Stress Drop Estimates Research Articles

Stress drop variations of induced earthquakes at the Basel geothermal site

We determine stress drops from P‐wave spectra of about 1000 earthquakes induced by hydraulic stimulation in crystalline rock for a deep heat mining project in Basel, Switzerland. We observe an increase in stress drop by about a factor of five with radial distance from 10 m to 300 m, which suggests that stress drop correlates with pore pressure perturbations due to the injection. We test this hypothesis by calculating the injection‐related pore pressure perturbation based on a simple linear pore pressure diffusion model and find a good correlation of the expected pore pressure perturbation with the estimated stress drops.

Quantifying Seismic Source Parameter Uncertainties

We use data from a small aperture array in southern California to quantify variations in source parameter estimates at closely spaced stations (distances ranging from ∼7 to 350 m) to provide constraints on parameter uncertainties. Many studies do not consider uncertainties in these estimates even though they can be significant and haveimportantimplicationsforstudiesofearthquakesourcephysics.Here,weestimate seismic source parameters in the frequency domain using empirical Green's function (EGF) methods to remove effects of the travel paths between earthquakes and their recordingstations.Weexamineuncertainties inourestimatesbyquantifyingtheresult- ing distributions over all stations in the array. For coseismic stress drop estimates, we find that minimum uncertainties of ∼30% of the estimate can be expected. To test the robustness of our results, we explorevariations of the dataset using different groupings of stations, different source regions, and different EGF earthquakes. Although these differences affect our absolute estimates of stress drop, they do not greatly influence thespreadinourresultingestimates.Thesesensitivitytestsshowthatstationselectionis not the primary contribution to the uncertainties in our parameter estimates for single stations. We conclude that establishing reliable methods of estimating uncertainties in sourceparameterestimates(includingcornerfrequencies,sourcedurations,andcoseis- mic static stress drops) is essential, particularly when the results are used in the com- parisons among different studies over a range of earthquake magnitudes and locations.

Source Modeling of the 2007 Niigataken Chuetsu-oki Earthquake Using the Empirical Green's Function Method

The 2007 Niigataken Chuetsu-oki earthquake (MJMA6.8) occurred on July 16th, 2007. In this study, we estimate a source model of this earthquake through forward modeling of local strong motion records using the empirical Green's function method. The target frequency range of this modeling is broadband (0.3 Hz to 10 Hz). As the result, the first asperity was estimated that it was located on the NW-dipping fault plane including the hypocenter, and the rupture then transferred to the conjugated fault plane (SE-dipping plane). On the SE-dipping plane, two asperities are identified: one is located just near the first asperity (the second asperity); the other is off the coast of Kashiwazaki city (the third asperity). The estimated three asperities are located in the gaps of the aftershock distribution. Our source model can successfully reproduce strong motion in a wider area than the modeling area selected for source estimation. The estimated stress drop from our source model is almost 15 to 20 MPa, and it is similar to the stress drop empirically expected from the seismic moment and area of asperities.

経験的グリーン関数法を用いた２００７年新潟県中越沖地震の震源のモデル化

The 2007 Niigataken Chuetsu-oki earthquake (MJMA6.8) occurred on July 16th, 2007. In this study, we estimate a source model of this earthquake through forward modeling of local strong motion records using the empirical Green's function method. The target frequency range of this modeling is broadband (0.3 Hz to 10 Hz). As the result, the first asperity was estimated that it was located on the NW-dipping fault plane including the hypocenter, and the rupture then transferred to the conjugated fault plane (SE-dipping plane). On the SE-dipping plane, two asperities are identified: one is located just near the first asperity (the second asperity); the other is off the coast of Kashiwazaki city (the third asperity). The estimated three asperities are located in the gaps of the aftershock distribution. Our source model can successfully reproduce strong motion in a wider area than the modeling area selected for source estimation. The estimated stress drop from our source model is almost 15 to 20 MPa, and it is similar to the stress drop empirically expected from the seismic moment and area of asperities.

