A relative moment tensor inversion technique applied to seismicity induced by mining - Andersen, Lindsay, Marguerite (University of the Witwatersrand, Johannesburg, 2001)
Three hybrid moment tensor inversion methods were developed for seismic sources originating from a small source region. These techniques attempt to compensate for various types of systematic error (or noise) that influence seismograms recorded in the underground environment in order to achieve an accurate and robust measure of the seismic moment tensor. The term 'hybrid' was used to distinguish between the relative method proposed by Dahm (1995) and the methods developed in this thesis. The hybrid methods were essentially weighting schemes designed to enhance the accuracy of the computed moment tensors by decreasing the influence of any low quality observations, to damp (or amplify) any signals that have been overestimated (or underestimated) due to local site effects, and to correct for raypath focussing or defocussing that results from inhomogeneities in the rockmass. The weighting or correction applied to a particular observation was derived from the residuals determined when observed data were compared with corresponding theoretical data (for a particular geophone site, sensor orientation and wave phase) and were calculated using a cluster of events rather than a single event. The first and second weighting schemes were indirectly related to the mean and the median of the residuals where the residuals were defined as the ratio of the theoretical to observed data. In the third scheme, the residuals were defined as the difference between the observed and theoretical data and the weights were based on the distance of a data point (measured in standard deviations) from the mean residual. In each of the weighting schemes, the correction was applied iteratively until the standard error of the least-squares solution (normalised to the scalar seismic moment) was a minimum. The schemes were non-linear because new weights were calculated for each iteration. A number of stability tests using synthetic data were carried out to quantify the source resolving capabilities of the hybrid methods under various extreme conditions. The synthetic events were pure double-couple sources having identical fault-plane orientations, and differing only in rake. This similarity in the mechanisms was chosen because the waveforms of tightly grouped events recorded underground often show high degrees of similarity. For each test, the results computed using the three hybrid methods were compared with one another and with those computed using the single event, absolute method and two relative methods (with and without a reference mechanism). In the noise-free situation, it was found that the relative method without reference mechanism showed the highest resolution of mechanisms, provided that the coverage of the focal sphere was not too sparse (> 3 stations). The hybrid method using a median correction was found to be the most robust of all the methods tested in the most extreme case of poor coverage (2 stations) of the focal sphere. When increasing levels of pseudo-random noise were applied to the data, the absolute moment tensor inversion method, the hybrid method using a median correction, and the hybrid method using a weighted mean correction all showed similar robustness and stability in extreme configurations concerning network coverage of the focal sphere and noise level. When increasing levels of systematic noise were added to the data, the hybrid methods using a median correction and weighted mean correction were found to exhibit similar robustness and stability in extreme configurations concerning network coverage of the focal sphere and systematic noise. In all situations investigated, these two hybrid methods outperformed the relative and absolute methods. The hybrid moment tensor inversion methods using a median and weighted mean correction were applied to a cluster of 14 events, having remarkably similar waveforms, recorded at Oryx Gold Mine. For comparative purposes, the absolute method was also applied. The inputs to the inversion methods consisted of the spectral plateaus of both P- and S-waves at frequencies below the comer frequency of the time-integrated displacement traces. The polarities of dominant motion were used as an additional constraint and were determined from cross-correlation of observed with synthetic P- or S-waves. The solutions computed using the hybrid moment tensor inversion using a median correction displayed a distinct improvement after the iterative residual correction procedure was applied. The radiation patterns and faultplane solutions showed a high degree of similarity, and are probably more accurate reflections of reality than those computed using the absolute moment tensor inversion methods. These observations are very encouraging and point towards the method's potential for use as a standard processing tool for mine seismicity. The implications of this work are a better understanding of the focal mechanisms of seismic events induced by mining activities, ultimately leading to improved safety underground.
Keywords: Induced seismicity -- South Africa; Seismic prospecting -- South Africa; Gold mines and mining -- South Africa; Earth movements; Rock bursts