A Student’s Guide to Point Sources in Homogeneous Media

1990 ◽  
Vol 61 (3-4) ◽  
pp. 209-224 ◽  
Author(s):  
Jose Pujol ◽  
R. B. Herrmann
Keyword(s):  
Body Force ◽  
Moment Tensor ◽  
Point Sources ◽  
S Wave ◽  
Elastic Wave Equation ◽  
Moment Tensors ◽  
Lower Hemisphere ◽  
Double Couple ◽  
Source Studies ◽  
Homogeneous Media

Abstract The analysis of point sources in homogeneous media is presented in an introductory but rigorous manner. Stokes solution to the elastic wave equation with a concentrated body force is extended to include couples and moment tensor sources. The single couple and the double couple without moment are discussed in detail because of their importance in earthquake source studies. To simplify the treatment, the transformation properties of tensors under rotations are used throughout. This guide is intended to complement that written by Jost and Herrmann (1989) on moment tensors. A FORTRAN 77 program is provided to plot P, SV, SH radiation patterns as well as S-wave polarizations on a lower hemisphere focal sphere for an arbitrary symmetric moment tensor.

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 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.

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.

Analysis of non-double-couple source mechanisms in an area of induced seismicity, West Texas (USA).

2021 ◽  
Author(s):  
Savvaidis Alexandros ◽  
Roselli Pamela
Keyword(s):  
Stress Field ◽  
Time Domain ◽  
Seismic Moment ◽  
Moment Tensor ◽  
P Wave ◽  
Seismic Moment Tensor ◽  
Ground Displacement ◽  
Moment Tensors ◽  
West Texas ◽  
Double Couple

<p>In the scope to investigate the possible interactions between injected fluids, subsurface geology, stress field and triggering earthquakes, we investigate seismic source parameters related to the seismicity in West Texas (USA). The analysis of seismic moment tensor is an excellent tool to understand earthquake source process kinematics; moreover, changes in the fluid volume during faulting leads to existence of non-double-couple (NDC) components (Frohlich, 1994; Julian et al., 1998; Miller et al., 1998). The NDC percentage in the source constitutes the sum of absolute ISO and CLVD components so that %NDC= % ISO + %CLVD and %ISO+%CLVD+%DC=100%. It is currently known that the presence of NDC implies more complex sources (mixed shear-tensile earthquakes) correlated to fluid injections, geothermal systems and volcano-seismology where induced and triggered seismicity is observed.</p><p>With this hypothesis, we analyze the micro-earthquakes (M <2 .7) recorded by the Texas Seismological Network (TexNet) and a temporary network constituted by 40 seismic stations (equipped by either broadband or 3 component geophones). Our study area is characterized by Northwest-Southeast faults that follow the local stress/field (SH<sub>max</sub>) and the geological characteristic of the shallow basin structure of the study area. After a selection based on signal-to-noise ratio, we filter (1-50 Hz) the seismograms and estimate P-wave pulse polarities and the first P-wave ground displacement pulse in time domain. Then, we perform the full moment tensor analysis by using hybridMT technique (Andersen, 2001; Kwiatek et al., 2016) with a detailed 1D velocity model. The key parameter is the polarity/area of the first P-wave ground displacement pulse in time domain. Uncertainties of estimated moment tensors are expressed by normalized root-mean-square (RMS errors) between theoretical and estimated amplitudes (Vavricuk et al., 2014). We also evaluate the quality of the seismic moment tensors by bootstrap and resampling. In our preliminary results we obtain NDC percentage (in terms of %ISO and %CLVD components), Mw, seismic moment, P, T and B axes orientation for each source inverted.</p>

Source processes of industrially‐induced earthquakes at The Geysers geothermal area, California

Geophysics ◽  
1999 ◽  
Vol 64 (6) ◽  
pp. 1877-1889 ◽  
Author(s):  
Alwyn Ross ◽  
G. R. Foulger ◽  
Bruce R. Julian
Keyword(s):  
Geothermal Area ◽  
S Wave ◽  
Induced Earthquakes ◽  
Stress Regime ◽  
Moment Tensors ◽  
Text Structures ◽  
Double Couple ◽  
Source Mechanisms ◽  
The Geysers ◽  
Steam Production

