A relative moment tensor inversion technique applied to seismicity induced by mining
Date
2001-07-18
Authors
Andersen, Lindsay, Marguerite
Journal Title
Journal ISSN
Volume Title
Publisher
University of the Witwatersrand, Johannesburg
Abstract
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.
Description
Keywords
Induced seismicity -- South Africa, Seismic prospecting -- South Africa, Gold mines and mining -- South Africa, Earth movements, Rock bursts