ABSTRACT:

A generalized, adaptively damped inversion technique with partitioned matrices was applied to determine the locations of mine tremors as well as the parameters of an assumed velocity model. This method is applied to two datasets of arrival times in order to determine the P-wave velocity anisotropy within underground seismic networks of radius 15m and 2000m respectively.

RESUME:

On s'est servi d'une methode generalisee d'inversion adaptable amortie avec des matrices cloisonnees pour determiner l'emplacement des secousses sismiques souterraines aussi que les paramètres d'un modèle à vitesse supposee. Cette methode est appliquee à deux ensembles de donnees d'heure d'arrivee afin de determiner l'anisotropie de la vitesse de l'onde P des reseaux sismiques souterraines d'un rayon de 15m et de 2000m respectivement.

ZUSAMMENFASSUNG;

Dargestellt wird die generalisierende und kontrollierbar gedamptfte Inversionstechnik zur Ortung von Bergwerksbeben wie auch zur Ermittlung der Parameter eines angenommenen Geshwindigkeitmodells. Diese Methode wird angewandt auf zwei Gruppen von Ankunftszeitmeszwerten, urndas anisotropische Charakter der P-Wellengeschwindigkeit in unterirdischen seismischen Bezirken. im Radius von jeweils 15 und 2000 Metern, zu ermitteln.

INTRODUCTION

The quantification of the velocity structure, in order to determine accurate locations of mine tremors. requires a number of calibration blasts that in the case of an extensive mine area. covered by one seismic network. can be prohibitively expensive.

This paper describes a method that uses the P arrival times (generalization for P+S or S-P is straightforward) from a group of mine tremors to evaluate simultaneously: the parameters of an assumed velocity structure (in this case the average values of velocities of seismic waves from the region of seismic activity to the particular stations) and the co-ordinates of hypocentres. An efficient algorithm of partitioned matrices (Spencer, 1985) was used, where unknown parameters are separated into two distinct sets on the ground of physical differences and for computational reasons. This enables joint hypocentre and velocity inversion to be carried out on a personal computer and at only marginally greater cost (in terms of Computer memory and processing time) than that of a velocity inversion alone. Additional procedures improving the numerical properties of the specific inverse problem have been used. namely weighting (Inman. 1975), centering (Draper and Smith, 1981; Lee and l.ahr. 1972; Lienert et al., 1986), scaling (Lee and Lahr, 1972; Inman. 1975; Smith. 1976; Lienert et al., 1986) and damping (Marquardt. 1970; Crosson. 1976; Aki and Lee. 1976; Lienert et al., 1986). These techniques are often used in geophysical inverse theory and are not fully described here.

The algorithm, on which a Fortran program for an IBM AT personal computer is based, is given in a general form below. This is followed by a description of the practical application of the technique to P-wave arrival time data sets from two seismic networks in South African gold mines. one of 15m radius and the other of 2000m radius.

GENERAL DESCRIPTION OF ALGORITHM

Consider the rock mass as a statistically slightly disturbed anisotropic and inhomogeneous medium. in which Vj is the average value of P-wave velocity for the rock mass containing the ray paths between the sources of NE events and the j-th seismic station. Thus. the arrival time. tij of the direct P-wave from the source of the i-th mine tremor. with co-ordinates Xqi (q-l.2,3.4), where x4i is origin time. to the j-th seismic station, XSqj (q-l,2,3) can be given as follow

(Equation in full paper)

APPLICATIONS
A very small Micro-Network

In 1985, a 15m radius seismic network of 8 geophones was installed by the SA Chamber of Hines Research Organisation in a pillar 2160. below surface in a gold mine in the Klerksdorp district. The main purpose was to investigate the fracture process ahead of the stope in the pre-remnant and remnant stages of mining by analysis of micro-seismicity (Legge and Spottiswoode, 1987). In order to obtain reliable locations of seismic activity, 8 calibration blasts were performed and average values of P-wave velocities to the particular geophones were determined. Arrival times of micro-seismic events were accumulated over a period of two months and a sample of the data was kindly made available for numerical analysis.

Seven of the eight calibration blasts form a relatively tight spatial group and seismic events were selected which cluster in the same source region. Fig.1 shows the mining situation, positions of the calibration blasts, the relocated positions of seismic events and contours of expected location errors (Mendecki and van Aswegen, 1986). The contour values were calculated assuming maximum errors for the P-wave arrival and the P-wave velocity of 0,05 me and 480 m/s respectively.

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