Accuracy of the moment-tensor inversion of far-field P waves

SUMMARY The far-field assumption is widely used and suitable for the moment-tensor inversion in which the source–receiver distance is quite long. However, the description of far field is uncertain and an explicit far-field range is missing. In this study, the explicit far-field range is determined and the errors of moment-tensor solutions produced by the far-field approximation are analysed. The distance, for which the far-field assumption is satisfied and the effect of the near-field term can be ignored, is directionally dependent. For the shear dislocation, in the directions near the nodal lines of the far-field P waves, the far-field distance is heavily dependent on the displacement component used to invert moment tensors. The radial component of displacement, which is parallel to the wave propagation direction, is recommended for the inversion and the corresponding far-field distance is quite short. In the directions far from the nodal lines, the selection of displacement components has little influence on the far-field distance. The maximum far-field distance appears in the directions of the pressure and tensile axes of the source and the value is about 30 wavelengths of radiated waves. Using more receivers (>6) in the moment-tensor inversion can shorten the far-field distance. The effect of the near-field term on the moment-tensor inversion for tensile dislocations and isotropic sources (explosion or implosion) can be ignored. The conclusions obtained in this study are helpful for determining the positions of receivers and evaluating the accuracy of moment-tensor solutions, with far-field assumption being applied in the inversion.

Download Full-text

Full-waveform based complete moment tensor inversion and source parameter estimation from downhole microseismic data for hydrofracture monitoring

Geophysics ◽

10.1190/geo2011-0027.1 ◽

2011 ◽

Vol 76 (6) ◽

pp. WC103-WC116 ◽

Cited By ~ 72

Author(s):

Fuxian Song ◽

M. Nafi Toksöz

Keyword(s):

Hydraulic Fracturing ◽

Moment Tensor ◽

Fracture Plane ◽

Far Field ◽

Field Range ◽

Full Waveform ◽

Microseismic Data ◽

Fracturing Process ◽

The Moment ◽

Additional Constraints

Downhole microseismic monitoring is a valuable tool in understanding the efficacy of hydraulic fracturing. Inverting for the moment tensor has gained increasing popularity in recent years as a way to understand the fracturing process. Previous studies utilize only part of the information in the waveforms, such as direct P- and S-wave amplitudes, and make far-field assumptions to determine the source mechanisms. The method is hindered in downhole monitoring, when only limited azimuthal coverage is available. In this study, we develop an approach to invert for complete moment tensor using full-waveform data recorded at a vertical borehole. We use the discrete wavenumber integration method to calculate full wavefields in the layered medium. By using synthetic data, we find that, at the near-field range, a stable, complete moment tensor can be retrieved by matching the waveforms without additional constraints. At the far-field range, we discover that the off-plane moment tensor component is poorly constrained by waveforms recorded at one well. Therefore, additional constraints must be introduced to retrieve the complete moment tensor. We study the inversion with three different types of constraints. For each constraint, we investigate the influence of velocity model errors, event mislocations, and data noise on the extracted source parameters by a Monte Carlo study. We test our method using a single well microseismic data set obtained during the hydraulic fracturing of the Bonner sands in East Texas. By imposing constraints on the fracture strike and dip range, we are able to retrieve the complete moment tensor for events in the far-field. Field results suggest that most events have a dominant double-couple component. The results also indicate the existence of a volumetric component in the moment tensor. The derived fracture plane orientation generally agrees with that derived from the multiple event location.

Download Full-text

Seismic Moment Tensor Solutions from GeoNet Data to Provide a Moment Magnitude Scale for New Zealand

10.26686/wgtn.16947268.v1 ◽

2021 ◽

Author(s):

◽

Elizabeth de Joux Robertson

Keyword(s):

