Complete Moment Tensor Research Articles

Focal mechanism determination for microseismic events and its application to the left bank slope of the Baihetan hydropower station in China

Determination of the focal mechanism of microseismic (MS) events occurring in rock engineering plays an important role in hazard evaluation and forecasting. A complete moment tensor inversion strategy is proposed to analyse MS events recorded at the left bank slope of the Baihetan hydropower station, southwest of China. A coordinate system rotation procedure is adopted to construct a reliable 1-D velocity model for the Green’s function calculation. The layered velocities are accurately determined by inversion using the recorded blasts and geological survey results. To reduce the influence of noise contamination, only the waveforms in the frequency range of 60–150 Hz are analysed. Before moment tensor inversion, a relocation procedure using an eikonal solver is performed to accurately locate seismic sources. A robust global optimization routine is applied to maximize the objective function, thereby determining the focal mechanism. The proposed method is tested using a hypothetical seismic source in the sensor network used for monitoring MS events in the rock slope. The synthetic test shows that the method is robust and can provide accurate solutions when subject to location error, noise contamination and velocity model disturbances. The analysis results of the 12 MS events show that the moment tensors characterizing MS events present significant non-double-couple components and that the majority of the MS events have a strike orientation in accordance with that of the main staggered zones.

On the feasibility of inversion of single-well microseismic data for full moment tensor

The existing paradigm, widely accepted in the microseismic community, asserts the impossibility of unambiguous estimation of full seismic moment tensor from three-component data recorded in a single straight borehole. The statement of inversion nonuniqueness, related to the lack of illumination of the off-plane moment component in the zero solid-angle ray apertures, tacitly assumes the slowness vectors, normal to the relevant wave fronts, to be confined to the plane containing the ray trajectories. Although such arrangements of the rays and slownesses do take place for vertical wells drilled in horizontally layered isotropic and VTI (transversely isotropic with a vertical symmetry axis) formations, azimuthal anisotropy commonly expected for hydraulically fractured, hydrocarbon bearing shales makes the slowness vectors deviate from a plane, arrange themselves into nonzero solid-angle apertures, and yield theoretically unique inverse problems for seismic moment tensors. This paper examines those problems for the anisotropy parameters characterizing fractured shales and siltstones in the Bakken. Their strong azimuthal anisotropy entails not only formally unique but, importantly for practical applications, well-posed inverse problems, resulting in robust estimates of the complete moment tensors from single-borehole data.

Full-waveform based microseismic source mechanism studies in the Barnett Shale: Linking microseismicity to reservoir geomechanics

Seismic moment tensors (MTs) of microearthquakes contain important information on the reservoir and fracturing mechanisms. Difficulties arise when attempting to retrieve complete MT with conventional amplitude inversion methods if only one well is available. With the full-waveform approach, near-field information and nondirect waves (i.e., refracted/reflected waves) help stabilize the inversion and retrieve complete MT from the single-well data set. However, for events which are at far field from the monitoring well, a multiple-well data set is required. In this study, we perform the inversion with a dual-array data set from a hydrofracture stimulation in the Barnett Shale. Determining source mechanisms from the inverted MTs requires the use of a source model, which in this case is the tensile earthquake model. The source information derived includes the fault plane solution, slip direction, VP/VS ratio in the focal area and seismic moment. The primary challenge of extracting source parameters from MT is to distinguish the fracture plane from auxiliary plane. We analyze the microseismicity using geomechanical analysis to determine the fracture plane. Furthermore, we investigate the significance of non-DC components by F-test. We also study the influence of velocity model errors, event mislocations, and data noise using synthetic data. The results of source mechanism analysis are presented for the events with good signal-to-noise ratios and low condition numbers. Some events have fracture planes with similar orientations to natural fractures delineated by core analysis, suggesting reactivation of natural fractures. Other events occur as predominantly tensile events along the unperturbed maximum horizontal principal stress direction, indicating an opening mode failure on hydraulic fractures. Microseismic source mechanisms not only reveal important information about fracturing mechanisms, but also allow fracture characterization away from the wellbore, providing critical constraints for understanding fractured reservoirs.

