Defining the scalar moment of a seismic source with a general moment tensor

1999 ◽  
Vol 89 (5) ◽  
pp. 1390-1394 ◽  
Author(s):  
David Bowers ◽  
John A. Hudson
Keyword(s):  
Seismic Moment ◽  
Moment Tensor ◽  
Seismic Source ◽  
Second Order ◽  
Seismic Moment Tensor ◽  
Total Moment ◽  
Double Couple ◽  
The Moment ◽  
Deviatoric Part ◽  
Scalar Moment

Abstract We compare several published definitions of the scalar moment M0, a measure of the size of a seismic disturbance derived from the second-order seismic moment tensor M (with eigenvalues m1 ≥ m3 ≥ m2). While arbitrary, a useful definition is in terms of a total moment, MT0 = MI + MD, where MI = |M|, with M = (m1 + m2 + m3)/3, is the isotropic moment, and MD = max(|mj − M|; j = 1, 2, 3), is the deviatoric moment. This definition is consistent with other definitions of M0 if M is a double couple. This definition also gives physically appealing and simple results for the explosion and crack sources. Furthermore, our definitions of MT0, MI and MD are in accord with the parameterization of the moment tensor into a deviatoric part (represented by T which lies in [−1,1]) and a volumetric part (represented by k which lies in [−1, 1]) proposed by Hudson et al. (1989).

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.

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 Generalized orthonormal moment tensor decomposition and its source-type diagram

2020 ◽  
Author(s):  
Ting-Chung Huang ◽  
Yih-Min Wu
Keyword(s):  
Seismic Moment ◽  
Decomposition Method ◽  
Moment Tensor ◽  
Tensor Decomposition ◽  
New Method ◽  
Seismic Moment Tensor ◽  
Linear Vector ◽  
Source Type ◽  
Sign Problem ◽  
Double Couple

Abstract Moment tensor decomposition is a method for deriving the isotropic (ISO), double-couple (DC), and compensated linear vector dipole (CLVD) components from a seismic moment tensor. Currently, there are two families of methods, namely, standard moment tensor decomposition and Euclidean moment tensor decomposition. Although both methods can usually provide workable solutions, there are some minor inconsistencies between the two methods: an equality inconsistency that occurs in standard moment tensor decomposition and the pure CLVD unity and flip basis inconsistency encountered in Euclidean moment tensor decomposition. Moreover, there is a sign problem when disentangling the CLVD component from a DC-dominated case. To address these minor inconsistencies, we propose a new moment tensor decomposition method inspired by both previous methods. The new method can not only avoid all these minor inconsistencies but also withstand deviations in ISO- or CLVD-dominated cases when using source-type diagrams.

A Discussion on the measurement and interpretation of changes of strain in the Earth - Derivation of source parameters from low-frequency spectra

1973 ◽  
Vol 274 (1239) ◽  
pp. 369-371 ◽  
Keyword(s):  
Focal Mechanism ◽  
Moment Tensor ◽  
Source Parameters ◽  
Low Frequency ◽  
Frequency Spectra ◽  
Isotropic Part ◽  
The Earth ◽  
Double Couple ◽  
The Moment ◽  
Deviatoric Part

By recording several components of tilt, strain and acceleration at one location, one can determine the focal mechanism, or moment tensor, of an earthquake. Alternatively, recordings made at several locations can be used. The moment tensor can be decomposed into its isotropic part and its deviatoric part. When the eigerrvalues of the deviator are in the sequence (— 1, 0, 1) the equivalent double couple can be found.

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

&lt;p&gt;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.&lt;/p&gt;&lt;p&gt;With this hypothesis, we analyze the micro-earthquakes (M &lt;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&lt;sub&gt;max&lt;/sub&gt;) 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.&lt;/p&gt;

Can plasticity explain microseismic source mechanisms?

2021 ◽  
Author(s):  
Viktoriya Yarushina ◽  
Alexander Minakov
Keyword(s):  
Seismic Moment ◽  
Field Experiments ◽  
Moment Tensor ◽  
Failure Process ◽  
Source Mechanism ◽  
Published Data ◽  
Seismic Moment Tensor ◽  
Special Cases ◽  
Source Mechanisms ◽  
The Moment

&lt;p&gt;The microseismic events can often be characterized by a complex non-double couple source mechanism. Recent laboratory studies recording the acoustic emission during rock deformation help connecting the components of the seismic moment tensor with the failure process. In this complementary contribution, we offer a mathematical model which can clarify these connections. We derive the seismic moment tensor based on classical continuum mechanics and plasticity theory. The moment tensor density can be represented by the product of elastic stiffness tensor and the plastic strain tensor. This representation of seismic sources has several useful properties: i) it accounts for incipient faulting as a microseismicity source mechanism, ii) it does not require a pre-defined fracture geometry, iii) it accounts for both shear and volumetric source mechanisms, iv) it is valid for general heterogeneous and anisotropic rocks, and v) it is consistent with elasto-plastic geomechanical simulators. We illustrate the new approach using 2D numerical examples of seismicity associated with cylindrical openings, analogous to wellbore, tunnel or fluid-rich conduit, and provide a simple analytic expression of the moment density tensor. We compare our simulation results with previously published data from laboratory and field experiments. &amp;#160;We consider three special cases corresponding to &quot;dry&quot; isotropic rocks, &quot;dry&quot; transversely isotropic rocks and &quot;wet&quot; isotropic rocks. The model highlights theoretical links between stress state, geomechanical parameters and conventional representations of the moment tensor such as Hudson source type parameters.&amp;#160;&lt;/p&gt;

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.

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