Moment Tensor Elements Research Articles

Impact of 3-D Earth structure on W-phase CMT parameters

SUMMARYWe investigate the impact of unmodelled 3-D structural heterogeneity on inverted W-phase source parameters. We generate a large data set of synthetic seismograms accounting for the Earths 3-D structure for 250 earthquakes globally distributed. The W-phase algorithm is then used to invert for earthquake CMT parameters, assuming a spherical Earth model. The impact of lateral heterogeneity is assessed by comparing inverted source parameters with those used to compute the 3-D synthetics. Results show that the 3-D structure mainly affects centroid location while the effect on the other source parameters remains small. Centroid mislocations present clear geographical patterns. In particular, W-phase solutions for earthquakes in South America are on average biased 17 km to the east of the actual centroid locations. This effect is significantly reduced using an azimuthally well balanced distribution of seismological stations. Source parameters are generally more impacted by mantle heterogeneity while the scalar moment of shallow earthquakes seems to be mainly impacted by the crustal structure. Shallow earthquakes present a variability of Mrθ and Mrϕ moment tensor elements, resulting both from the small amplitude and a larger uncertainty of the associated Green’s functions.

Rock Damage and Seismic Radiation: A Case Study of the Chemical Explosions in New Hampshire

Research Article| October 30, 2018 Rock Damage and Seismic Radiation: A Case Study of the Chemical Explosions in New Hampshire Anastasia Stroujkova Anastasia Stroujkova aWeston Geophysical Corp., 181 Bedford Street, Suite 1, Lexington, Massachusetts 02420, ana@westongeo.com Search for other works by this author on: GSW Google Scholar Bulletin of the Seismological Society of America (2018) 108 (6): 3598–3611. https://doi.org/10.1785/0120180117 Article history first online: 30 Oct 2018 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation Anastasia Stroujkova; Rock Damage and Seismic Radiation: A Case Study of the Chemical Explosions in New Hampshire. Bulletin of the Seismological Society of America 2018;; 108 (6): 3598–3611. doi: https://doi.org/10.1785/0120180117 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyBulletin of the Seismological Society of America Search Advanced Search Abstract The effect of the medium damage on seismic waves generated by underground chemical explosions in hard rock is investigated. An explosion experiment conducted in New Hampshire in 2016 has demonstrated that the amount of explosive gas products released in the cavity improves seismic coupling, which is manifested in higher seismic amplitudes. It has also shown that detonating explosions in water‐filled boreholes has similar effects on the spectra as increasing the amount of the gaseous detonation products by changing the explosive type. A postexplosion well logging survey revealed that using explosives releasing higher amount of gaseous products results in an increase in length and aperture of the explosion generated macrofractures. Placing the charges into water‐filled rather than drained boreholes results in a similar increase in fracture dimensions. Thus, the extent and intensity of postexplosion macrofracturing correlates with improved seismic coupling expressed as P and Rg amplitude increase, particularly in the low‐frequency range.The radiation patterns of the P waves are different for the waveforms bandpassed in a low‐frequency range (1–15 Hz) and a high‐frequency range (15–100 Hz). The symmetry of the radiation patterns indicates the presence of nonzero terms associated with the off‐diagonal moment tensor terms (⁠Mxz and Myz⁠). The amplitude of the seismic component attributed to the off‐diagonal moment tensor elements is significant and can be as large as 15%–16% of the isotropic moment. The observed P‐wave radiation pattern is consistent with either sliding along the pre‐existing fractures and zones of weakness or shear failure along the high‐angle borehole parallel fractures during the explosions. You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

The February 2014 Cephalonia Earthquake (Greece): 3D Deformation Field and Source Modeling from Multiple SAR Techniques

