Estimation of seismic source parameters in 3D elastic media using the reciprocity theorem

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. R963-R976
Author(s):  
Petr V. Petrov ◽  
Gregory A. Newman
Keyword(s):  
Heterogeneous Media ◽  
Source Parameters ◽  
Synthetic Data ◽  
Seismic Source ◽  
Optimization Methods ◽  
Geothermal Field ◽  
Second Order ◽  
Order Moment ◽  
Elastic Media ◽  
Moment Tensors

We have developed a novel method based upon reciprocity principles to simultaneously estimate the location of a seismic event and its source mechanism in 3D heterogeneous media. The method finds double-couple (DC) and non-DC mechanisms of microearthquakes arising from localized induced and natural seismicity. Because the method uses an exhaustive search of the 3D elastic media, it is globally convergent. It does not suffer from local minima realization observed with local optimization methods, including Newton, Gauss-Newton, or gradient-descent algorithms. The computational efficiency of our scheme is derived from the reciprocity principle, in which the number of 3D model realizations corresponds to the number of measurement receivers. The 3D forward modeling is carried out in the damped Fourier domain with a 3D finite-difference frequency-domain fourth- and second-order code developed to simulate elastic waves generated by seismic sources defined by forces and second-order moment density tensors. We evaluate the results of testing this new methodology on synthetic data for the Raft River geothermal field, Idaho, as well as determine its applicability in designing optimal borehole monitoring arrays in a fracking experiment at the Homestake Mine, South Dakota. We also find that the method proposed here can retrieve the moment tensors of the space distributed source with data arising from spatially restricted arrays with limited aperture. The effects of uncertainties on the source parameter estimation are also examined with respect to data noise and model uncertainty.

A Student’s Guide to and Review of Moment Tensors

1989 ◽  
Vol 60 (2) ◽  
pp. 37-57 ◽  
Author(s):  
M. L. Jost ◽  
R. B. Herrmann
Keyword(s):  
Point Source ◽  
Moment Tensor ◽  
Tensor Decomposition ◽  
Seismic Source ◽  
Order Moment ◽  
Review Of Literature ◽  
Moment Tensors ◽  
Numerical Examples ◽  
Testing Algorithms ◽  
The Moment

Abstract A review of a moment tensor for describing a general seismic point source is presented to show a second order moment tensor can be related to simpler seismic source descriptions such as centers of expansion and double couples. A review of literature is followed by detailed algebraic expansions of the moment tensor into isotropic and deviatoric components. Specific numerical examples are provided in the appendices for use in testing algorithms for moment tensor decomposition.

scholarly journals Coda-wave decorrelation sensitivity kernels in 2-D elastic media: a numerical approach

2020 ◽  
Vol 223 (2) ◽  
pp. 934-943
Author(s):  
Alejandro Duran ◽  
Thomas Planès ◽  
Anne Obermann
Keyword(s):  
Analytical Solution ◽  
Numerical Simulations ◽  
Heterogeneous Media ◽  
Synthetic Data ◽  
Numerical Approach ◽  
Coda Waves ◽  
Coda Wave ◽  
Elastic Media ◽  
S Wave ◽  
Velocity Changes

SUMMARY Probabilistic sensitivity kernels based on the analytical solution of the diffusion and radiative transfer equations have been used to locate tiny changes detected in late arriving coda waves. These analytical kernels accurately describe the sensitivity of coda waves towards velocity changes located at a large distance from the sensors in the acoustic diffusive regime. They are also valid to describe the acoustic waveform distortions (decorrelations) induced by isotropically scattering perturbations. However, in elastic media, there is no analytical solution that describes the complex propagation of wave energy, including mode conversions, polarizations, etc. Here, we derive sensitivity kernels using numerical simulations of wave propagation in heterogeneous media in the acoustic and elastic regimes. We decompose the wavefield into P- and S-wave components at the perturbation location in order to construct separate P to P, S to S, P to S and S to P scattering sensitivity kernels. This allows us to describe the influence of P- and S-wave scattering perturbations separately. We test our approach using acoustic and elastic numerical simulations where localized scattering perturbations are introduced. We validate the numerical sensitivity kernels by comparing them with analytical kernel predictions and with measurements of coda decorrelations on the synthetic data.