Global variations of stress drop for moderate to large earthquakes

We investigate the global variation of earthquake stress drops using spectra of about 2000 events of mb ≥ 5.5 between 1990 and 2007. We use an iterative least squares method to isolate source displacement spectra from travel path and receiver contributions, based on a convolutional model. The observed P wave source spectra are corrected with a globally averaged empirical correction spectrum and estimates of near‐source attenuation. Assuming a Brune‐type source model, we estimate corner frequencies and compute stress drops. Stress drop estimates for individual earthquakes range from about 0.3 to 50 MPa, but the median stress drop of about 4 MPa does not vary with moment, implying earthquake self‐similarity over the Mw = 5.2 to 8.3 range of our data. A comparison of our results with previous studies confirms this observation over most of the instrumentally observable magnitude range. While the absolute values of our estimated stress drops depend upon the assumed source model, we identify relative regional variations of stress drop that are robust with respect to the processing parameters and modeling assumptions, which includes an inherent assumption of constant rupture velocity. We find a dependence of median stress drop on focal mechanism, with a factor of 3–5 times higher stress drops for strike‐slip earthquakes and also find a factor of 2 times higher stress drops for intraplate earthquakes compared to interplate earthquakes.

Spectral characteristics of natural and artificial seismic events in the Lop Nor test site, China

Seismic discriminants based on the spectral seismogram and spectral magnitude techniques have been tested to discriminate between three events; a nuclear explosion which took place in Lop Nor, China with mb 6.1 and two earthquakes from the closest area with mb 5.5 and 5.3, respectively. The spectral seismogram of the three events shows that the frequency content of the nuclear explosion differs from that of the earthquakes where the P wave is richier in high frequency content in the nuclear explosion than the corresponding earthquakes. It is also observed that the energy decays more rapidly for the nuclear explosion than for the earthquakes. Furthermore, the spectral magnitudes reveal significant differences in the spectra between the nuclear explosion and the two earthquakes. The observed differences appear to be quite enough to provide a reliable discriminant. The estimated stress drop from the magnitude spectra indicates a higher stress drop of the nuclear explosion relative to the earthquakes of the same tectonic region.

A High-Frequency Secondary Event During the 2004 Parkfield Earthquake

By using seismic records of the 2004 magnitude 6.0 Parkfield earthquake, we identified a burst of high-frequency seismic radiation that occurred about 13 kilometers northwest of the hypocenter and 5 seconds after rupture initiation. We imaged this event in three dimensions by using a waveform back-projection method, as well as by timing distinct arrivals visible on many of the seismograms. The high-frequency event is located near the south edge of a large slip patch seen in most seismic and geodetic inversions, indicating that slip may have grown abruptly at this point. The time history obtained from full-waveform back projection suggests a rupture velocity of 2.5 kilometers per second. Energy estimates for the subevent, together with long-period slip inversions, indicate a lower average stress drop for the northern part of the Parkfield earthquake compared with that for the region near its hypocenter, which is in agreement with stress-drop estimates obtained from small-magnitude aftershocks.

Can One Determine Seismic Focal Parameters from the Far-Field Radiation?

Summary A number of postulates concerning the nature of faulting have been used in the construction of kinematical models, which give the source parameters of seismic moment, fault length, and stress drop from the spectral properties of d.c. level and knee frequency. Several one-dimensional models of faulting, calculated as well-posed boundary value problems, are obtained which give both the source parameters and the far-field radiation, providing a test for these empirical relations. The results for these models show that the high-frequency content of the seismogram is usually associated not with the onset of fracture, but with the onset of healing, that is, when the cessation of relative motion on the fault begins. In some cases, the high-frequency part of the seismogram is also associated with the termination of rupture. For different distributions of tectonic stress, dynamical friction and cohesion, healing can take place sonically, supersonically, or instantaneously over the entire fault. The final state of stress may be less than or greater than the dynamical friction. For four selected models of one-dimensional faulting, the calculation of fault parameters from the theoretical seismograms give internally consistent estimates of seismic moment. Unfortunately, the theory shows that the estimates of fault length and stress drop made from the empirical formulas may be completely without value, without additional information not usually derived from the radiation spectrum.