New Zealand ◽

Seismic Moment ◽

Moment Tensor ◽

Velocity Model ◽

Moment Tensor Inversion ◽

Moment Magnitude ◽

Seismic Moment Tensor ◽

Waveform Data ◽

Moment Tensors ◽

The Moment

The aim of this project is to enable accurate earthquake magnitudes (moment magnitude, MW) to be calculated routinely and in near real-time for New Zealand earthquakes. This would be done by inversion of waveform data to obtain seismic moment tensors. Seismic moment tensors also provide information on fault-type. I use a well-established seismic moment tensor inversion method, the Time-Domain [seismic] Moment Tensor Inversion algorithm (TDMT_INVC) and apply it to GeoNet broadband waveform data to generate moment tensor solutions for New Zealand earthquakes. Some modifications to this software were made. A velocity model can now be automatically used to calculate Green's functions without having a pseudolayer boundary at the source depth. Green's functions can be calculated for multiple depths in a single step, and data are detrended and a suitable data window is selected. The seismic moment tensor solution that has either the maximum variance reduction or the maximum double-couple component is automatically selected for each depth. Seismic moment tensors were calculated for 24 New Zealand earthquakes from 2000 to 2005. The Global CMT project has calculated CMT solutions for 22 of these, and the Global CMT project solutions are compared to the solutions obtained in this project to test the accuracy of the solutions obtained using the TDMT_INVC code. The moment magnitude values are close to the Global CMT values for all earthquakes. The focal mechanisms could only be determined for a few of the earthquakes studied. The value of the moment magnitude appears to be less sensitive to the velocity model and earthquake location (epicentre and depth) than the focal mechanism. Distinguishing legitimate seismic signal from background seismic noise is likely to be the biggest problem in routine inversions.

Download Full-text

Strain microseismics: Radiation patterns, synthetics, and moment tensor resolvability with distributed acoustic sensing in isotropic media

Geophysics ◽

10.1190/geo2019-0373.1 ◽

2020 ◽

Vol 85 (3) ◽

pp. KS101-KS114

Author(s):

Ismael Vera Rodriguez ◽

Andreas Wuestefeld

Keyword(s):

Moment Tensor ◽

Near Field ◽

Gauge Length ◽

P Wave ◽

Far Field ◽

S Wave ◽

Acoustic Sensing ◽

Moment Tensors ◽

Isotropic Media ◽

Distributed Acoustic Sensing

We have derived analytical formulations for the strain field produced by a moment tensor source in homogeneous isotropic media. Such formulations are important for microseismic projects that increasingly are monitored with fiber-optic distributed acoustic sensing (DAS) systems. We find that the spatial derivative of displacement produces new terms in strain proportional to [Formula: see text] with [Formula: see text]. In viscoelastic media, the derivative also produces an additional far-field term that is scaled by a frequency-dependent factor. When comparing with full wavefield synthetic data, we observe that the new terms proportional to [Formula: see text] can be considered part of a near-field in strain, similar to the practice with the displacement formulation. Analyses of moment tensor resolvability show that full moment tensors are resolvable with P-wave information from two or more noncoplanar vertical DAS cable geometries if intermediate- and far-field terms are considered and that S-wave information alone cannot constrain full moment tensors using only vertical wells. These results mirror previous observations made with displacement measurements. Furthermore, the addition of the new terms proportional to [Formula: see text] in strain improves the moment tensor resolvability but only in the case of a single vertical array. In the case of a single deviated/horizontal well, we can, in theory, resolve a full moment tensor but a case-by-case analysis is necessary to identify regions of full constraint around the well and the necessary noise conditions to guarantee reliable solutions. Real DAS measurements also are affected by the gauge length and interrogator details. In the case of the gauge length, we observe that this operator does not change the resolvability of the problem but it does affect inversion stability. The results derived here represent theoretical limits or in some cases specific examples. Practical implementations require analyses of conditioning, noise, coupling, and the effect of gauge length on a case-by-case basis.

