Simplified moment tensor analysis and unified decomposition of acoustic emission source: Application to in situ hydrofracturing test

An application of a moment tensor analysis to acoustic emission (AE) is studied to elucidate crack types and orientations of AE sources. In the analysis, simplified treatment is desirable, because hundreds of AE records are obtained from just one experiment and thus sophisticated treatment is realistically cumbersome. Consequently, a moment tensor inversion based on P wave amplitude is employed to determine six independent tensor components. Selecting only P wave portion from the full-space Green's function of homogeneous and isotropic material, a computer code named SiGMA (simplified Green's functions for the moment tensor analysis) is developed for the AE inversion analysis. To classify crack type and to determine crack orientation from moment tensor components, a unified decomposition of eigenvalues into a double-couple (DC) part, a compensated linear vector dipole (CLVD) part, and an isotropic part is proposed. The aim of the decomposition is to determine the proportion of shear contribution (DC) and tensile contribution (CLVD + isotropic) on AE sources and to classify cracks into a crack type of the dominant motion. Crack orientations determined from eigenvectors are presented as crack-opening vectors for tensile cracks and fault motion vectors for shear cracks, instead of stereonets. The SiGMA inversion and the unified decomposition are applied to synthetic data and AE waveforms detected during an in situ hydrofracturing test. To check the accuracy of the procedure, numerical experiments are performed on the synthetic waveforms, including cases with 10% random noise added. Results show reasonable agreement with assumed crack configurations. Although the maximum error is approximately 10% with respect to the ratios, the differences on crack orientations are less than 7°. AE waveforms detected by eight accelerometers deployed during the hydrofracturing test are analyzed. Crack types and orientations determined are in reasonable agreement with a predicted failure plane from borehole TV observation. The results suggest that tensile cracks are generated first at weak seams and then shear cracks follow on the opened joints.

[1]  F. R. Breckenridge,et al.  Acoustic emission: some applications of Lamb’s problem , 1974 .

[2]  M. Ohtsu,et al.  Determination of crack orientation by acoustic emission , 1987 .

[3]  Lane R. Johnson,et al.  Source Characteristics of Two Underground Nuclear Explosions , 1988 .

[4]  M. Ohtsu,et al.  AE source location and orientation determination of tensile cracks from surface observation , 1988 .

[5]  M. J. Randall,et al.  The compensated linear‐vector dipole: A possible mechanism for deep earthquakes , 1970 .

[6]  Masayasu Ohtsu,et al.  GENERALIZED THEORY AND SOURCE REPRESENTATIONS OF ACOUSTIC EMISSION. , 1985 .

[7]  S. Sipkin,et al.  Earthquake processes in the Long Valley Caldera Area, California , 1985 .

[8]  K. Mahrer,et al.  Seismic wave motion for a new model of hydraulic fracture with an induced low‐velocity zone , 1987 .

[9]  B. Stump.  Mathematical representation and physical interpretation of a contained chemical explosion in alluvium , 1987 .

[10]  Hiroo Kanamori,et al.  Use of long-period surface waves for rapid determination of earthquake-source parameters , 1981 .

[11]  Takuo Maruyama,et al.  On the force equivalences of dynamic elastic dislocations with reference to the earthquake mechanisms , 1963 .

[12]  Ahmet N. Ceranoglu,et al.  Propagation of Elastic Pulses and Acoustic Emission in a Plate—Part 1: Theory , 1981 .

[13]  Brian W. Stump,et al.  The determination of source properties by the linear inversion of seismograms , 1977, Bulletin of the Seismological Society of America.

[14]  D. Lockner,et al.  Hydrofracture in Weber Sandstone at high confining pressure and differential stress , 1977 .

[15]  John H. Woodhouse,et al.  CENTROID-MOMENT TENSOR SOLUTIONS FOR 201 MODERATE AND LARGE EARTHQUAKES OF 1981 , 1983 .

[16]  Paul G. Richards,et al.  Quantitative Seismology: Theory and Methods , 1980 .

[17]  Charles A. Langston,et al.  Source inversion of seismic waveforms: The Koyna, India, earthquakes of 13 September 1967 , 1981 .

[18]  B. Chouet,et al.  Dynamics of an expanding fluid-filled crack , 1985 .