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.

Toward real-time estimation of regional moment tensors

1996 ◽  
Vol 86 (5) ◽  
pp. 1255-1269 ◽  
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.

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

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.

scholarly journals Long-period mechanism of the 8 November 1980 Eureka, California, earthquake

1982 ◽  
Vol 72 (2) ◽  
pp. 439-456
Author(s):  
Thorne Lay ◽  
Jeffrey W. Given ◽  
Hiroo Kanamori
Keyword(s):  
Point Source ◽  
Seismic Moment ◽  
Moment Tensor ◽  
Strike Slip ◽  
The Body ◽  
Body Waves ◽  
Long Period ◽  
Amplitude Data ◽  
The Moment ◽  
Scalar Moment

Abstract The seismic moment and source orientation of the 8 November 1980 Eureka, California, earthquake (Ms = 7.2) are determined using long-period surface and body wave data obtained from the SRO, ASRO, and IDA networks. The favorable azimuthal distribution of the recording stations allows a well-constrained mechanism to be determined by a simultaneous moment tensor inversion of the Love and Rayleigh wave observations. The shallow depth of the event precludes determination of the full moment tensor, but constraining Mzx = Mzy = 0 and using a point source at 16-km depth gives a major double couple for period T = 256 sec with scalar moment M0 = 1.1 · 1027 dyne-cm and a left-lateral vertical strike-slip orientation trending N48.2°E. The choice of fault planes is made on the basis of the aftershock distribution. This solution is insensitive to the depth of the point source for depths less than 33 km. Using the moment tensor solution as a starting model, the Rayleigh and Love wave amplitude data alone are inverted in order to fine-tune the solution. This results in a slightly larger scalar moment of 1.28 · 1027 dyne-cm, but insignificant (<5°) changes in strike and dip. The rake is not well enough resolved to indicate significant variation from the pure strike-slip solution. Additional amplitude inversions of the surface waves at periods ranging from 75 to 512 sec yield a moment estimate of 1.3 ± 0.2 · 1027 dyne-cm, and a similar strike-slip fault orientation. The long-period P and SH waves recorded at SRO and ASRO stations are utilized to determine the seismic moment for 15- to 30-sec periods. A deconvolution algorithm developed by Kikuchi and Kanamori (1982) is used to determine the time function for the first 180 sec of the P and SH signals. The SH data are more stable and indicate a complex bilateral rupture with at least four subevents. The dominant first subevent has a moment of 6.4 · 1026 dyne-cm. Summing the moment of this and the next three subevents, all of which occur in the first 80 sec of rupture, yields a moment of 1.3 · 1027 dyne-cm. Thus, when the multiple source character of the body waves is taken into account, the seismic moment for the Eureka event throughout the period range 15 to 500 sec is 1.3 ± 0.2 · 1027 dyne-cm.

The Global Centroid Moment Tensor Catalog: Heterogeneities and improvements

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

<p>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.</p><p>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.</p><p>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.</p><p>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.</p><p>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° (normal), 0° or ±180° (strike-slip) or +90° (thrust). Even disregarding such events, rake histograms until 2003 and since 2004 are not equivalent to each other.</p><p>The magnitude of completeness (<em>M</em><sub>c</sub>) of the catalog is analyzed here separately for each era. It clearly improved along time (average <em>M</em><sub>c</sub> values being ~6.4 in 1976, ~5.7 in 1977-1985, ~5.4 in 1986-2003, and ~5.0 since 2004). Maps of <em>M</em><sub>c</sub> for different eras show significant spatial variations.</p>

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

2019 ◽  
Vol 220 (1) ◽  
pp. 218-234 ◽  
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.

A New Uniform Moment Tensor Catalog for Yunnan, China, from January 2000 through December 2014

2020 ◽  
Vol 91 (2A) ◽  
pp. 891-900
Author(s):  
Yan Xu ◽  
Keith D. Koper ◽  
Relu Burlacu ◽  
Robert B. Herrmann ◽  
Dan-Ning Li
Keyword(s):  
Stress Field ◽  
Seismic Hazard ◽  
Moment Tensor ◽  
Horizontal Stress ◽  
Strike Slip ◽  
Moment Tensors ◽  
Yunnan Region ◽  
Seismic Waveforms ◽  
The Moment ◽  
Maximum Horizontal Stress

Abstract Because of the collision of the Indian and Eurasian tectonic plates, the Yunnan Province of southwestern China has some of the highest levels of seismic hazard in the world. In such a region, a catalog of moment tensors is important for estimating seismic hazard and helping understand the regional seismotectonics. Here, we present a new uniform catalog of moment tensor solutions for the Yunnan region. Using a grid-search technique to invert seismic waveforms recorded by the permanent regional network in Yunnan and the 2 yr ChinArray deployment, we present 1833 moment tensor solutions for small-to-moderate earthquakes that occurred between January 2000 and December 2014. Moment magnitudes in the new catalog vary from Mw 2.2 to 6.1, and the catalog is complete above Mw∼3.5–3.6. The moment tensors are constrained to be purely double-couple and show a variety of faulting mechanisms. Normal faulting events are mainly concentrated in northwest Yunnan, while farther south along the Sagaing fault the earthquakes are mostly thrust and strike slip. The remaining area includes all three styles of faulting but mostly strike slip. We invert the moment tensors for the regional stress field and find a strong correlation between spatially varying maximum horizontal stress and Global Positioning System observations of horizontal ground velocity. The stress field reveals clockwise rotation around the eastern Himalayan syntaxis, with northwest–southeast compression to the east of the Red River fault changing to northeast–southwest compression west of the fault. Almost 88% of the centroid depths are shallower than 16 km, consistent with a weak and ductile lower crust.