Download Full-text

Seismic Moment Tensor Solutions from GeoNet Data to Provide a Moment Magnitude Scale for New Zealand

10.26686/wgtn.16947268 ◽

2021 ◽

Author(s):

◽

Elizabeth de Joux Robertson

Keyword(s):

New Zealand ◽

Seismic Moment ◽

Moment Tensor ◽

Velocity Model ◽

Moment Tensor Inversion ◽

Moment Magnitude ◽

Seismic Moment Tensor ◽

Waveform Data ◽

Moment Tensors ◽

The Moment

Download Full-text

How to Assess the Moment Tensor Inversion Resolution for Mining Induced Seismicity: A Case Study for the Rudna Mine, Poland

Frontiers in Earth Science ◽

10.3389/feart.2021.671207 ◽

2021 ◽

Vol 9 ◽

Author(s):

Alicja Caputa ◽

Łukasz Rudziński ◽

Simone Cesca

Keyword(s):

Moment Tensor ◽

Waveform Inversion ◽

Moment Tensor Inversion ◽

Seismic Network ◽

P Wave ◽

Induced Earthquakes ◽

Mining Operations ◽

Moment Tensors ◽

The Moment ◽

Inversion Techniques

Underground exploitation of georesources can be highly correlated with induced seismic activity. In order to reduce the risk and improve the mining operations safety, the mining activity is monitored by a dedicated seismic network. Moment tensor inversion is a powerful method to investigate the rupture process of earthquakes in mines, providing information on the geometry of the earthquake source and the moment release. Different approaches have been proposed to estimate the source mechanisms, with some advantages and limitations. One of the simplest and most used methods rely on the fit of the polarity and amplitude of first P wave onsets. More advanced techniques fit the full waveforms and their spectra. Here, we test and compare moment tensor and focal mechanism estimations for both inversion techniques. In order to assess the inversion resolution, we built realistic synthetic data, accounting for real seismic noise conditions and network geometry for the Rudna copper mine, SW Poland. The Rudna mine pertains to the Legnica-Glógow Copper District, where thousands of mining induced earthquakes are detected yearly, representing a serious hazard for miners and mining infrastructures. We simulate a range of different processes and locations, considering pure double couple, deviatoric and full moment tensors with different magnitudes and located in different mining panels. Results show that the P-wave first onset inversion is very sensitive to the geometry of the seismic network, which is limited by the existing underground infrastructure. On the other hand, the quality of the moment tensor solutions for the full waveform inversion is mainly determined by the strength of mining tremor and the signal-to-noize ratio. We discuss the performance of both inversion techniques and provide recommendations toward a reliable moment tensor analysis in mines.

Download Full-text

The waveform inversion of mainshock and aftershock data of the 2006 M6.3 Yogyakarta earthquake

Geoscience Letters ◽

10.1186/s40562-021-00176-w ◽

2021 ◽

Vol 8 (1) ◽

Author(s):

Hijrah Saputra ◽

Wahyudi Wahyudi ◽

Iman Suardi ◽

Ade Anggraini ◽

Wiwit Suryanto

Keyword(s):

Joint Inversion ◽

Body Wave ◽

Moment Tensor ◽

Near Field ◽

Source Parameters ◽

Waveform Inversion ◽

Moment Tensor Inversion ◽

Slip Distribution ◽

Aftershock Distribution ◽

Velocity Models

AbstractThis study comprehensively investigates the source mechanisms associated with the mainshock and aftershocks of the Mw = 6.3 Yogyakarta earthquake which occurred on May 27, 2006. The process involved using moment tensor inversion to determine the fault plane parameters and joint inversion which were further applied to understand the spatial and temporal slip distributions during the earthquake. Moreover, coseismal slip distribution was overlaid with the relocated aftershock distribution to determine the stress field variations around the tectonic area. Meanwhile, the moment tensor inversion made use of near-field data and its Green’s function was calculated using the extended reflectivity method while the joint inversion used near-field and teleseismic body wave data which were computed using the Kikuchi and Kanamori methods. These data were filtered through a trial-and-error method using a bandpass filter with frequency pairs and velocity models from several previous studies. Furthermore, the Akaike Bayesian Information Criterion (ABIC) method was applied to obtain more stable inversion results and different fault types were discovered. Strike–slip and dip-normal were recorded for the mainshock and similar types were recorded for the 8th aftershock while the 9th and 16th June were strike slips. However, the fault slip distribution from the joint inversion showed two asperities. The maximum slip was 0.78 m with the first asperity observed at 10 km south/north of the mainshock hypocenter. The source parameters discovered include total seismic moment M0 = 0.4311E + 19 (Nm) or Mw = 6.4 with a depth of 12 km and a duration of 28 s. The slip distribution overlaid with the aftershock distribution showed the tendency of the aftershock to occur around the asperities zone while a normal oblique focus mechanism was found using the joint inversion.