Spatial and temporal stress drop variations in small earthquakes near Parkfield, California

We estimate source parameters from spectra of 42367 earthquakes between 1984 and 2005 that occurred in the Parkfield segment of the San Andreas Fault in central California. We use a method that isolates the source term of the displacement spectra based on a convolutional model and correct the observed P wave source spectra with a spatially varying empirical Green's function (EGF). Our Brune‐type stress drop estimates vary from 0.1 to over 100 MPa with a median value of 6.75 MPa, which is nearly constant with moment, implying self‐similarity over the ML = 0.5 to 3.0 range of our data. The corner frequency decreases for earthquakes at shallower depths, consistent with slower rupture velocities and reduced shear wave velocities in local velocity models. The estimated median stress drops show significant lateral variations: we find lower stress drops in the Middle Mountain asperity and along the creeping fault section, and higher stress drops in the hypocentral region of the 2004 M6.0 Parkfield earthquake. The main shock did not alter the overall pattern of high and low stress drop regions. However, a statistical test reveals areas with significant changes in computed stress drops after the main shock, which we compare to estimated absolute shear stress changes from a main shock slip model. By calculating Δt* from the spectral EGF ratio, we also identify areas with increased attenuation after the main shock, and we are able to distinguish source effects and near‐source attenuation effects in the spectral analysis. These results are confirmed independently from spectral ratios of repeating microearthquake clusters.

Estimation of Source Parameters for the Aftershocks of the 2001 Mw 7.7 Bhuj Earthquake, India

The source parameters for 213 Bhuj aftershocks of moment magnitude varying from 2.16 to 5.74 have been estimated using the spectral analysis of the SH- waveform on the transverse component of the three-componnet digital seismograms as well as accelerograms. The estimated stress drop values for Bhuj aftershocks show more scatter (Mo0.5 to 1 ∞ Δσ) toward the larger seismic moment values (log Mo ≥ 1014.5 N-m, larger aftershocks), whereas, they show a more systematic nature (Mo3 ∞ Δσ) for smaller seismic moment (log Mo 15 MPa)) lying in 22–26km depth range beneath the region. We suggest that the concentration of large stress drop values at 10–36km depth may be related to the large stress/strain associvated with a brittle, competent intrusive body of mafic nature.

Empirical Attenuation of Ground-Motion Spectral Amplitudes in Southwestern Western Australia

A dataset comprising some 389 strong- and weak-motion records for 69 events from the Burakin 2001–2002 earthquake swarm, and additional recent events, is compiled to develop a regional ground-motion model for the Yilgarn Craton, southwestern Western Australia. Events range in size from moment magnitude 2.2 ≤ M ≤ 4.6. The decay of horizontal-component spectral amplitudes can be approximated by a geometrical attenuation coefficient of R −1.0 within 80 km of the source. The associated regional seismic quality factor can be expressed as Q ( f ) = 457 f 0.37 for frequencies 1.07 ≤ f ≤ 25.0 Hz. Average corner frequencies for events with magnitude M >3.0 do not vary significantly with seismic moment M 0 , indicating a steep distribution of M 0 versus corner frequency. This causes anomalously low estimates of stress drop for smaller magnitude events ( M Fourier spectral amplitudes, corrected for geometric and anelastic attenuation, were regressed with M to obtain quadratic attenuation coefficients. Modeled horizontal-component displacement spectra fit the observed data well. Amplitude residuals (predicted–observed amplitudes) are, on average, relatively small and do not vary significantly with hypocentral distance. Source spectra (i.e., at R = 1 km) predicted from the regression parameters give self-consistent amplitudes at low frequency ( f less than approximately 2 Hz), equivalent to predictive models from eastern North America (ena) for the same moment magnitude. However, our model predicts lower spectral amplitudes with increasing frequency as a consequence of the low- stress-drop events. This is particularly apparent for the smaller magnitudes. Western Australian source spectra begin to converge with ena models at increasing magnitudes. If hypocentral distance is increased (i.e., R ≫ 1 km), the models begin to diverge at low frequencies owing to differences in geometrical attenuation coefficients. The bulk of these data were recorded from an earthquake swarm with very shallow focal depths ( h