Microearthquake activity at The Geysers geothermal area, California, mirrors the steam production rate, suggesting that the earthquakes are industrially induced. A 15-station network of digital, three‐component seismic stations was operated for one month in 1991, and 3,900 earthquakes were recorded. Highly‐accurate moment tensors were derived for 30 of the best recorded earthquakes by tracing rays through tomographically derived 3-D [Formula: see text] and [Formula: see text] structures, and inverting P- and S-wave polarities and amplitude ratios. The orientations of the P- and T-axes are very scattered, suggesting that there is no strong, systematic deviatoric stress field in the reservoir, which could explain why the earthquakes are not large. Most of the events had significant non‐double‐couple (non-DC) components in their source mechanisms with volumetric components up to ∼30% of the total moment. Explosive and implosive sources were observed in approximately equal numbers, and must be caused by cavity creation (or expansion) and collapse. It is likely that there is a causal relationship between these processes and fluid reinjection and steam withdrawal. Compensated linear vector dipole (CLVD) components were up to 100% of the deviatoric component. Combinations of opening cracks and shear faults cannot explain all the observations, and rapid fluid flow may also be involved. The pattern of non-DC failure at The Geysers contrasts with that of the Hengill‐Grensdalur area in Iceland, a largely unexploited water‐dominated field in an extensional stress regime. These differences are poorly understood but may be linked to the contrasting regional stress regimes and the industrial exploitation at The Geysers.

The Structure of Moment Tensors in Transversely Isotropic Focal Regions

2019 ◽  
Vol 109 (6) ◽  
pp. 2415-2426
Author(s):  
Çağrı Diner
Keyword(s):  
Moment Tensor ◽  
Transversely Isotropic ◽  
Geometric Interpretation ◽  
Elasticity Tensor ◽  
Point Of View ◽  
Focal Region ◽  
Moment Tensors ◽  
Double Couple ◽  
Isotropic Elasticity ◽  
The Moment

Abstract Full moment tensor inversion has become a standard method for understanding the mechanisms of earthquakes as the resolution of the inversion process increases. Thus, it is important to know the possible forms of non–double‐couple (non‐DC) moment tensors, which can be obtained because of either the different source mechanisms or the anisotropy of the focal regions. In this study, the form of the moment tensors of seismic sources occurring in transversely isotropic (TI) focal regions is obtained using the eigendecomposition of the elasticity tensor. More precisely, a moment tensor is obtained as a linear combination of the eigenspaces of TI elasticity tensor in which the coefficients of the terms are the corresponding eigenvalues multiplied with the projection of the potency tensor onto the corresponding eigenspaces. Moreover, the eigendecomposition method is also applied to obtain the three different forms of moment tensors in isotropic focal regions, in particular, for the shear source, tensile source, and for any type of potency tensor whose rank is three. This linear algebra point of view makes the structure of the moment tensors more apparent; for example, a shear source tensor is an eigenvector of isotropic elasticity tensor, and hence the resulting moment tensor is proportional to its shear source tensor. Moreover, a geometric interpretation for the scalar seismic moment, which is the norm of the moment tensor, for anisotropic focal regions is achieved through the eigendecomposition method. This method also gives a simple way to quantify the percentage of the isotropic component of the moment tensor of shear sources in TI focal regions. Hence, the complexities in the moment tensor introduced by the anisotropy of the focal region and by the source mechanism can be differentiated.

Uncertainties in Seismic Moment Tensors Inferred from Differences between Global Catalogs

2021 ◽  
Author(s):  
Boris Rösler ◽  
Seth Stein ◽  
Bruce D. Spencer
Keyword(s):  
Moment Tensor ◽  
Centroid Moment Tensor ◽  
Moment Tensors ◽  
Double Couple ◽  
Source Mechanisms ◽  
Order Of Magnitude ◽  
The Difference ◽  
The Moment ◽  
Source Geometry ◽  
Scalar Moment