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

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

A preliminary catalog of moment tensors for the Pyrenees

Using waveform data gathered from the different organizations that operate seismological networks in the Pyrenees, we have obtained a complete moment tensor catalog of Pyrenean earthquakes with magnitude larger than 3 covering the time period 2001–2011. Our moment tensor solutions are in good agreement with those previously reported by other institutions. We find absolutely no evidence for inverse faulting in the Pyrenees. On the opposite, almost all the events have extensional focal mechanisms, while only one event has a clear strike-slip mechanism. The T axes are consistently oriented along a NNE–SSW direction, giving further support for a currently active extensional regime of deformation in the Pyrenees. The scaling relation between moment magnitude and local magnitude has a slope close to unity. In contrast, the scaling between our moment magnitudes obtained by waveform inversion and the moment magnitudes determined by inversion of shear wave spectra from Drouet et al. (2010) has a slope of 1.31. Further work is thus required to identify the source of this discrepancy and to define a robust magnitude scale for the quantification of earthquakes in the Pyrenees.

On deformation sources in volcanic areas: Modeling the Campi Flegrei (Italy) 1982–84 unrest

Deformation sources in volcanic areas are generally modeled in terms of pressurized tri-axial ellipsoids or pressurized cracks with simple geometrical shapes, embedded in a homogeneous half-space. However, the assumption of a particular source mechanism and the neglect of medium heterogeneities bias significantly the estimate of source parameters. A more general approach describes the deformation source in terms of a suitable moment tensor. Ratios between moment tensor eigenvalues are shown to provide a strong diagnostic tool for the physical interpretation of the deformation source and medium heterogeneities may be accounted for through 3D finite element computations. Leveling and EDM data, collected during the 1982–84 unrest episode at Campi Flegrei (Italy), are employed to retrieve the complete moment tensor according to a Bayesian inversion procedure, considering the heterogeneous elastic structure of the volcanic area. Best fitting moment tensors are found to be incompatible with any pressurized ellipsoid or crack. Taking into account the deflation of a deeper magma reservoir, which accompanies the inflation of a shallower source, data fit improves considerably but the retrieved moment tensor of the shallow source is found to be incompatible with pressurized ellipsoids, still. Looking for alternative physical models of the dislocation source, we find that the best fit moment tensor can be best interpreted in terms of a mixed mode (shear and tensile) dislocation at 5.5 km depth, striking EW and dipping by ~ 25°–30° to the North. Gravity changes are found to be compatible with the intrusion of ~ 60–70 · 10 6 m 3 of volatile rich magma with density ~ 2400 kg/m 3.

The Puzzle of the 1996 Bardarbunga, Iceland, Earthquake: No Volumetric Component in the Source Mechanism

A volcanic earthquake with M w 5.6 occurred beneath the Bardarbunga caldera in Iceland on 29 September 1996. This earthquake is one of a decade-long sequence of ![Graphic][1] events at Bardarbunga with non-double-couple mechanisms in the Global Centroid Moment Tensor catalog. Fortunately, it was recorded well by the regional-scale Iceland Hotspot Project seismic experiment. We investigated the event with a complete moment tensor inversion method using regional long-period seismic waveforms and a composite structural model. The moment tensor inversion using data from stations of the Iceland Hotspot Project yields a non-double-couple solution with a 67% vertically oriented compensated linear vector dipole component, a 32% double-couple component, and a statistically insignificant (2%) volumetric (isotropic) contraction. This indicates the absence of a net volumetric component, which is puzzling in the case of a large volcanic earthquake that apparently is not explained by shear slip on a planar fault. A possible volcanic mechanism that can produce an earthquake without a volumetric component involves two offset sources with similar but opposite volume changes. We show that although such a model cannot be ruled out, the circumstances under which it could happen are rare. [1]: /embed/inline-graphic-1.gif

Identifying isotropic events using a regional moment tensor inversion

We calculate the deviatoric and isotropic source components for 17 explosions at the Nevada Test Site, as well as 12 earthquakes and 3 collapses in the surrounding region of the western United States, using a regional time domain full waveform inversion for the complete moment tensor. The events separate into specific populations according to their deviation from a pure double‐couple and ratio of isotropic to deviatoric energy. The separation allows for anomalous event identification and discrimination between explosions, earthquakes, and collapses. Confidence regions of the model parameters are estimated from the data misfit by assuming normally distributed parameter values. We investigate the sensitivity of the resolved parameters of an explosion to imperfect Earth models, inaccurate event depths, and data with low signal‐to‐noise ratio (SNR) assuming a reasonable azimuthal distribution of stations. In the band of interest (0.02–0.10 Hz) the source‐type calculated from complete moment tensor inversion is insensitive to velocity model perturbations that cause less than a half‐cycle shift (<5 s) in arrival time error if shifting of the waveforms is allowed. The explosion source‐type is insensitive to an incorrect depth assumption (for a true depth of 1 km), and the goodness of fit of the inversion result cannot be used to resolve the true depth of the explosion. Noise degrades the explosive character of the result, and a good fit and accurate result are obtained when the signal‐to‐noise ratio is greater than 5. We assess the depth and frequency dependence upon the resolved explosive moment. As the depth decreases from 1 km to 200 m, the isotropic moment is no longer accurately resolved and is in error between 50 and 200%. However, even at the most shallow depth the resultant moment tensor is dominated by the explosive component when the data have a good SNR.

