A relative moment tensor inversion technique applied to seismicity induced by mining

[摘要] Three hybrid moment tensor inversion methods were developed for seismic sourcesoriginating from a small source region. These techniques attempt to compensate forvarious types of systematic error (or noise) that influence seismograms recorded in theunderground environment in order to achieve an accurate and robust measure of theseismic moment tensor. The term 'hybrid' was used to distinguish between therelative method proposed by Dahm (1995) and the methods developed in this thesis.The hybrid methods were essentially weighting schemes designed to enhance theaccuracy of the computed moment tensors by decreasing the influence of any lowquality observations, to damp (or amplify) any signals that have been overestimated(or underestimated) due to local site effects, and to correct for raypath focussing ordefocussing that results from inhomogeneities in the rockmass.The weighting or correction applied to a particular observation was derived from theresiduals determined when observed data were compared with correspondingtheoretical data (for a particular geophone site, sensor orientation and wave phase) andwere calculated using a cluster of events rather than a single event. The first andsecond weighting schemes were indirectly related to the mean and the median of theresiduals where the residuals were defined as the ratio of the theoretical to observeddata. In the third scheme, the residuals were defined as the difference between theobserved and theoretical data and the weights were based on the distance of a datapoint (measured in standard deviations) from the mean residual. In each of theweighting schemes, the correction was applied iteratively until the standard error ofthe 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 sourceresolving capabilities of the hybrid methods under various extreme conditions. Thesynthetic events were pure double-couple sources having identical fault-planeorientations, and differing only in rake. This similarity in the mechanisms was chosenbecause the waveforms of tightly grouped events recorded underground often showhigh degrees of similarity. For each test, the results computed using the three hybridmethods were compared with one another and with those computed using the singleevent, absolute method and two relative methods (with and without a referencemechanism). In the noise-free situation, it was found that the relative method withoutreference mechanism showed the highest resolution of mechanisms, provided that thecoverage of the focal sphere was not too sparse (> 3 stations). The hybrid methodusing a median correction was found to be the most robust of all the methods tested inthe 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 absolutemoment tensor inversion method, the hybrid method using a median correction, andthe hybrid method using a weighted mean correction all showed similar robustnessand stability in extreme configurations concerning network coverage of the focalsphere and noise level. When increasing levels of systematic noise were added to thedata, the hybrid methods using a median correction and weighted mean correctionwere found to exhibit similar robustness and stability in extreme configurationsconcerning network coverage of the focal sphere and systematic noise. In allsituations investigated, these two hybrid methods outperformed the relative andabsolute methods.The hybrid moment tensor inversion methods using a median and weighted meancorrection were applied to a cluster of 14 events, having remarkably similarwaveforms, recorded at Oryx Gold Mine. For comparative purposes, the absolutemethod was also applied. The inputs to the inversion methods consisted of the spectralplateaus of both P- and S-waves at frequencies below the comer frequency of thetime-integrated displacement traces. The polarities of dominant motion were used asan additional constraint and were determined from cross-correlation of observed withsynthetic P- or S-waves. The solutions computed using the hybrid moment tensorinversion using a median correction displayed a distinct improvement after theiterative residual correction procedure was applied. The radiation patterns and faultplanesolutions showed a high degree of similarity, and are probably more accuratereflections of reality than those computed using the absolute moment tensor inversionmethods. These observations are very encouraging and point towards the method'spotential for use as a standard processing tool for mine seismicity.The implications of this work are a better understanding of the focal mechanisms ofseismic events induced by mining activities, ultimately leading to improved safetyunderground.

[发布机构] University of the Witwatersrand