Online Material: Tables of moment tensor elements; SAR image pairs and coseismic displacement gradients; figures of InSAR data, model parameter tradeoffs, and observed and modeled displacements. On 26 January 2014 at 13:55 UTC, an M w 6.0 earthquake struck the island of Cephalonia, Greece, followed five hours later by an M w 5.3 aftershock and by an M w 5.9 event on 3 February 2014 at 03:08 UTC (National Observatory of Athens, Institute of Geodynamics [NOA‐GI]). The epicenter of the M w 6.0 event was relocated 2 km east of the town of Lixouri, and that of the M w 5.9 event at the tip of the Gulf of Argostoli, in the northern part of the Paliki peninsula (Fig. 1; Karastathis et al. , 2014; Papadopoulos et al. , 2014). Extensive structural damage and widespread environmental effects were induced throughout the Paliki peninsula and along the eastern coast of the Gulf of Argostoli (Valkaniotis et al. , 2014). Quays, sidewalks, and piers were damaged in the waterfront areas of the towns of Lixouri and Argostoli, the island capital, and liquefactions, road failures, rock falls, and small landslides were observed. Most of the latter effects took place in the aftermath of the 26 January 2014 event and were reactivated one week later by the 3 February earthquake. Figure 1. Location map showing the tectonic context of the Aegean Sea and the main faults on the island of Cephalonia. Colored rectangles and magenta triangles indicate the Synthetic Aperture Radar (SAR) frame coverage and the continuous Global Positioning System (cGPS) stations, respectively. Yellow stars indicate the relocated epicenters of the three largest events of the 2014 sequence (Karastathis et al. , 2014). Diverging and converging arrows in the top‐right map indicate approximate horizontal projections of the P axis (compression) and T axis (extension), respectively, based on figure 5b in …

New Regional Moment Tensors in South Africa

Regional moment tensors (RMTs) provide important information for seismotectonic and hazard studies in regions with low to moderate seismicity, where infrequent earthquakes of Mw ≥ ∼4.0–4.5 occur that are too small for global momenttensor techniques. Moment-tensor analysis involves fitting theoretical waveforms with observed broadband waveforms and inverting for the moment-tensor elements ( e.g. , Aki and Richards 1980; Jost and Herrmann 1989). One powerful tool to calculate RMTs is the time domain surface wave waveform inversion code TDMT_INVC (Dreger and Helmberger 1993; Pasyanos et al. 1996; Dreger 2003). In recent years RMTs have been routinely calculated with this software in many parts of the world such as western Canada (Ristau et al. 2003, 2007), California (Dreger and Helmberger 1993; Romanowicz et al. 1993; Pasyanos et al. 1996), Alaska (Ratchkovski and Hansen 2002), Japan (Kubo et al. 2002), Taiwan (Kao et al. 1998), the European–Mediterranean region (Bernardi et al. 2004), and New Zealand (Ristau 2008). Only a few moment tensors/focal mechanisms are available for South Africa. This is due to moderate tectonic and deep mine-related seismicity, as well as, until recently, a sparse distribution of broadband seismometers in the South African National Seismograph Network (SANSN) (Saunders et al. 2008). A unique opportunity presented itself when the dense, very broadband Incorporated Research Institutions in Seismology (IRIS) PASSCAL Kaapvaal craton array was deployed in South Africa ( e.g. , Nguuri et al. 2001). From this array we identified three near regional Mw ∼4.0 earthquakes with suitable waveform data to calculate RMTs with the TDMT_INVC software. Our goal is to determine the moment magnitude, earthquake mechanism, and focal depth in order to 1) make progress in resolving the difference between local and moment magnitudes routinely determined with the SANSN; and 2) expand our understanding of the regional …

A note on the surface volume change of shallow earthquakes

This note presents an exact analytical formula for determining the magnitude of coseismic surface volume change (δV) of earthquake faults in a half-space. For a Poisson solid, the formula is remarkably simple; δV=Mzz|8µ, where Mzz is one of the moment tensor elements of the source. Maximum δV values derive from dip slip on faults plunging 45°. For these events, surface volume changes of 0.0001 and 4.3 km3 can be expected for magnitude 5 and 8 earthquakes respectively. All of the coseismic surface volume change is recovered in the interseismic period through relaxation of the Earth and rebound of the surface. A useful rule of thumb for estimating the magnitude of vertical rebound in 45° dip slip events is δhp=Δs/24, where Δs is the coseismic slip on the fault.