A systematic study of source time functions and moment tensors of intermediate and deep earthquakes

We developed an inversion algorithm to determine the Source Time Function and Moment Tensor of intermediate and deep earthquakes from a set of teleseismic body wave records. The method proceeds in two stages. First, a nonlinear inversion by simulated annealing is performed to simultaneously (a) align the waveforms in time, (b) determine a common source time function, and (c) measure a collection of observed station amplitudes. The station amplitudes are then used, in a second stage, as secondary observables to invert for the moment tensors. We perform three different inversions to estimate the complete moment tensor solution, the pure deviatoric solution, and the double‐couple solution. All the calculations are extremely simple and, in particular, it is not necessary to compute synthetic seismograms. The method requires well‐isolated phases at different stations, which restricts its application to intermediate and deep events. The algorithm is applied to the FDSN broadband records corresponding to the period 1990–2005 of worldwide intermediate and deep seismicity (depth100 km) of magnitude greater than 6.5. The source time functions are compared to those obtained from other studies of intermediate and deep events. The moment tensors are also systematically compared to the Harvard‐CMT and USGS solutions. Both show a very good agreement with previous studies.

On the retrieval of moment tensors from borehole data

ABSTRACTThe complete moment tensors of seismic sources in homogeneous or vertically inhomogeneous isotropic structures cannot be retrieved using receivers deployed in one vertical borehole. The complete moment tensors can be retrieved from amplitudes of P‐waves, provided that receivers are deployed in at least three boreholes. Using amplitudes of P‐ and S‐waves, two boreholes are, in principle, sufficient. Similar rules also apply to transversely isotropic media with a vertical axis of symmetry.In the case of limited observations, the inversion can be stabilized by imposing the zero‐trace constraint on the moment tensors. However, this constraint is valid only if applied to observations of shear faulting on planar faults in isotropic media, which produces double‐couple mechanisms. For shear faulting on non‐planar faults, for tensile faulting, and for shear faulting in anisotropic media, the zero‐trace constraint is no longer valid and can distort the retrieved moment tensor and bias the fault‐plane solution.Numerical modelling simulating the inversion of the double‐couple mechanism from real data reveals that the errors in the double‐couple and non‐double‐couple percentages of the moment tensors rapidly decrease with increase in the number of boreholes used. For noisy P‐ and S‐wave amplitudes with noise of 15% of the top amplitude at each channel and for a velocity model biased by 10%, the errors in the double‐couple percentage attain 25, 13 and 6% when inverting for the double‐couple mechanism from one, two and three boreholes.

Complete moment tensor retrieval for weak events: application to orogenic and volcanic areas

Aiming to study the mechanism and time history of weak local events we invert the dominant part of high-frequency seismograms (S and surface waves) by using two methods which implement moment tensor description of the focus. The point-source approximation is applied since we assume that the size of the focus with respect to the minimum wavelength of the analyzed signals is relatively small. Various constraints of the moment tensor are applied to cover local events of different origin - both the tectonic earthquakes and seismic events induced by volcanic activity. In the former case the double-couple constraint is applied, in the latter one a full moment tensor is decomposed into a volumetric part (V), representing volume changes, a compensated linear vector-dipole part (CLVD), describing opening of a fluid-filled lenticular crack, and a double couple part (DC), representing a shear slip. In the full moment tensor inversion the hypocentral depth and structural model may vary within pre-defined intervals. In the orogenic area of Friuli, Northern Italy, both the method looking for a DC only and the procedure implying the complete moment tensor arrive produce a DC mechanism, the orientation of which is consistent with the polarity readings. In the volcanic area of Phlegrean Fields, Southern Italy, the possible existence of fluid motion, which can be associated to volume changes and crack openings has to be taken into account, therefore, we used only the full moment tensor description to analyze several events in the magnitude range from 1.3 to 3. The obtained source durations vary from a few tenths of a second to about two seconds, suggesting that even small events may be characterized by relatively complex rupture history, although some of the retrieved complexities may be an artifact due to lateral inhomogeneities and other unmodelled structural effects. The percentage of the V component was found to be as large as 30% here, while it was negligible in the orogenic area of Friuli. Therefore, the retrieved V component, even though partly corrupted by imprecise structural modeling, can be used to distinguish between events with and without significant volume changes in the source. This might lead to a better understanding of the source processes in volcanic areas and to the use of source properties as possible precursors of explosive eruptions.

