Correlations in aftershock and seismicity patterns

Correlations in space and time play a fundamental role in earthquake processes. One direct manifestation of the effects of correlations is the occurrence of aftershocks due to the stress transfer in the vicinity of a main shock. Less obvious and more speculative changes in correlations may occur in the background seismicity before large earthquakes. Using statistical physics it is possible to introduce a measure of spatial correlations through a correlation length. This quantity characterizes how local fluctuations can influence the occurrence of earthquakes over distances comparable with the correlation length. In this work, the physical basis of spatial correlations of earthquakes is discussed in the context of critical phenomena and the percolation problem. The method of two-point correlation function is applied to the seismicity of California. Well defined variations in time of the correlation length are found for aftershock sequences and background seismicity. The scaling properties of our obtained distributions are analyzed with respect to changes in several scaling parameters such as lower magnitude cutoff of earthquakes, the maximum time interval between earthquakes, and the spatial size of the area considered. This scaling behavior can be described in a unified manner by utilizing the multifractal fit. Utilizing the percolation approach the time evolution of clusters of earthquakes is studied with the correlation length defined in terms of the radius of gyration of clusters. This method is applied to the seismicity of California.     

Modèles géostatistiques de concentrations ou de débits le long des cours d'eau

Estimating concentrations or flow rates along a stream network requires specific models. Two classes of models, recently proposed in the literature, are generalized, to the intrinsic case in particular. We present a global construction by ‘streams’, i.e. on the whole set of paths between sources and outlet. Combining stationary or intrinsic one-dimensional random functions leads to stationary or intrinsic models on segments, with discontinuities at the forks. A construction from outlet to sources, leads to stationary or intrinsic models on each stream, without any discontinuity at the forks. The linear variogram is found as a particular case. The extension to the linear model of coregionalization is immediate, allowing a multivariate modelling of concentrations. To cite this article: C. de Fouquet, C. Bernard-Michel, C. R. Geoscience 338 (2006).     

Optimization of nonconventional wells under uncertainty using statistical proxies

The determination of the optimal type and placement of a nonconventional well in a heterogeneous reservoir represents a challenging optimization problem. This determination is significantly more complicated if uncertainty in the reservoir geology is included in the optimization. In this study, a genetic algorithm is applied to optimize the deployment of nonconventional wells. Geological uncertainty is accounted for by optimizing over multiple reservoir models (realizations) subject to a prescribed risk attitude. To reduce the excessive computational requirements of the base method, a new statistical proxy (which provides fast estimates of the objective function) based on cluster analysis is introduced into the optimization process. This proxy provides an estimate of the cumulative distribution function (CDF) of the scenario performance, which enables the quantification of proxy uncertainty. Knowledge of the proxy-based performance estimate in conjunction with the proxy CDF enables the systematic selection of the most appropriate scenarios for full simulation. Application of the overall method for the optimization of monobore and dual-lateral well placement demonstrates the performance of the hybrid optimization procedure. Specifically, it is shown that by simulating only 10% or 20% of the scenarios (as determined by application of the proxy), optimization results very close to those achieved by simulating all cases are obtained.     

A comparison of chironomid biostratigraphy from Lake Vuolep Njakajaure with vegetation, lake-level, and climate changes in Abisko National Park, Sweden

Chironomid remains from the sediment of Lake Vuolep Njakajaure reflect limnological conditions resulting from changing climate and vegetation throughout the Holocene, but do not strictly follow accepted climate trends or the vegetation history based on regional pollen and macrofossil analyses. Chironomid community changes appear to be influenced by organic nutrient input from the surrounding catchment vegetation and lake hydrology, both of which are indirectly responding to some combination of climate change, hypolimnetic oxygen concentration, and changes in basin morphology. The chironomid-based quantitative mean July air-temperature reconstruction differs from other regional quantitative records; this discrepancy is likely related to limnological conditions particular to Lake Vuolep Njakajaure. Comparison of a northern Swedish temperature transfer function and one from western Canada reveals differences in the mean July air-temperature optima of several common taxa, suggesting that the existing conservative estimates of Holocene climate change in northern Sweden may be underestimated due to the limited temperature gradient captured by the Swedish training set.     