Effects of three-dimensional Earth structure on CMT earthquake parameters

We investigate errors in centroid earthquake parameters due to unmodeled structural heterogeneity. We generate a simulated dataset consisting of synthetic seismograms for 50 earthquakes and 150 stations distributed globally. To generate the synthetic seismograms we use a spectral-element wave-propagation package (SPECFEM3D_GLOBE) that accounts for the Earth’s three-dimensional structure. An established centroid–moment-tensor inversion algorithm from the Global CMT project is used to invert the synthetic dataset, with and without added noise, for earthquake source parameters. This algorithm uses a one-dimensional earth structure, together with approximate corrections for three-dimensional structure, to model the seismograms. We interpret the differences between the estimated source parameters and the parameters used to compute the synthetic dataset as errors due to unmodeled structural heterogeneity and the presence of noise. We expect that the errors obtained in this study are representative of the errors in the Global CMT catalogue. We find that the errors in scalar moment, moment-tensor elements and location are small on average. The depth and centroid time are, however, biased by a small amount. We find that the error in depth can be reduced significantly by applying corrections for the difference in the velocity structure at the source and receiver locations from the Earth’s average structure in the CMT inversions. This modification has a minimal effect on the errors in centroid time. We do not find large errors in scalar moments, even where the crustal thickness at the source is very different from the Earth’s average crustal thickness.

Estimation of inner-core rotation rate by using the Earth’s free oscillation

We estimate a rate of inner-core differential rotation from time variations of splitting functions of seven core modes of the Earth’s free oscillations excited by eight large earthquakes in a period of 1994–2003. The splitting functions and moment tensor elements are simultaneously determined for each core mode by a spectral fitting technique. The estimated moment tensor well agrees with Harvard CMT solution. The splitting functions are corrected for the effect of mantle heterogeneity using a 3D mantle velocity model. Inner-core rotation angle about the Earth’s spin axis is determined for each core mode as a function of event year by comparison of the corrected and reference splitting functions. Mean rotation rate of six core modes is estimated at 0.03±0.18° per year westward, and this value is insignificantly different from zero. Therefore, the inner core is not rotating at a significant rate relatively to the crust and mantle.

울진지진(2004/05/29)의 지진원 특성에 관한 연구

The seismic source parameters of the Uljin earthquake on 29 May 2004, including focal depth, focal mechanism, magnitude, and moment tensor elements for source characteristics, are analysed using moment tensor seismic source inversion. The Green‘s function for 3 crust models representing the southern Korean Peninsula are used. Also 3 kinds of epicenters are used to find optimum solution for seismic source parameters. Results show that seismic source parameters have a little dependency of azimuthal distribution and epicentral distances of seismic stations. Final results show that the event, considering 6 moment tensor elements, is caused by the typical reverse fault with nearly NS strike. The focal mechanism implies that the tectonic force around epicenter area currently has compressive environment, with nearly EW principal axis. The focal depth is estimated to be about 12km. The resultant focal mechanism show fairly good agreement to those of other studies. However, focal depth is much different from that of other studies.

Strain Green's Tensors, Reciprocity, and Their Applications to Seismic Source and Structure Studies

Green's function approach is widely used in modeling seismic wave- form. The representation theorem expresses the wave field as the inner product of the moment tensor and the spatial gradients of the Green's tensor. Standard practice in waveform calculations has been to compute the Green's tensors first and then obtain their gradients by numerical differentiation. The reciprocity of the Green's tensor enables us to express the wave field explicitly in terms of the strain Green's tensor, a third-order tensor composed of the spatial gradients of the Green's tensor elements. We propose here to use the strain Green's tensors rather than the Green's tensors themselves in computing the waveforms. By bypassing the need for Green's tensors and directly using the strain Green's tensors, we can improve the computa- tional efficiency in waveform modeling while eliminating the possible errors from numerical differentiation. The strain Green's tensor elements are also directly related to the partial derivatives of the waveforms with respect to moment tensor elements and structural parameters. Through the inversion of the focal mechanisms of 27 small events in the Los Angeles region, we demonstrate the effectiveness of the strain Green's tensor database approach in quickly recovering source parameters based on realistic 3D models. We show that the same database can also be used to improve the efficiency and accuracy in computing the Frechet kernels for tomography inver- sions.