Estimates of Stress Drop of the Chi-Chi, Taiwan, Earthquake of 20 September 1999 from Near-Field Seismograms

The apparent stress and stress drop of the Chi-Chi, Taiwan, earthquake are estimated from near-field seismograms. The estimated apparent stress and stress drop for the southern part of the fault are about 100 bars lower than those for the northern part. The estimated ratio E s/ M also suggests that there is a higher dynamic stress drop in the northern part than in the southern one. This indicates the transformation of a higher percentage of strain energy into the seismic-wave energy in the northern part than in the southern part. Based on a parameter proposed by Ramon Zuniga (1993), we propose that the stress model of frictional overshoot can interpret the rupture of the Chelungpu fault, on which the Chi-Chi, Taiwan, earthquake occurred. Manuscript received 31 July 2000.

Source and Qp parameters from pulse width inversion of microearthquake data in southeastern Sicily, Italy

Source and Qp parameters were estimated from the inversion of first arrival P waveform durations of about 300 microearthquakes recorded at a digital seismic network operating in southeastern Sicily. The average risetime and pulse width at each station do not show large differences, allowing us to exclude significant differential attenuation site effects. A first Qp estimate was obtained by applying the classical risetime method, under the assumption of a point‐like source time function. In order to investigate the effect of directivity due to the finiteness of seismic sources, new nonlinear relationships, based on a circular crack model rupturing at a constant velocity, were numerically built. These relationships were used to formulate a nonlinear inverse method for retrieving source (radius, dip, and strike of the circular crack) and Qp parameters from the inversion of risetime and pulse width data. The application of the method produced a better fit of the observed data and a Qp value higher than that obtained by applying the risetime method. The discrepancy between the different Q estimates may be due to a trade‐off among source dimension and Qp, as we inferred from a test on a subset of low‐magnitude events (Ml ≤ 2.5). A good agreement with independent estimates of fault plane solutions, as inferred from P polarities and S polarizations, was found. The estimated stress drops are generally very low (0.1–10 bars). This suggests that the background seismic activity in southeastern Sicily is related to fault segments and/or weakened zones where great stress accumulations are hindered.

Observational constraints on the fracture energy of subduction zone earthquakes

We relate seismologically observable parameters such as radiated energy, seismic moment, rupture area, and rupture speed to the dynamics of faulting. To achieve this objective, we computed the radiated energy for 23 subduction zone earthquakes recorded between 1992 and 2001; most of these earthquakes have a magnitude Mw > 7.5, but we also included some smaller (Mw ∼ 6.7) well‐studied subduction zone earthquakes and six crustal earthquakes. We compiled static stress drop estimates for these 29 earthquakes from literature and used a slip‐weakening model to determine the radiation efficiency of these earthquakes. We also determined the rupture speed of these earthquakes from literature. From fracture mechanics, fracture energy, and hence radiation efficiency, can be related to the rupture speed. The radiation efficiencies estimated from the partitioning of energy as given by the slip‐weakening model are consistent with the rupture speed estimated for these earthquakes. Most earthquakes have radiation efficiencies between 0.25 and 1 and are hence efficient in generating seismic waves, but tsunami earthquakes and two deep earthquakes, the 1994 Bolivia and the 1999 Russia‐China border earthquakes, have very small radiation efficiencies (<0.25) and hence dissipate a large amount of energy during faulting. We suggest that differences in the radiation efficiencies of different types of earthquakes could be due to fundamental differences in their rupture mechanics. In deep events, the energy is probably dissipated in thermal processes in the fault zone, while it is possible that the morphology of the trench causes large energy dissipation during the rupture process of tsunami earthquakes.