Optimization of SAGD Well Elevation

The application of steam-assisted gravity drainage (SAGD) to recover heavy oil sands is becoming increasingly important in the northern Alberta McMurray Formation because of the vast resources/reserves accessible with this mechanism. Selecting the stratigraphic elevations of SAGD well pairs is a vital decision for reservoir evaluation and planning. The inherent uncertainty in the distribution of geological variables significantly influences this decision. Geostatistical simulation is used to capture geological uncertainty, which is used can be transformed into a distribution of the best possible well pair elevations. A simple exhaustive calculation scheme is used to determine the optimum stratigraphic location of a SAGD well pair where the recovery R is maximized. There are three basic steps to the methodology: (1) model the uncertainty in the top continuous bitumen (TCB) and bottom continuous bitumen (BCB) surfaces, (2) calculate the recovery at all possible elevation increments within the TCB and BCB interval, and (3) identify the elevation that maximizes R. This is repeated for multiple TCB/BCB pairs of surfaces to assess uncertainty. The methodology is described and implemented on a subset of data from the Athabasca Oilsands in Fort McMurray, Alberta.     

Biological and Geochemical Record of Anthropogenic Impacts in Recent Sediments from Lake Pupuke, Auckland City, New Zealand

Frozen sediment cores from Lake Pupuke in Auckland City, New Zealand, contain a high resolution decadal to annual scale record of changing lake paleoenvironments and geochemistry that reflects changing landuse and hydrology in the catchment over the past c. 190 years. A reliable chronology is available from AMS ¹⁴C and ²¹⁰Pb dating of the sediments, with the timing of the older part of the record supported by the first appearance of pollen of introduced Pinus and Plantago lanceolata associated with European settlement of Auckland in the early 1840s. Diatom stratigraphy, sediment elemental and carbon isotope geochemistry reflect changes in sediment sources and lake conditions commensurate with European development of the Lake Pupuke catchment, in particular enhanced algal productivity controlled by the influx of nutrients after c. 1920 AD. Attempts to prevent nuisance algal blooms in 1933, 1934 and 1939 using CuSO₄ addition produced Cu spikes in the sediment that allowed confirmation of the accuracy of the ²¹⁰Pb chronology. Hence, the elemental and isotopic composition of the Lake Pupuke sediments reflect the timing of significant anthropogenic activities, rather than climatic variations, that have occurred within the watershed over the past c. 190 years. The comparison of records of land use change in the catchment with the multi-proxy record of changes in the sediments usually allowed unambiguous identification of the signatures of change and their causes.     

Fast computation of Hankel Transform using orthonormal exponential approximation of complex kernel function

The computation of electromagnetic (EM) fields, for 1-D layered earth model, requires evaluation of Hankel Transform (HT) of the EM kernel function. The digital filtering is the most widely used technique to evaluate HT integrals. However, it has some obvious shortcomings. We present an alternative scheme, based on an orthonormal exponential approximation of the kernel function, for evaluating HT integrals. This approximation of the kernel function was chosen because the analytical solution of HT of an exponential function is readily available in literature. This expansion reduces the integral to a simple algebraic sum. The implementation of such a scheme requires that the weights and the exponents of the exponential function be estimated. The exponents were estimated through a guided search algorithm while the weights were obtained using Marquardt matrix inversion method. The algorithm was tested on analytical HT pairs available in literature. The results are compared with those obtained using the digital filtering technique with Anderson filters. The field curves for four types (A-, K-, H-and Q-type) of 3-layer earth models are generated using the present scheme and compared with the corresponding curves obtained using the Anderson sc heme. It is concluded that the present scheme is more accurate than the Anderson scheme