Current deformation of the Himalaya–Tibet–Burma seismic belt: inferences from seismic activity and strain rate analysis

A new measure of seismic activity in a region is defined, which is based on the concept of integrated fault surface area of earthquakes in the region. Using this concept, we analyze the Harvard CMT data of the Himalaya–Tibet–Burma seismic belt to estimate the relative proportions of seismic activity corresponding to reverse, strike-slip and normal faulting in the region. Further, strain rates are computed through summation of moment tensor elements of earthquakes. The study indicates that the deformation patterns of the Himalaya and the adjoining Tibetan plateau regions are distinct. For instance, the seismic activity of the reverse fault category changes from 93% in the Himalaya to a mere 2% in Tibet, which is dominated instead, by strike-slip faulting (59%). Strain rate computation indicates predominant crustal thickening in the Himalaya with a clear transition to crustal thinning in the Tibetan plateau region, just across the Indus-Tsangpo suture zone where EW extension is the predominant mechanism. A model of a thinning seismic upper crust in the EW direction decoupled from a thickening aseismic lower crust, both in equilibrium, in the Tibetan plateau, is proposed. In the Burmese arc region, crustal thickening is indicated, but coupled with NS compression. The observed seismic activity is predominantly of the strike-slip type (56%), uncharacteristic of subduction zones, which generally display up to 75% of seismic activity of the reverse fault category. This has implications for Indian plate motion along the Burmese arc, rather than in the direction of the subducted slab.

Scattering of spherical elastic waves from a small-volume spherical inclusion

SUMMARY A theory is presented for the scattering of spherical elastic waves by a small, spherical inclusion. The domain of validity of the treatment is ka′« 1, where k is the wavenumber and a′ is the radius of the spherical inclusion. The treatment is an extension of that of Gritto, Korneev & Johnson (1995), who derived exact expressions for the scattered wavefield from a plane P wave incident on a spherical inclusion in the low-frequency limit. Since neither treatment assumes small perturbations, they are also valid for an arbitrary material property contrast between the spherical inclusion and the background medium. For spherical elastic wavefields propagating through an infinite, homogeneous medium and interacting with a single small, spherical inclusion, the scattered wavefield is obtained directly as a sum of spheroidal motions of degrees 0, 1 and 2 in scatterer-centred coordinates, with nine independent amplitude coefficients which depend on the contrast in material properties and are proportional to the volume of the inclusion. If the inclusion is embedded in a stratified and bounded medium, then these scattering coefficients provide a valid local description of the scattered wavefield in the vicinity of the inclusion. Exploiting this fact, source equivalents in the frequency domain (six moment tensor elements and three single forces) are derived from the scattering coefficients. To first order in material property contrasts, equivalence is established between these source equivalents and the coupled mode theory developed for surface waves and long-period body waves using perturbation theory.

The determination of the best fitting and the extreme source models by a global inversion method

In this paper, a global inversion method is developed for seismic moment tensor inversion by using the body wave forms. The algorithm depends on neither the selection of starting model nor the forms of objective function and constraints. When the error function, measure of the difference between the observed and synthetic waveforms, is chosen as the objective function, the best fitting source model is found; when a certain combination in seismic moment tensor elements is selected as the objective function and the values of error function are constrained in a suitable bound, the extreme source models can be produced by minimizing or maximizing this combination. By changing the form of the combination of moment tensor elements, a variety of different source characteristics can be considered. Therefore the extreme solution provides an estimation of the uncertainty in the best fitting source model. The seismic waveform data was used to evaluate the effectiveness of this algorithm.

