The Effect of Green’s Functions on the Determination of Source Mechanisms by the Linear Inversion of Seismograms

Stump, Brian W.; Johnson, Lane R.

doi:10.1007/978-94-009-8531-5_9

Cited by 64 publications

(92 citation statements)

References 11 publications

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“…This approach is described and tested with synthetic data in STUMP and JOHNSON (1977). KIRKPATRICK et al (1996) used this method to obtain static moment tensors for a large number earthquakes at The Geysers by measuring the amplitudes of p and s wave pulses, correcting for the instrument response, and then using ray theory to calculate Green functions.…”

Section: Static Moment Tensor Resultsmentioning

confidence: 99%

“…The method of estimating the moment tensor in this study follows that of STUMP and JOHNSON (1977). It is assumed that the earthquake source process can be adequately represented by the symmetric firstdegree moment tensor m ij (t), which is equivalent to assuming that the wavelengths of interest are large compared to the dimensions of the source volume.…”

Section: Moment Tensor Methodsmentioning

confidence: 99%

“…Following STUMP and JOHNSON (1977), it is convenient to obtain the solution to this inverse problem using singular value decomposition (LANCZOS 1961).…”

Section: Moment Tensor Methodsmentioning

confidence: 99%

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Source Mechanisms of Induced Earthquakes at The Geysers Geothermal Reservoir

Johnson

2014

Pure Appl. Geophys.

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Abstract-At The Geysers geothermal reservoir in northern California, evidence strongly suggests that activities associated with production of electric power cause an increase in the number of small earthquakes. First-degree dynamic moment tensors are used to investigate the relationship between induced earthquakes and injection of water into a well as part of a controlled experiment in the northwest Geysers. The estimation of dynamic moment tensors in the complex shallow crust at The Geysers is challenging, so the method is described in detail with particular attention given to the uncertainty in the results. For seismic events in the moment magnitude range of 0.9-2.8, spectral moduli of dynamic moment tensors are reliably recovered in the frequency range of 1-100 Hz, but uncertainty in the associated spectral phases limits their use to a few simple results. A number of different static moment tensors are investigated, with the preferred one obtained from parameters of a model fitted to the spectral modulus of the dynamic moment tensor. Moment tensors estimated for a group of 20 earthquakes exhibit a range of source mechanisms, with over half having significant isotropic parts of either positive or negative sign. Corner frequencies of the isotropic part of the moment tensor are about 40 % larger than the average of the deviatoric moment tensor. Some spatial patterns are present in source mechanisms, with earthquakes closely related in space tending to have similar mechanisms, but at the same time, some nearby earthquakes have very different mechanisms. Tensional axes of displacement in the source regions are primarily horizontal, while the pressure axes range from near horizontal to vertical. Injection of water into the well in the center of the study area clearly causes an increase in the number of earthquakes per day, but an effect upon source mechanisms is not evident.

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Section: Static Moment Tensor Resultsmentioning

confidence: 99%

Section: Moment Tensor Methodsmentioning

confidence: 99%

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Source Mechanisms of Induced Earthquakes at The Geysers Geothermal Reservoir

Johnson

2014

Pure Appl. Geophys.

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“…This form of the Rayleigh-and Love-wave expressions is convenient for separating the contribution to the Rayleigh wave from the P-and S-wave source radiation and the contribution of the upgoing and downgoing source radiation for both Rayleigh and Love waves. Because of the ease of using different compression and shear-wave source time functions, these formulas are especially suited for sources for which second-and higher-order moment tensors (Backus and Mulcahy, 1976;Stump and Johnson, 1977;Doornbos, 1982;Stump and Johnson, 1982) are needed to describe the source, such as the initial value problem of the instantaneous formation of a cavity in a prestressed medium (Ben-Menahem and Singh, 1981, pp. 221-229).…”

Section: Introductionmentioning

confidence: 99%

Theoretical Rayleigh and Love waves from an explosion in prestressed source regions