Seismic observations of the 22/11/1995 Gulf of Aqaba earthquake sequence

We analyzed the aftershock sequence of the Gulf of Aqaba earthquake recorded by short period and broad band stations between November 1995 and December 1996. The seismicity pattern reveals significant activity often confined to known surface traces of active faults or within local grabens. Most of the aftershock activity is concentrated north of the main shock in the Aragonese and Eilat basins, while the activity is diffused south of the main shock in the Dakar and Tiran basins. Most of the moderate to strong aftershocks of the whole aftershock sequence occurred in the Aragonese basin, mainly in the first 100 days following the main shock. The Eilat basin is characterized by a larger number of aftershocks composed mainly of small-magnitude implying a slower decay rate. Assuming a detection level of M L=3.2 we obtain b-values of 1.01, 1.15, and 0.89 for the whole Gulf of Aqaba, and Eilat and Aragonese basins, respectively, in good agreement with recent studies of the Dead Sea fault. Following Omori's law, we obtained a decay parameter of 0.94, 0.88, and 0.96 for the aftershock sequences in the whole Gulf of Aqaba, and the Eilat and Aragonese basins, respectively, correlative with regions of low heat flow. For 1630 events in the local magnitude range of 0.6≤ M L≤6.2 we found seismic moment estimates, M 0, of 5×10 18≤ M 0≤7.7×10 26 dyn cm, and Brune stress drop estimates, Δ σ, between 1 and 200 bars, with a characteristic value of 90 bars in the Eilat and Aragonese basins for M 0>5×10 21 dyn cm. These characteristics are comparable to those for events occurring on the main Dead Sea–Jordan fault. Most of the moment release in the basins occurred shortly after the occurrence of the main shock. The total moment release in the Eilat and Aragonese basins is only a fraction of the moment release of the main shock suggesting an almost complete stress release.

Source depth dependence of micro-tsunamis recorded with ocean-bottom pressure gauges: the January 28, 2000 Mw 6.8 earthquake off Nemuro Peninsula, Japan

Micro-tsunami waves with a maximum amplitude of 4–6 mm were detected with the ocean-bottom pressure gauges on a cabled deep seafloor observatory south of Hokkaido, Japan, following the January 28, 2000 earthquake ( M w 6.8) in the southern Kuril subduction zone. We model the observed micro-tsunami and estimate the focal depth and other source parameters such as fault length and amount of slip using grid searching with the least-squares method. The source depth and stress drop for the January 2000 earthquake are estimated to be 50 km and 7 MPa, respectively, with possible ranges of 45–55 km and 4–13 MPa. Focal depth of typical inter-plate earthquakes in this region ranges from 10 to 20 km and stress drop of inter-plate earthquakes generally is around 3 MPa. The source depth and stress drop estimates suggest that the earthquake was an intra-slab event in the subducting Pacific plate, rather than an inter-plate event. In addition, for a prescribed fault width of 30 km, the fault length is estimated to be 15 km, with possible ranges of 10–20 km, which is the same as the previously determined aftershock distribution. The corresponding estimate for seismic moment is 2.7×10 19 Nm with possible ranges of 2.3×10 19–3.2×10 19 Nm. Standard tide gauges along the nearby coast did not record any tsunami signal. High-precision ocean-bottom pressure measurements offshore thus make it possible to determine fault parameters of moderate-sized earthquakes in subduction zones using open-ocean tsunami waveforms.

Source Properties of Earthquakes near the Salton Sea Triggered by the 16 October 1999 M 7.1 Hector Mine, California, Earthquake

We analyze the source properties of a sequence of triggered earthquakes that occurred near the Salton Sea in southern California in the immediate aftermath of the M 7.1 Hector Mine earthquake of 16 October 1999. The sequence produced a number of early events that were not initially located by the regional network, including two moderate earthquakes: the first within 30 sec of the P-wave arrival and a second approximately 10 minutes after the mainshock. We use available amplitude and waveform data from these events to estimate magnitudes to be approximately 4.7 and 4.4, respectively, and to obtain crude estimates of their locations. The sequence of small events following the initial M 4.7 earthquake is clustered and suggestive of a local aftershock sequence. Using both broadband TriNet data and analog data from the Southern California Seismic Network (SCSN), we also investigate the spectral characteristics of the M 4.4 event and other triggered earthquakes using empirical Green's function (EGF) analysis. We find that the source spectra of the events are consistent with expectations for tectonic (brittle shear failure) earthquakes, and infer stress drop values of 0.1 to 6 MPa for six M 2.1 to M 4.4 events. The estimated stress drop values are within the range observed for tectonic earthquakes elsewhere. They are relatively low compared to typically observed stress drop values, which is consistent with expectations for faulting in an extensional, high heat flow regime. The results therefore suggest that, at least in this case, triggered earthquakes are associated with a brittle shear failure mechanism. This further suggests that triggered earthquakes may tend to occur in geothermal–volcanic regions because shear failure occurs at, and can be triggered by, relatively low stresses in extensional regimes.