Determination of earthquake source parameters using a hybrid global search algorithm

AbstractA hybrid global optimization algorithm using a combination of simulated annealing and downhill simplex methods is used to invert teleseismic body waves for earthquake source parameters. Time-domain constraints on the source-time function, inversion for double-couple parameters rather than moment tensor elements, and consideration of multiple sources lead to a nonlinear and multimodal problem, in which the objective function contains many local minima. Traditional approaches that linearize the problem and use iterative least squares are dependent on the starting model and the order in which multiple sources are processed, and can converge to a local minimum. Also, grid searches are impractical for the number of parameters we treat simultaneously. The hybrid global method provides an attractive alternative because it converges to the global minimum of a prescribed objective function and can be used to invert for multiple sources simultaneously. Model parameter constraints are easy to incorporate into the global search process, if they are desired.A multiple point-source parameterization of the 1992 Landers, California, earthquake is used as an example of the inversion method. Rupture in this earthquake occurred along three main fault segments: the Johnson Valley fault, the Homestead fault, and the Emerson/Rock Creek faults. We invert for the strike, dip, and rake of each source, the time separation of the sources, and the farfield source-time function of each source. Parameters obtained from the inversion are consistent with field observations and the results of other investigations. Strikes vary consistently with the trend of the surface ruptures. The dip is near 90° along the entire length of the rupture, and the rake is nearly pure right-lateral strike slip. The estimated moment is 7.6 × 1026 dyne-cm. The continuity of the moment release across the junction of the Homestead and Emerson faults suggests that these two faults may be more continuous at depth than at the surface. Moment release in the transition from the Johnson Valley to the Homestead faults is complex, indicating a complicated time history of faulting and a less direct relationship between the primary mapped faults.

A procedure for obtaining the complete horizontal motions within zones of distributed deformation from the inversion of strain rate data

We present a new method for obtaining relative horizontal motions on the surface of a sphere from strain rate data. Strain rates can be obtained from the summation of earthquake moment tensors or from estimates of Quaternary rates of deformation on major faults. The method is particularly useful for determining the kinematics within zones of distributed continental deformation, or any region where there is distributed strain. All relative motions, including rotation rates about the vertical axis, are uniquely determined when the three rates of horizontal strain are everywhere defined within the region of interest. The forward problem is set up such that all relative velocities on the surface of the sphere are defined by , where is the three‐dimensional rotation vector that describes the velocities uθ and uϕ at all points on the surface of Earth of radius r with position unit radial vectors . The three‐dimensional rotation vector is expressed as an infinite power series expansion, truncated at finite order N‐1. Coefficients of this polynomial are sought in a damped least squares inversion such that the strain rates , which define all of the coefficients in the power series expansion of , are optimally matched by the smooth polynomial function. Formal uncertainties are introduced that take into account observational error as well as the inability of the polynomial function to accommodate the more rapid spatial variations of the rate‐of‐strain field. We demonstrate the method on a deforming part of Asia. Strain rates for the region were obtained from the summation of moment tensor elements of moderate and large‐sized earthquakes in this century. Solutions, both velocity fields and rotation rates, are investigated as a function of polynomial smoothing and polynomial order. We demonstrate that the velocity field, obtained by the polynomial fitting of the regions where strain rates were averaged, is by nature extremely robust and is almost independent of the amount of polynomial smoothing. The rotation rate field on the other hand shows the same order of smoothing as the polynomials used in the fitting procedure.

Inversion of regional surface-wave spectra for source parameters of aftershocks from the Loma Prieta earthquake

Abstract Surface waves recorded at regional distances are used to study the source parameters for three of the larger aftershocks of the 18 October 1989, Loma Prieta, California, earthquake. The short-period P-wave first-motion focal mechanisms indicate a complex aftershock sequence with a wide variety of mechanisms. Many of these events are too small for teleseismic body-wave analysis; therefore, the regional surface-waves provide important long-period information on the source parameters. Intermediate-period Rayleigh- and Love-wave spectra are inverted for the seismic moment tensor elements at a fixed depth and repeated for different depths to find the source depth that gives the best fit to the observed spectra. For the aftershock on 19 October at 10:14:35 (md = 4.2), we find a strike-slip focal mechanism with right lateral motion on a NW-trending vertical fault consistent with the mapped trace of the local faults. For the aftershock on 18 October at 10:22:04 (md = 4.4), the surface waves indicate a pure reverse fault with the nodal planes striking WNW. For the aftershock on 19 October at 09:53:50 (md = 4.4), the surface waves indicate a strike-slip focal mechanism with a NW-trending vertical nodal plane consistent with the local strike of the San Andreas fault. Differences between the surface-wave focal mechanisms and the short-period P-wave first-motion mechanisms are observed for the aftershocks analyzed. This discrepancy may reflect the real variations due to differences in the band width of the two observations. However, the differences may also be due to (1) errors in the first-motion mechanism due to incorrect near-source velocity structure and (2) errors in the surface-wave mechanisms due to inadequate propagation path corrections.