1995

International Journal of Rock Mechanics and Mining Sciences &am

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Expressions and synthetics for Rayleigh and Love waves generated by theoretical tectonic release models are presented. The multipole formulas are given in terms of the strengths and time functions of the source potentials. This form of the Rayleigh and Love wave expressions is convenient for separating the contribution to the Rayleigh wave due to the compressional and shear-wave source radiation and the contribution of the upgoing and downgoing source radiation for both Rayleigh and Love waves. Because of the ease of using different compression and shear-wave source time functions, these formulas are especially suited for sources for which second-and higher-order moment tensors are needed to describe the source, such as the initial value cavity release problem.A frequently used model of tectonic release is a double couple superimposed on an explosion. Eventually, we will compare synthetics of this and more realistic models in order to determine for what dimensions of the tectonic release model this assumption is valid and whether the Rayleigh wave is most sensitive to the compressional or shear-wave source history. The pure shear cavity release model is a double couple with separate P-and S-wave source histories. The time scales are proportional to the source region's dimension and differ by their respective body-wave velocities. Thus, a convenient way to model the effect of differing shot point velocities and source dimensions is to run a suite of doublecouple source history calculations for the P-and SV-wave sources separately and then sum the different combinations.One of the more interesting results from this analysis is that the well-known effect of vanishing Rayleigh-wave amplitude as a vertical or horizontal dip-slip double-couple model approaches the free surface is due to the destructive interference between the P-and SV-wave generated Rayleigh waves. The individual Rayleigh-wave amplitudes, unlike the SH-generated Love waves, are comparable in size to those from other double-couple orientations. This has important implications to the modeling of Rayleigh waves from shallow dipslip fault models. Also, the P-wave radiation from double-couple sources is a more efficient generator of Rayleigh waves than the associated SV wave or the P wave from explosions. The latter is probably due to the vertical radiation pattern or amplitude variation over the wave front. This effect should be similar to that of the interaction of wave-front curvature with the free surface.

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“…Using the estimated source function, it is possible to infer the dislocation mechanisms of the crack that generates the MS energy. This technique has been routinely implemented by geophysicists to invert seismic source functions using seismograms ͑e.g., Stump and Johnson, 1977͒ and by researchers in nondestructive testing ͑e.g., Michaels et al, 1981͒ and fracture mechanics ͑e.g., Scruby et al, 1985;Kim and Sachse, 1986͒ to determine the fracture mechanisms of cracks in solids.…”

Section: Introductionmentioning

confidence: 99%

Microseismic source deconvolution: Wiener filter versus minimax, Fourier versus wavelets, and linear versus nonlinear

Ching

Glaser

2004

The Journal of the Acoustical Society of America

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Deconvolution is commonly performed on microseismic signals to determine the time history of a dislocation source, usually modeled as combinations of forces or couples. This paper presents a new deconvolution method that uses a nonlinear thresholding estimator, which is based on the minimax framework and operates in the wavelet domain. Experiments were performed on a steel plate using artificially generated microseismic signals, which were recorded by high-fidelity displacement sensors at various locations. The source functions were deconvolved from the recorded signals by Wiener filters and the new method. Results were compared and show that the new method outperforms the other methods in terms of reducing noise while keeping the sharp features of the source functions. Other advantages of the nonlinear thresholding estimator include ͑1͒ its performance is close to that of a minimax estimator, ͑2͒ it is nonlinear and takes advantage of sparse representations under wavelet bases, and ͑3͒ its computation is faster than the fast Fourier transform.

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The Effect of Green’s Functions on the Determination of Source Mechanisms by the Linear Inversion of Seismograms

Cited by 64 publications

References 11 publications

Source Mechanisms of Induced Earthquakes at The Geysers Geothermal Reservoir

Source Mechanisms of Induced Earthquakes at The Geysers Geothermal Reservoir

Theoretical Rayleigh and Love waves from an explosion in prestressed source regions

Microseismic source deconvolution: Wiener filter versus minimax, Fourier versus wavelets, and linear versus nonlinear

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