configuration and connectivity of the deformation bands, together with the permeability contrast between the bands and the host rock and the mean band thickness, are the most important controls on the effective permeability. Our findings represent new insight into the influence of deformation bands on fluid flow in subsurface aquifers and reservoirs, indicating that thickness variations of individual deformation bands are of less significance than previously thought.

In order to study the effect of the micro‐CT scan resolution and size on the accuracy of upscaled digital rock property estimation of core samples Bentheimer sandstone images with the resolution varying from 0.9 μm to 24 μm are used. We statistically show that the correlation length of the pore‐to‐matrix distribution can be reliably determined for the images with the resolution finer than 9 voxels per correlation length and the representative volume for this property is about 153 correlation length. Similar resolution values for the statistically representative volume are also valid for the estimation of the total porosity, specific surface area, mean curvature, and topology of the pore space. Only the total porosity and the number of isolated pores are stably recovered, whereas geometry and the topological measures of the pore space are strongly affected by the resolution change. We also simulate fluid flow in the pore space and estimate permeability and tortuosity of the sample. The results demonstrate that the representative volume for the transport property calculation should be greater than 50 correlation lengths of pore‐to‐matrix distribution. On the other hand, permeability estimation based on the statistical analysis of equivalent realizations shows some weak influence of the resolution on the transport properties. The reason for this might be that the characteristic scale of the particular physical processes may affect the result stronger than the model (image) scale.

[1] The statistical analysis of fault attributes scaling relationships is discussed. Dependences of length, width of damage zone and thickness of fault core on displacement were studied assuming power law relations. The approximation forms a piecewise-linear function with few slopes in log-log scale. The Bayesian Information Criterion (BIC) was used to find the best fit for an optimal number of parameters. Numerical tests show that the best fit was obtained when using power law relations with two slopes. Bayesian analysis of model parameters' probability distribution was performed. For length-displacement relation (L-D), the slope decreases from one scale of faults to another. This change occurs at $1 m displacement for reverse and normal faults in siliciclastic rocks, at $1500 m displacement for strike slip and at $300 m displacement for normal faults in non-siliciclastic rocks. The slope of the damage zone width-displacement (W-D) relation decreases at $10 m, while it slightly increases for fault core thickness-displacement (T-D) relation at $10 cm. The result of the probability density of changepoints confirms the calculated changepoints, which correspond to maximal BIC in most cases. We propose an evolutionary growth pattern of faults based on the statistical results, in which faults lengthen during the initial stage. During subsequent overlapping and linkage between the faults, mainly displacement accumulates. Fault damage zone and fault core form early in the process of faulting. In mature faults, the development of damage zone would be slower than for small faults, whereas fault core slightly thickens with further localization.Citation: Kolyukhin, D., and A. Torabi (2012), Statistical analysis of the relationships between faults attributes, J. Geophys.

We present an efficient implementation of the method for sampling spatial realisations of a 3-D random fields with given power spectrum. The method allows for a multi-scale resolution and approaches well for parallel implementations, overcoming the physical limitation of computer memory when dealing with large 3-D problems. We implement the random field generator to execute on graphical processing units (GPU) using the CUDA C programming language.We compare the memory footprint and the wall-time of our implementation to FFT-based solutions. We illustrate the efficiency of the proposed numerical method using examples of an acoustic scattering problem which can be encountered both in controlled-source and earthquake seismology. In particular, we apply our method to study the scattering of seismic waves in 3-D anisotropic random media with a particular focus on P-wave coda observations and seismic monitoring of hydrocarbon reservoirs.

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Fault damage zones in highly porous reservoirs are dominated by deformation bands that generally have permeability-reducing properties. Due to an absence of sufficiently detailed measurements and the irregular distribution of deformation bands, a statistical approach is applied to study their influence on flow. A stochastic model of their distribution is constructed, and band density, distribution, orientation, and flow properties are chosen based on available field observations. The sensitivity of these different parameters on the upscaled flow is analyzed. The influence of a heterogeneous permeability distribution was also studied by assuming the presence of high permeability holes within bands. The fragmentation and position of these holes affect significantly the block-effective permeability. Results of local upscaling with a diagonal and full upscaled permeability tensor are compared, and qualitatively similar results for the flow characteristics are obtained. Further, the procedure of iterative localglobal upscaling is applied to the problem.

We have studied three‐dimensional fault geometries through a geologically integrated analysis of fault seismic attribute volumes. We used a series of coherence (semblance) and filtered coherence attribute volumes with parameters optimised for imaging faults in the studied seismic volumes. Fault geometric attributes such as along strike segment length and displacement were measured on fault seismic attributes. The scaling relationships of fault geometric attributes were studied using statistical methods such as the Bayesian information criterion, the likelihood ratio test, and the bootstrap method. Univariate distributions of fault segment length and maximum displacement show a truncated power law for most of the fault data. The statistical results indicate a piecewise‐linear relation with two slopes between depth and fault segments lengths: depth and mean displacement. For these relations, we observe consistent increases in fault segment lengths and mean displacements from the lower tip of the fault at depth toward a point of inflection at shallower depth at the vertical section. From that point, a reduction in fault segment lengths and mean displacements toward the upper tip of the fault at the shallower depth occurs. Fault segmentation along strike increases toward the lower and upper tips of the fault, but the maximum number of segments are located near the lower tip of the fault in two of the studied faults. The fault segment length is maximum, where the number of segments (along strike) is least close to the middle of the fault in the vertical section.

The seismic oceanography method is based on extracting and stacking the low-frequency acoustic energy scattered by the ocean heterogeneity. However, a good understanding on how this acoustic wavefield is affected by physical processes in the ocean is still lacking. In this work an acoustic waveform modeling and inversion method is developed and applied to both synthetic and real data. In the synthetic example, the temperature field is simulated as a homogeneous Gaussian isotropic random field with the Kolmogorov–Obukhov spectrum superimposed on a background stratified ocean structure. The presented full waveform inversion method is based on the ray-Born approximation. The synthetic seismograms computed using the ray-Born scattering method closely match the seismograms produced with a more computationally expensive finite-difference method. The efficient solution to the inverse problem is provided by the multiscale nonlinear inversion approach that is specifically stable with respect to noise. Full waveform inversion tests are performed using both the stationary and time-dependent sound speed models. These tests show that the method provides a reliable reconstruction of both the spatial sound speed variation and the theoretical spectrum due to fully developed turbulence. Finally, the inversion approach is applied to real seismic reflection data to determine the heterogeneous sound speed structure at the west Barents Sea continental margin in the northeast Atlantic. The obtained model illustrates in more detail the processes of diapycnal mixing near the continental slope.