Source models of the Harzer explosion from regional observations of fundamental-mode and higher mode surface waves.

Abstract For shallow source depths, the moment-tensor elements with isotropic radiation patterns, M zz and M xx + M yy , are not resolvable in moment-tensor inversions of long-period surface-wave data because their respective Green9s functions have similar frequency dependence. Examination of Green9s functions at higher frequencies shows that, while resolution for some momenttensor elements improves, it is still not possible to resolve the isotropic-radiating moments from fundamental-mode data recorded at regional distances. On the other hand, the addition of higher mode Rayleigh-wave amplitudes can improve the resolution of these moments significantly, since there are appreciable differences between the higher mode Green9s functions. An extension of Romanowicz9s algorithm is presented to invert fundamental-mode and higher mode data for the second-order moment tensor. A source of “noise” in the estimation of the moment tensor for underground explosions is the spallation of geologic strata at ground zero, since this too can be a significant source of higher modes. The inversion proposed in this paper accounts for possible higher mode excitation due to spall using the source model of Day et al . The inversion is applied to regional recordings of the Harzer explosion of 6 June 1981 at the Nevada Test Site. The results of the inversion demonstrate a trade-off between the second-order moment tensor representation and the single, directed force used to represent spall. Observations and numerical simulations of spall provide estimates of spall source parameters, which in turn constrain the moment-tensor representation of Harzer. The results of this study demonstrate the clear need for observations to characterize the spall source associated with underground explosions. Furthermore, they demonstrate the potential benefit of using higher modes to refine estimates of the explosion moment with reduced uncertainties compared to moment determinations from fundamental-mode data alone.

A tensile — shear crack model for the mechanism of volcanic earthquakes

Temporary seismic observations were carried out for about 1 month at Miyakejima Island on the Izu-Bonin arc after an eruption on October 3, 1983. More than 3000 seismic events were observed and they are classified into 4 different categories: short-period earthquakes, long-period earthquakes, isolated tremors and continuous tremors. Two active source regions of the short-period earthquakes were located along the old caldera rim of the Miyakejima volcano. One region was very close to the eruptive fissures. Another was about 1–2 km northwest of the fissures. Almost all the earthquakes in the former region showed dilatant first motions of P-waves at all the stations in the island. On the other hand, almost all events in the latter region showed compressive first motions of P-waves at all the stations. The first motions of P-waves for these earthquakes cannot be explained by the quadrant-type pattern due to a double-couple force system. Nucleation of a tensile crack coupled with a shear crack (a tensile-shear crack model) is proposed as a source mechanism of the short-period earthquakes. Moment tensor elements of tensile and shear cracks have been determined by the least squares method using observed P- and S-wave data. Results suggest that tensile cracking (opening or closing) is dominant for generating those earthquakes in comparison with shear cracking. The strikes of the tensile cracks for the earthquakes are shown to be nearly parallel to the strike of the fissures. The earthquakes that occurred in the northwestern region of the fissures are considered to be generated by a sudden opening of tensile-shear cracks due to the excess pressure of intrusive magma. In contrast, the earthquakes occurring beneath the fissures are probably generated by a sudden closing of tensile-shear cracks, and this suggests that the magmatic pressure under the fissures rapidly decreased after the eruption. Moment tensor analysis of the tensile-shear crack model in this study demonstrates the non double-couple source mechanism for volcanic earthquakes related to magmatic activity.