Download Full-text

Toward real-time estimation of regional moment tensors

Bulletin of the Seismological Society of America ◽

10.1785/bssa0860051255 ◽

1996 ◽

Vol 86 (5) ◽

pp. 1255-1269 ◽

Cited By ~ 6

Author(s):

Michael E. Pasyanos ◽

Douglas S. Dreger ◽

Barbara Romanowicz

Keyword(s):

Moment Tensor ◽

Time Estimation ◽

Computer Data ◽

Moment Tensors ◽

Central California ◽

Tensor Methods ◽

Real Time Estimation ◽

The Moment ◽

Computer Data Processing ◽

Data Processing Methods

Abstract Recent advances in broadband station coverage, continuous telemetry systems, moment-tensor procedures, and computer data-processing methods have given us the opportunity to automate the two regional moment-tensor methods employed at the UC Berkeley Seismographic Station for events in northern and central California. Preliminary solutions are available within minutes after an event has occurred and are subsequently human reviewed. We compare the solutions of the two methods to each other, as well as the automatic and revised solutions of each individual method. Efforts are being made to establish robust criteria for determining accurate solutions with human review and to fully automate the moment-tensor procedures into the already-existing automated earthquake-location system.

Download Full-text

A teleseismic body-wave analysis of the May 1980 Mammoth Lakes, California, earthquakes

Bulletin of the Seismological Society of America ◽

10.1785/bssa0730020419 ◽

1983 ◽

Vol 73 (2) ◽

pp. 419-434

Author(s):

Jeffery S. Barker ◽

Charles A. Langston

Keyword(s):

Body Wave ◽

Moment Tensor ◽

Normal Fault ◽

Strike Slip ◽

Body Waves ◽

P Wave ◽

Moment Tensors ◽

Double Couple ◽

The Moment ◽

Mammoth Lakes

abstract Teleseismic P-wave first motions for the M ≧ 6 earthquakes near Mammoth Lakes, California, are inconsistent with the vertical strike-slip mechanisms determined from local and regional P-wave first motions. Combining these data sets allows three possible mechanisms: a north-striking, east-dipping strike-slip fault; a NE-striking oblique fault; and a NNW-striking normal fault. Inversion of long-period teleseismic P and SH waves for the events of 25 May 1980 (1633 UTC) and 27 May 1980 (1450 UTC) yields moment tensors with large non-double-couple components. The moment tensor for the first event may be decomposed into a major double couple with strike = 18°, dip = 61°, and rake = −15°, and a minor double couple with strike = 303°, dip = 43°, and rake = 224°. A similar decomposition for the last event yields strike = 25°, dip = 65°, rake = −6°, and strike = 312°, dip = 37°, and rake = 232°. Although the inversions were performed on only a few teleseismic body waves, the radiation patterns of the moment tensors are consistent with most of the P-wave first motion polarities at local, regional, and teleseismic distances. The stress axes inferred from the moment tensors are consistent with N65°E extension determined by geodetic measurements by Savage et al. (1981). Seismic moments computed from the moment tensors are 1.87 × 1025 dyne-cm for the 25 May 1980 (1633 UTC) event and 1.03 × 1025 dyne-cm for the 27 May 1980 (1450 UTC) event. The non-double-couple aspect of the moment tensors and the inability to obtain a convergent solution for the 25 May 1980 (1944 UTC) event may indicate that the assumptions of a point source and plane-layered structure implicit in the moment tensor inversion are not entirely valid for the Mammoth Lakes earthquakes.