Aftershock Analysis of the 2018 Mw 7.1 Anchorage, Alaska, Earthquake: Relocations and Regional Moment Tensors

2019 ◽  
Vol 91 (1) ◽  
pp. 114-125 ◽  
Author(s):  
Natalia A. Ruppert ◽  
Avinash Nayak ◽  
Clifford Thurber ◽  
Cole Richards
Keyword(s):  
Moment Tensor ◽  
Hanging Wall ◽  
Velocity Model ◽  
Aftershock Sequence ◽  
Fault Rupture ◽  
Moment Tensors ◽  
3D Velocity Model ◽  
The Moment ◽  
The Relationship ◽  
Alaska Earthquake

Abstract The 30 November 2018 magnitude 7.1 Anchorage earthquake occurred as a result of normal faulting within the lithosphere of subducted Yakutat slab. It was followed by a vigorous aftershock sequence with over 10,000 aftershocks reported through the end of July 2019. The Alaska Earthquake Center produced a reviewed aftershock catalog with a magnitude of completeness of 1.3. This well‐recorded dataset provides a rare opportunity to study the relationship between the aftershocks and fault rupture of a major intraslab event. We use tomoDD algorithm to relocate 2038 M≥2 aftershocks with a regional 3D velocity model. The relocated aftershocks extend over a 20 km long zone between 47 and 57 km depth and are primarily confined to a high VP/VS region. Aftershocks form two clusters, a diffuse southern cluster and a steeply west‐dipping northern cluster with a gap in between where maximum slip has been inferred. We compute moment tensors for the Mw>4 aftershocks using a cut‐and‐paste method and careful selection of regional broadband stations. The moment tensor solutions do not exhibit significant variability or systematic differences between the northern and southern clusters and, on average, agree well with the mainshock fault‐plane parameters. We propose that the mainshock rupture initiated in the Yakutat lower crust or uppermost mantle and propagated both upward into the crust to near its top and downward into the mantle. The majority of the aftershocks are confined to the seismically active Yakutat crust and located both on and in the hanging wall of the mainshock fault rupture.

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

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

<p>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.</p>

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

2019 ◽  
Vol 220 (1) ◽  
pp. 248-256 ◽  
Author(s):  
Yue Kong ◽  
Min Li ◽  
Weimin Chen ◽  
Boqi Kang
Keyword(s):  
Moment Tensor ◽  
Near Field ◽  
Radial Component ◽  
Moment Tensor Inversion ◽  
Far Field ◽  
Field Range ◽  
P Waves ◽  
Moment Tensors ◽  
Nodal Lines ◽  
The Moment

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.

Inversion of teleseismic body waves for the moment tensor of the 1978 Thessaloniki, Greece, earthquake

1981 ◽  
Vol 71 (5) ◽  
pp. 1423-1444
Author(s):  
Jeffrey S. Barker ◽  
Charles A. Langston
Keyword(s):  
Point Source ◽  
Moment Tensor ◽  
Source Parameters ◽  
Source Model ◽  
Body Waves ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Initial Rupture ◽  
Short Period ◽  
The Moment

abstract Seismograms from WWSSN and Canadian network stations were modeled to determine the source parameters of the 20 June 1978 Thessaloniki, Greece, earthquake (Ms = 6.4). The depth of the initial rupture was constrained to 11 ± 1 km by comparison of the arrival times of surface reflections with synthetic short-period seismograms. A focal sphere plot of first motion polarities provided little constraint on other focal parameters, except to indicate that predominantly normal faulting was involved. A generalized inverse technique utilizing the moment tensor formalism was applied to teleseismic P and SH waves for six increments of depth. The moment tensor obtained indicated a nearly horizontal, N-trending tension axis and a nearly vertical compression axis, and yielded the following double-couple source parameters: strike 280° ± 7°; dip 55° ± 3°; rake −65° ± 5°; seismic moment 5.7 × 1025 dyne-cm; and a skewed triangular source time function with a rise time of about 1 sec and duration of 6 to 8 sec. Due to indications of multiple or finite source effects for this event, and the assumption in the moment tensor formalism of a point source, a low-pass filter was applied to the data and the inversions were repeated. The results were nearly identical with those of the original inversion, suggesting that any individual sources had similar mechanisms, or that the point source model is sufficient for this earthquake.

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