Mathematical representation and physical interpretation of a contained chemical explosion in alluvium

Abstract The characterization of the equivalent elastic source for a small (253 lb TNT) chemical explosion detonated in alluvium is given. The representation is constrained by a well-known propagation path. Data from the nonlinear region ( 1/3 ) are used in interpreting the moment tensor representation. The results of this study are: (1) the applicability of frequency domain moment tensor representation is shown; (2) the source is composed of two parts—the initially spherical explosion followed by the cylindrically symmetric spall; and (3) the deviatoric source components are an order of magnitude smaller than the spherical explosion and cylindrical spall contributions. The spherical explosion is shorter in duration (50 to 80 msec) than the spall source (200 msec), which is delayed in time. The initial explosion can be modeled by the isotropic moment tensor while the spall source is represented as the moment tensor elements with the ratio: M 11 = 1; M 22 = 1; and M 33 = 2. Comparison of these results with those from nuclear explosions suggests that similar phenomena occur in these cases also.

Estimation of earthquake source parameters by the inversion of waveform data: Global seismicity, 1981-1983

Abstract A waveform inversion algorithm, based on optimal filter theory, has been applied to the P waves from 260 of the largest earthquakes occurring during the years 1981 through 1983. Estimates of average focal depth, scalar moment, and deviatoric source mechanism have been obtained. For all except the largest events (M0 > 1027 dyne-cm), the scalar moments obtained in this study are close to, but somewhat larger than, the Harvard centroid-moment tensor (CMT) scalar moments. The CMT estimates of scalar moment are probably biased to low values due to the way unmodeled lateral heterogeneity affects the fitting procedure. For the largest events, however, source complexity can bias the scalar moments determined in this study to lower values, and the CMT scalar moments are probably more accurate. The moment tensor, CMT, and U.S. Geological Survey first-motion source mechanisms have been objectively compared by computing the locations of the vector representations of the mechanisms on the unit sphere. We find that the similarities and differences between these mechanisms can be related to the uncertainties inherent in each method for certain types of earthquakes: (1) lack of constraint on one of the nodal planes for dip-slip type mechanisms from first-motion analysis; (2) lack of resolution of the moment tensor elements defining the dip-slip component of faulting for shallow-focus earthquakes in the CMT method; and (3) lack of resolution of the moment tensor elements defining the strike-slip component of faulting in the P-wave inversion method used here. Thus, on the average, the first-motion and CMT methods yield the more reliable mechanisms for strike-slip-type earthquakes, and the method used in this study gives a more reliable result for shallow-focus earthquakes with dip-slip-type mechanisms. Finally, both of the moment tensor methods should yield reliable solutions for intermediate- and deep-focus earthquakes.

Application of waveform modeling to determine focal mechanisms of four 1982 Miramichi aftershocks

The objective of this study is to determine the focal mechanisms of small earthquakes at very near epicentral distances and use them to predict the observed waveforms. To achieve our objectives, the following steps were adopted before attempting to match the entire waveform: (a) obtain an appropriate velocity model; (b) calculate the Green's functions and predict ground motions due to an earthquake specified by dip (δ), slip (λ), and strike ( ϕ ) of a fault; (c) select all mechanisms which satisfy the first-motion polarity at all stations; (d) select a subset of focal mechanisms from those obtained in step (c) which produce P and S amplitudes and P/SV and SV/SH amplitude ratios correctly; and (e) use focal mechanisms of step (d) to match waveforms. As an alternative approach, a least-squares inversion for the moment-tensor elements was performed and decomposition of moment tensor matrix to two double couples (major and minor) was performed. Green's functions were computed using the Cagniard-de-Hoop theory (Helmberger and Harkrider, 1978). We applied the above approaches to four aftershocks ( mbLg ≦ 3.5) of the New Brunswick earthquake of 9 January 1982 and succeeded in obtaining focal mechanisms and producing synthetic waveforms very similar to the observed waveforms. Two groups of focal mechanisms are found. Two of the earthquakes are found to have reverse fault geometry similar to that of the main event of 9 January 1982 ( mb = 5.7), while the other two have significant components of strike-slip motion on a dipping plane. The results obtained from the least-squares analysis support the results of the search method. The fault geometries determined by the search method correspond well to the results of the major double couple of the least-square inversion. For completeness of the source characteristics investigation, spectral analysis of the seismograms was performed to determine the source parameters: corner frequencies, fc , seismic moments, source dimensions, and stress drops.