[1] We examine the question of proximity of the global earthquake population to the critical point characterised by the energy E and entropy S based on annual frequency data from the Harvard CMT catalogue. The results are compared with a theoretical model corresponding to a Boltzmann probability density distribution of the form p(E) / E ÀBÀ1 e ÀE/q . The data are consistent with the model predictions for fluctuations in the characteristic energy q at constant B value, of the form S$BhlnEi. This approximation is valid for large q, relative to the maximum possible event size, confirming that the Earth is perpetually in a near-critical state, reminiscent of self-organized criticality. However, the results also show fluctuations of ±10% in entropy that may be more consistent with the notion of intermittent criticality. A more precise definition of the two paradigms, and a similar analysis of numerical models, are both needed to distinguish between these competing models.

A borehole network consisting of 5 monitoring wells was used to monitor the induced seismicity at a producing petroleum field for a period of about 11 months. Nearly 5400 microseismic events were analyzed and utilized in imaging the reservoir based on a new doubledifference (DD) seismic tomography. The DD tomography method simultaneously solves for event locations and Vp, Vs, and Vp/Vs models using absolute and differential P, S and S-P arrival times. Microseismicity in the field was primarily caused by compaction of the reservoir in and above the gas bearing formation and was distributed along the two major northeastsouthwest (NE-SW) faults in the field. The model resolution analysis based on the checkerboard test and the resolution matrix showed that the central part of the model was relatively well resolved for the depth range of 0.7 to 1.1 km. Clear velocity contrasts were imaged across most parts of the two NE-SW faults. Vp/Vs ratio estimations from the tomographic inversion were low (<1.75) in the shallow depth range, likely due to lithology and gas content, whereas they were large (>1.75) in the deeper part of the model, likely due to fluid saturated formation. In this study seismic tomography showed a great potential for reservoir imaging and property estimation using induced seismicity.2

Summary The spatial cross‐correlation and power spectra of porosity and log(permeability) sequences are analysed for a total of 750 m of reservoir rock drill‐core from four vertical wells in the Brae Formation, an important coarse‐grained clastic North Sea hydrocarbon reservoir rock. The well core sequences are 80 ± 4 per cent cross‐correlated at zero lag and have power‐law‐scaling spatial power spectra S(k)∝1/kβ, β≈ 1 ± 0.4, for spatial frequencies 5 km−1 < k < 3000 km−1. The strong spatial cross‐correlation of porosity and log(permeability) and the systematic power‐law scaling of log(permeability) spatial fluctuation spectra fit into a broad physical context of (1) the 1/k spectral scaling observed in several hundred well logs of sedimentary and crystalline rock recorded world‐wide; (2) the 1/f spectral scaling of temporal sequences in a wide range of physical systems; and (3) analogy with power‐law‐scaling spatial fluctuation spectra in a wide range of critical‐state thermodynamic systems. In this physical context, the spatial fluctuations of log(permeability) of clastic reservoir rock are interpreted as due to long‐range correlated random fracture‐permeability networks in a fluid‐saturated granular medium where the range ξ of spatial correlation is effectively infinite. Fracture‐permeability spatial fluctuations with long‐range correlations and 1/k‐scaling spectra have practical implications for geofluid reservoir management. Inadequate models of reservoir flow structure are widely attributed to uncertainty in fault and fracture location and connectivity. As a general phenomenon, spatial configurations of large‐amplitude, long‐range spatially correlated random fluctuations are unpredictable from the statistics of small‐scale samples. The observed 1/k spectral scaling of porosity and log(permeability) distributions thus implies that large‐scale, large‐amplitude fracture‐related flow heterogeneity (1) can determine the drainage pattern of crustal reservoirs but (2) cannot be accurately predicted using statistical techniques based on small‐scale reservoir samples. Incompatibility of the physics of reservoir heterogeneity and the statistical approaches to reservoir models can thus explain the persistent under‐performance of stochastic reservoir models. Accurate reservoir flow models can, however, be determined by direct observation of fluid flow at the reservoir scale. Recent advances in seismic time‐lapse reservoir‐fluid monitoring may provide data for significantly more effective management of hydrocarbon reservoirs, waste burial sites, mining works and groundwater aquifers.