Power-law distributions describe many phenomena related to rock fracture. Data collected to measure the parameters of such distributions only represent samples from some underlying population. Without proper consideration of the scale and size limitations of such data, estimates of the population parameters, particularly the exponent D, are likely to be biased. A Monte Carlo simulation of the sampling and analysis process has been made, to test the accuracy of the most common methods of analysis and to quantify the confidence interval for D. The cumulative graph is almost always biased by the scale limitations of the data and can appear non-linear, even when the sample is ideally power law. An iterative correction procedure is outlined which is generally successful in giving unbiased estimates of D. A standard discrete frequency graph has been found to be highly inaccurate, and its use is not recommended. The methods normally used for earthquake magnitudes, such as a discrete frequency graph of logs of values and various maximum likelihood formulations can be used for other types of data, and with care accurate results are possible. Empirical equations are given for the confidence limits on estimates of D, as a function of sample size, the scale range of the data and the method of analysis used. The predictions of the simulations are found to match the results from real sample D-value distributions. The application of the analysis techniques is illustrated with data examples from earthquake and fault population studies.

Four basins surround the Falkland Islands, but only the North Falkland Basin has been drilled; six wells were drilled there in 1998. Although all six wells encountered good quality sandstones, none of them targeted the basin margins, on what are now thought to be the optimum migration pathways associated with the basin's thick lacustrine source rocks. Subsequently, a 3D seismic survey acquired in 2004 was designed to identify potential basin-margin -derived sandstones entering the basin along transfer zones. From this survey, a number of basin-margin -attached fans have been identified; these prograded into lacustrine waters of varying depths. These Early Cretaceous alluvial/fan delta/deep-lacustrine fan systems are interpreted to provide excellent potential reservoir facies as they are intimately associated with thick, mature source rocks. They will provide the focus for the next planned phase of exploration in the North Falkland Basin.A phase of drilling is also planned for the basins to the south of the Islands, where large deltaic and fan systems, slightly younger than those imaged in the North Falkland Basin, are seen on seismic to prograde from the same Palaeozoic hinterland that produced the older, North Falkland Basin fans.This paper attempts to show how sedimentary models derived from targeted seismic programmes following initial exploration can be utilised to plan and improve new drilling campaigns in a frontier basin. It presents an analysis of sediment dispersal patterns in basins of marine and lacustrine origin linked to a single hinterland area, and highlights the nature of the relationship between relay ramp/transfer zone development and sediment dispersal patterns in the subsurface.

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Fault displacement populations have been shown to follow a power-law scaling relationship characterized by an exponent D. This relationship can be used to make predictions of the sub-seismic fault population from data derived from seismic surveys. Although fault populations exist in three dimensions the use of section data is recommended. D-values derived from sections can be applied directly to several problems, and are also related to the D-value for the fault set in higher dimensions. Accurate determination of D requires proper consideration of the scale range and sample size limitations of available data. The most common technique of using a cumulative frequency graph often leads to an upwards bias. An iterative correction procedure is proposed. Discrete frequency methods avoid this bias, but as a standard linear interval graph has other associated problems, a log-interval graph method is preferred. Simulations of these methods, applied to random computer generated samples from power-law distributions, have been made to examine the accuracy of D-values derived from typical data. Equations to estimate the confidence intervals for these D-values have been derived from a synthesis of the results. The application of the techniques is shown using fault data measured on seismic sections from the Southern North Sea and the Inner Moray Firth. Where local differences in D are shown to be significant, there is usually a marked change in structural style. Fault data are used to make improved estimates of crustal extension (B) by extrapolating the derived powerlaw relationship. A value of 13 = 1.20 is calculated for the Inner Moray Firth. Applications predicting the intersection of horizontal wells with 'large' sub-seismic faults and quality control of fault interpretation on seismic sections are also described.

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