Abstract Catalogs of moment tensors form the foundation for a wide variety of seismological studies. However, assessing uncertainties in the moment tensors and the quantities derived from them is difficult. To gain insight, we compare 5000 moment tensors in the U.S. Geological Survey (USGS) and the Global Centroid Moment Tensor (Global CMT) Project catalogs for November 2015–December 2020 and use the differences to illustrate the uncertainties. The differences are typically an order of magnitude larger than the reported errors, suggesting that the errors substantially underestimate the uncertainty. The catalogs are generally consistent, with intriguing differences. Global CMT generally reports larger scalar moments than USGS, with the difference decreasing with magnitude. This difference is larger than and of the opposite sign from what is expected due to the different definitions of the scalar moment. Instead, the differences are intrinsic to the tensors, presumably in part due to different phases used in the inversions. The differences in double-couple components of source mechanisms and the fault angles derived from them decrease with magnitude. Non-double-couple (NDC) components decrease somewhat with magnitude. These components are moderately correlated between catalogs, with correlations stronger for larger earthquakes. Hence, small earthquakes often show large NDC components, but many have large uncertainties and are likely to be artifacts of the inversion. Conversely, larger earthquakes are less likely to have large NDC components, but these components are typically robust between catalogs. If so, these can indicate either true deviation from a double couple or source complexity. The differences between catalogs in scalar moment, source geometry, or NDC fraction of individual earthquakes are essentially uncorrelated, suggesting that the differences reflect the inversion rather than the source process. Despite the differences in moment tensors, the location and depth of the centroids are consistent between catalogs. Our results apply to earthquakes after 2012, before which many moment tensors were common to both catalogs.

scholarly journals The Motu River earthquake of 8 March 1984

1985 ◽  
Vol 18 (1) ◽  
pp. 41-54
Author(s):  
Martin Reyners ◽  
Stuart Hodder
Keyword(s):  
Strong Ground Motion ◽  
Strong Motion ◽  
Wave Radiation ◽  
Frequency Content ◽  
S Wave ◽  
Double Couple ◽  
Source Studies ◽  
A Site ◽  
Spatial Distribution Of Intensity ◽  
Strong Ground

The Motu River earthquake of 8 March 1984 (M = 6.4) was the largest event to occur at the Hikurangi Margin of New Zealand since 1973. It originated in the upper part of the subducted Pacific plate at a depth of 73 kilometres, and appears typical of previous larger events in the region. The earthquake was widely felt, and has provided valuable data on the spatial distribution of intensity from intermediate depth events. The earthquake produced records of strong ground motion at nine sites within 152 kilometres of the epicentre, though the accelerograms of only one site were of sufficient amplitude to permit digitisation. The distribution of recorded peak accelerations correlates reasonably well with the pattern of S-wave radiation expected from a double-couple point source. A strong-motion instrument near the mouth of the Motu River recorded a relatively short-duration, moderate amplitude motion of extremely monochromatic frequency content. It is likely that a site resonance dominates the data at this location, thus severely limiting the usefulness of the accelerograms for earthquake source studies.

scholarly journals Moment tensor catalogue of microearthquakes in West Bohemia from 2008 to 2018

2021 ◽  
Author(s):  
Václav Vavryčuk ◽  
Petra Adamová ◽  
Jana Doubravová ◽  
Josef Horálek
Keyword(s):  
Seismic Anisotropy ◽  
Moment Tensor ◽  
Technical Specification ◽  
Local Stress ◽  
Velocity Model ◽  
Tectonic Stress ◽  
Moment Tensors ◽  
West Bohemia ◽  
Double Couple ◽  
Tensile Fracturing

Abstract. We present a unique catalogue of full moment tensors (MTs) of microearthquakes that occurred in West Bohemia, Czech Republic, in the period from 2008 to 2018. The catalogue is exceptional in several aspects: (1) it represents an extraordinary extensive dataset of more than 5.000 MTs, (2) it covers a long period of seismicity in the studied area, during which several prominent earthquake swarms took place, (3) the locations and retrieved MTs of microearthquakes are of a high accuracy. Additionally, we provide three-component records at the West Bohemia (WEBNET) seismic stations, the velocity model in the region, and the technical specification of the stations. The dataset is ideal for being utilized by a large community of researchers for various seismological purposes, e.g., for studies of (1) the migration of foci and the spatiotemporal evolution of seismicity, (2) redistribution of stress during periods of intense seismicity, (3) the interaction of faults, (4) the Coulomb stress along the faults and local stress anomalies connected to fault irregularities, (5) diffusivity of fluids along the activated faults, or (6) the time-dependent seismic risk due to the migration of seismicity in the region. In addition, the dataset is optimum for developing and testing new inversions for MTs and for tectonic stress. Since most of the earthquakes are non-shear, the dataset can contribute to studies of non-double-couple components of MTs and their relation to shear-tensile fracturing and/or seismic anisotropy in the focal zone.

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

Geophysics ◽  
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.

Sign in / Sign up

Export Citation Format

Share Document