Download Full-text

The Global Centroid Moment Tensor Catalog: Heterogeneities and improvements

10.5194/egusphere-egu21-3038 ◽

2021 ◽

Author(s):

Álvaro González

Keyword(s):

Subduction Zones ◽

Moment Tensor ◽

Statistical Seismology ◽

Centroid Moment Tensor ◽

Moment Tensors ◽

Global Database ◽

Intermediate Period ◽

Data Compilation ◽

Forecast Models ◽

The Moment

Statistical seismology relies on earthquake catalogs as homogeneous and complete as possible. However, heterogeneities in earthquake data compilation and reporting are common and frequently are not adverted.The Global Centroid Moment Tensor Catalog (www.globalcmt.org) is considered as the most homogeneous global database for large and moderate earthquakes occurred since 1976, and it has been used for developing and testing global and regional forecast models.Changes in the method used for calculating the moment tensors (along with improvements in global seismological monitoring) define four eras in the catalog (1976, 1977-1985, 1986-2003 and 2004-present). Improvements are particularly stark since 2004, when intermediate-period surface waves started to be used for calculating the centroid solutions.Fixed centroid depths, used when the solution for a free depth did not converge, have followed diverse criteria, depending on the era. Depth had to be fixed mainly for shallow earthquakes, so this issue is more common, e.g. in the shallow parts of subduction zones than in the deep ones. Until 2003, 53% of the centroids had depths calculated as a free parameter, compared to 78% since 2004.Rake values have not been calculated homogenously either. Until 2003, the vertical-dip-slip components of the moment tensor were assumed as null when they could not be constrained by the inversion (for 3.3% of the earthquakes). This caused an excess of pure focal mechanisms: rakes of -90&#176; (normal), 0&#176; or &#177;180&#176; (strike-slip) or +90&#176; (thrust). Even disregarding such events, rake histograms until 2003 and since 2004 are not equivalent to each other.The magnitude of completeness (Mc) of the catalog is analyzed here separately for each era. It clearly improved along time (average Mc values being ~6.4 in 1976, ~5.7 in 1977-1985, ~5.4 in 1986-2003, and ~5.0 since 2004). Maps of Mc for different eras show significant spatial variations.

Download Full-text

Moving from 1-D to 3-D velocity model: automated waveform-based earthquake moment tensor inversion in the Los Angeles region

Geophysical Journal International ◽

10.1093/gji/ggz435 ◽

2019 ◽

Vol 220 (1) ◽

pp. 218-234 ◽

Cited By ~ 4

Author(s):

Xin Wang ◽

Zhongwen Zhan

Keyword(s):

Los Angeles ◽

Moment Tensor ◽

Velocity Model ◽

Primary Control ◽

Lateral Velocity ◽

Real Time System ◽

Moment Tensors ◽

Velocity Models ◽

Double Couple ◽

The Moment

SUMMARY Earthquake focal mechanisms put primary control on the distribution of ground motion, and also bear on the stress state of the crust. Most routine focal mechanism catalogues still use 1-D velocity models in inversions, which may introduce large uncertainties in regions with strong lateral velocity heterogeneities. In this study, we develop an automated waveform-based inversion approach to determine the moment tensors of small-to-medium-sized earthquakes using 3-D velocity models. We apply our approach in the Los Angeles region to produce a new moment tensor catalogue with a completeness of ML ≥ 3.5. The inversions using the Southern California Earthquake Center Community Velocity Model (3D CVM-S4.26) significantly reduces the moment tensor uncertainties, mainly owing to the accuracy of the 3-D velocity model in predicting both the phases and the amplitudes of the observed seismograms. By comparing the full moment tensor solutions obtained using 1-D and 3-D velocity models, we show that the percentages of non-double-couple components decrease dramatically with the usage of 3-D velocity model, suggesting that large fractions of non-double-couple components from 1-D inversions are artifacts caused by unmodelled 3-D velocity structures. The new catalogue also features more accurate focal depths and moment magnitudes. Our highly accurate, efficient and automatic inversion approach can be expanded in other regions, and can be easily implemented in near real-time system.

Download Full-text