Seismic Source Processes of 25 Earthquakes (Mw>5) in the Gulf of California

2022 ◽  
Author(s):  
Eduardo Huesca-Pérez ◽  
Edahí Gutierrez-Reyes ◽  
Luis Quintanar
Keyword(s):  
Gulf Of California ◽  
Moment Tensor ◽  
Source Parameters ◽  
Seismic Source ◽  
Focal Mechanisms ◽  
Process Models ◽  
Moment Tensors ◽  
Time Space ◽  
Double Couple ◽  
Broadband Seismograms

ABSTRACT The Gulf of California (GoC) is a complex tectonic boundary that has been instrumented in the past several decades to record broadband seismograms. This volume of data has allowed us to study several source parameters systematically. Before, only a few source parameters of earthquakes greater than magnitude five had been studied in the GoC area. We re-examined the focal mechanisms of several earthquakes in the southern GoC that occurred over the last 20 yr using local–regional distance broadband seismograms. These focal mechanisms were then used as input data to retrieve the time–space history of the rupture for each earthquake. This work contributes to the study of 25 rupture-process models computed with the method proposed by Yagi et al. (1999). To investigate more about the nature of the seismicity in the GoC, we also calculated the non-double-couple component of moment tensors for 45 earthquakes. Previous studies (e.g., Ortega et al., 2013, 2016) have shown that non-double-couple components from moment tensors in this region are associated with complex faulting, suggesting that oblique faults or several parallel faults are interacting simultaneously. Our results show that, at least for moderate earthquakes (5 < M < 6), rupture processes in the GoC show a complex interaction between fault systems. It is revealed on the important contribution of non-double-couple component obtained in the full moment tensor analysis.

scholarly journals Focal mechanism of seismic events with a dipolar component

1995 ◽  
Vol 38 (3-4) ◽  
Author(s):  
F. Batini ◽  
M. Caputo ◽  
R. Console
Keyword(s):  
Synthetic Data ◽  
High Standard ◽  
Seismic Source ◽  
Real Data ◽  
Computer Code ◽  
Geothermal Field ◽  
Observation Data ◽  
Amplitude Data ◽  
Double Couple ◽  
Fault Mechanism

In this paper we model the geometry of a seismic source as a dislocation occurring on an elemental flat fault in an arbitrary direction with respect to the fault plane. This implies the use of a fourth parameter in addition to the three usual ones describing a simple double couple mechanism. We applied the radiation pattern obtained from the theory to a computer code written for the inversion of the observation data (amplitudes and polarities of the first onsets recorded by a network of stations). It allows the determination of the fault mechanism gener- alized in the above mentioned way. The computer code was verified on synthetic data and then applied to real data recorded by the seismic network operated by the Ente Nazionale per l'Energia Elettrica (ENEL), monitoring the geothermal field of Larderello. The experimental data show that for some events the source mechanism exhibits a significant dipolar component. However, due to the high standard deviation of the amplitude data, F-test applied to the results of the analysis shows that only for two events the confidence level for the general- ized model exceeds 90%.

Second-order moment tensors of microearthquakes at The Geysers geothermal field, California

1988 ◽  
Vol 78 (5) ◽  
pp. 1674-1692
Author(s):  
Daniel R. H. O'Connell ◽  
Lane R. Johnson
Keyword(s):  
Moment Tensor ◽  
Geothermal Field ◽  
Strike Slip ◽  
P Wave ◽  
Order Moment ◽  
Principal Moment ◽  
Moment Tensors ◽  
First Motion ◽  
The Geysers ◽  
Using Data

Abstract The Geysers geothermal field is the site of intense microseismicity which appears to be associated with steam production. It seems that focal mechanisms of earthquakes at The Geysers vary systematically with depth, but P-wave first-motion focal mechanism studies have been hampered by inadequate resolution. In this study an unconstrained frequency domain moment tensor inversion method is used to over come P-wave first-motion focal sphere distribution problems and to investigate microearthquake source properties. A goal was to investigate the feasibility of using waveforms to invert for the second-order moment tensor of microearthquakes in the complex setting of The Geysers. Derived frequency-domain moment tensors for two earthquakes were verified by mechanisms estimated from P-wave first motions and required far fewer stations. For one event, 19 P-wave first motions were insufficient to distinguish between normal-slip and strike-slip focal mechanisms, but a well-constrained strike-slip solution was obtained from the waveform principal moment inversion using data from six stations. Improved waveform focal mechanism resolution was a direct consequence of using P- and S-wave data together in a progressive velocity-hypocenter inversion to minimize Green function errors. The effects of hypocenter mislocation and velocity model Green function errors on moment tensor estimates were investigated. Synthetic tests indicate that these errors can introduce spurious isotropic and compensated linear vector dipole components as large as 26 per cent for these events, whereas principal moment orientations errors were <8°. In spite of unfavorable recording geometries and large (0.6 km) station elevation differences, the results indicate that waveform moment tensor estimates for microearthquake sources can be robust and constrain source mechanisms using data from a relatively small number of stations.