Moment tensors of ten witwatersrand mine tremors

Ground motions, recorded both underground and on the surface in two of the South African Gold mining districts, were inverted to determine complete moment tensors for 10 mining-induced tremors in the magnitude range 1.9 to 3.3. The resulting moment tensors fall into two separate categories. Seven of the events involve substantial coseismic volumetric reduction-ΔV together with normal faulting entailing shear deformation ΣAD, where the summation is over fault planes of areaA and average slipD. For these events the ratio-ΔV/ΣAD ranges from 0.58 to 0.92, with an average value of 0.71. For the remaining three events ΔV is not significantly different from zero; these events are largely double-couple sources involving normal faulting. Surprisingly, the two types of source mechanism appear to be very distinct in that there is not a continuous distribution of the source mix from ΔV=0 to-ΔV≈ΣAD. Presumably, the coseismic closure indicates substantial interaction between a mine stope and adjacent shear failure in the surrounding rock, under the influence of an ambient stress for which the maximum principal stress is oriented vertically.

Effects of centroid location on determination of earthquake mechanisms using long-period surface waves

AbstractDetermination of shallow earthquake source mechanisms by inversion of long-period (150 to 300 sec) Rayleigh waves requires epicentral locations with greater accuracy than that provided by routine source locations of the National Earthquake Information Center (NEIC) and International Seismological Centre (ISC). The effects of epicentral mislocation on such inversions are examined using synthetic calculations as well as actual data for three large Mexican earthquakes. For Rayleigh waves of 150-sec period, an epicentral mislocation of 30 km introduces observed source spectra phase errors of 0.6 radian for stations at opposing azimuths along the source mislocation vector. This is larger than the 0.5-radian azimuthal variation of the phase spectra at the same period for a thrust fault with 15° dip and 24-km depth. The typical landward mislocation of routinely determined epicenters of shallow subduction zone earthquakes causes source moment tensor inversions of long-period Rayleigh waves to predict larger fault dip than indicated by teleseismic P-wave first-motion data. For dip-slip earthquakes, inversions of long-period Rayleigh waves that use an erroneous source location in the down-dip or along-strike directions of a nodal plane, overestimate the strike, dip, and slip of that nodal plane. Inversions of strike-slip earthquakes that utilize an erroneous location along the strike of a nodal plane overestimate the slip of that nodal plane, causing the second nodal plane to dip incorrectly in the direction opposite to the mislocation vector. The effects of epicentral mislocation for earthquakes with 45° dip-slip fault mechanisms are more severe than for events with other fault mechanisms. Existing earth model propagation corrections do not appear to be sufficiently accurate to routinely determine the optimal surface-wave source location without constraints from body-wave information, unless extensive direct path (R1) data are available or empirical path calibrations are performed. However, independent surface-wave and body-wave solutions can be remarkably consistent when the effects of epicentral mislocation are accounted for. This will allow simultaneous unconstrained body-wave and surface-wave inversions to be performed despite the well known difficulties of extracting the complete moment tensor of shallow sources from fundamental modes.

A reexamination of the moment tensor solutions of the 1980 Mammoth Lakes Earthquakes

The moment tensor solutions determined from both long‐period body and surface waves for most of the large earthquakes in the 1980 Mammoth Lakes sequence have substantial deviations from a pure double‐couple mechanism. Julian (1983) and Aki (1984) argue that these deviations require nonshear faulting seismic sources such as a compensated linear vector dipole (CLVD) which could represent magmatic dike injection. Here we reexamine the moment tensor solutions and investigate the effects of the non‐double‐couple source on body wave synthetics. An error function which is based on the cross correlation of a synthetic and an observed waveform was used to assess the difference in fit between the complete moment tensor solution and one constrained to be a double couple. For the main shock (May 25, 1980; 1633) the sum of the errors differed by less than 5% for the two models. Similarly, the errors differed by only 3% for the aftershock on May 27, 1980. The conclusion is that the CLVD mechanism is not resolved in the long‐period data. In addition, the complete moment tensor solution has an extra parameter; a χ2 test was applied to normalize the number of parameters, and it was found that the complete solution was slightly less significant than the double‐couple solution. Finally, the complete solution was compared to a pure CLVD solution; for all the events examined, the total moment tensor is as far removed from a CLVD as it is a double couple. Although this does not rule out the possibility of dike injection, it strongly suggests that faulting can account for the long‐period seismic observations in the 1980 swarm.