scholarly journals Method for Measuring the Second-Order Moment of Atmospheric Turbulence

Atmosphere ◽  
2021 ◽  
Vol 12 (5) ◽  
pp. 564
Author(s):  
Hong Shen ◽  
Longkun Yu ◽  
Xu Jing ◽  
Fengfu Tan
Keyword(s):  
Atmospheric Turbulence ◽  
Weighting Function ◽  
Structure Constant ◽  
Turbulence Models ◽  
Second Order ◽  
Index Structure ◽  
Order Moment ◽  
Site Testing ◽  
Optical Effects ◽  
Novel Method

The turbulence moment of order m (μm) is defined as the refractive index structure constant Cn2 integrated over the whole path z with path-weighting function zm. Optical effects of atmospheric turbulence are directly related to turbulence moments. To evaluate the optical effects of atmospheric turbulence, it is necessary to measure the turbulence moment. It is well known that zero-order moments of turbulence (μ0) and five-thirds-order moments of turbulence (μ5/3), which correspond to the seeing and the isoplanatic angles, respectively, have been monitored as routine parameters in astronomical site testing. However, the direct measurement of second-order moments of turbulence (μ2) of the whole layer atmosphere has not been reported. Using a star as the light source, it has been found that μ2 can be measured through the covariance of the irradiance in two receiver apertures with suitable aperture size and aperture separation. Numerical results show that the theoretical error of this novel method is negligible in all the typical turbulence models. This method enabled us to monitor μ2 as a routine parameter in astronomical site testing, which is helpful to understand the characteristics of atmospheric turbulence better combined with μ0 and μ5/3.

A second-order moment method applied to gas-solid risers

AIChE Journal ◽  
2012 ◽  
Vol 58 (12) ◽  
pp. 3653-3675 ◽  
Author(s):  
Juhui Chen ◽  
Shuyan Wang ◽  
Dan Sun ◽  
Huilin Lu ◽  
Dimitri Gidaspow ◽  
...  
Keyword(s):  
Moment Method ◽  
Second Order ◽  
Order Moment

scholarly journals Fully probabilistic seismic source inversion – Part 1: Efficient parameterisation

2013 ◽  
Vol 5 (2) ◽  
pp. 1125-1162 ◽  
Author(s):  
S. C. Stähler ◽  
K. Sigloch
Keyword(s):  
Moment Tensor ◽  
Source Parameters ◽  
Practical Importance ◽  
Principal Component ◽  
Seismic Source ◽  
Empirical Orthogonal Functions ◽  
Time Function ◽  
Source Inversion ◽  
Source Time Function ◽  
Earthquake Parameters

Abstract. Seismic source inversion is a non-linear problem in seismology where not just the earthquake parameters themselves, but also estimates of their uncertainties are of great practical importance. Probabilistic source inversion (Bayesian inference) is very adapted to this challenge, provided that the parameter space can be chosen small enough to make Bayesian sampling computationally feasible. We propose a framework for PRobabilistic Inference of Source Mechanisms (PRISM) that parameterises and samples earthquake depth, moment tensor, and source time function efficiently by using information from previous non-Bayesian inversions. The source time function is expressed as a weighted sum of a small number of empirical orthogonal functions, which were derived from a catalogue of >1000 STFs by a principal component analysis. We use a likelihood model based on the cross-correlation misfit between observed and predicted waveforms. The resulting ensemble of solutions provides full uncertainty and covariance information for the source parameters, and permits to propagate these source uncertainties into travel time estimates used for seismic tomography. The computational effort is such that routine, global estimation of earthquake mechanisms and source time functions from teleseismic broadband waveforms is feasible.

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