Source parameters and three‐dimensional attenuation structure from the inversion of microearthquake pulse width data: Qp imaging and inferences on the thermal state of the Campi Flegrei caldera (southern Italy)

The three‐dimensional P wave attenuation structure of the Campi Flegrei caldera and the estimate of source parameters for 87 local microearthquakes is obtained by the nonlinear inversion of pulse width and rise time measurements by using the method described by Zollo and de Lorenzo (this issue). Source radii represent the better resolved parameters with values ranging from 70 m to 230 m; the dip and strike angles defining fault orientations are usually affected by larger uncertainties and are well constrained only for 11 events. The dip fault is usually confined in the range 30°–60° (with an average uncertainty of 12°); the fault strikes mainly range between −60° and 60° and seem to define preferential directions oriented radially from the symmetry axis of the ground deformation. Stress drop estimates indicate rather low values (0.01–1 MPa) which suggest low strength properties of the incoherent and brittle materials filling the caldera (primarily yellow tuffs). The three‐dimensional Qp images obtained from the inversion of P pulse durations show two significant low‐Qp anomalies between 0 and 1 km of depth, in the north‐eastern sector and at 2–3 km of depth in the central eastern sector of the caldera. The high degree of spatial correlation of the low‐Qp zone and low‐Vs (as inferred by Aster and Meyer (1988)) at 0–1 km in depth and other geophysical and geochemical observations suggest that this anomaly can be related to the presence of densely fractured, porous, and fluid‐filled rocks in the NE sector of the caldera. The deeper low‐Qp anomaly is interpreted as being related to a dominant thermal effect. We used the surface and deep borehole temperature measurements available in the area to obtain a local calibration curve to convert Qp in temperature at Campi Flegrei. The retrieved T(Qp) map shows a high thermal deep disturbance (450°–500°C) at depths between 2 and 3 km in the eastern sector of the caldera, where the most recent eruptive activity is concentrated. The present‐day temperature field retrieved by Qp images has been interpreted by using a three‐dimensional thermal conduction model assuming an extended heat source (initial temperature of 800°C) located underneath the attenuation anomalous region. The results indicate that the Qp‐inferred temperature field can be related to the heat conduction effect of one or more molten bodies whose top should be at about 4‐km depth, consistent with recent seismic estimates of the magma chamber top at Campi Flegrei (Ferrucci et al., 1992). This study suggests that the present thermal state and rock rheology of the inner caldera could be controlled by the cooling of molten bodies that originally intruded at depths of 1.4–1.6 km, during one or more recent (time of <10 kyr) eruptive events.

Repeating Earthquakes as Low-Stress-Drop Events at a Border between Locked and Creeping Fault Patches

The source of repeating earthquakes on creeping faults is modeled as a weak asperity at a border between much larger locked and creeping patches on the fault plane. The x –1/2 decrease in stress concentration with distance x from the boundary is shown to lead directly to the observed scaling 〈 T 〉∞〈 M 〉1/6 between the average repeat time and average scalar moment for a repeating sequence. The stress drop in such small events at the border depends on the size of the large locked patch. For a circular patch of radius R and representative fault parameters, Δσ = 7.6( m / R )3/5 MPa, which yields stress drops between 0.08 and 0.5 MPa (0.8–5 bars) for R between 2 km and 100 m. These low stress drops are consistent with estimates of stress drop for small earthquakes based on their seismic spectra. However, they are orders of magnitude smaller than stress drops calculated under the assumption that repeating sources are isolated stuck asperities on an otherwise creeping fault plane, whose seismic slips keep pace with the surrounding creep rate. Linear streaks of microearthquakes observed on creeping fault planes are trivially explained by the present model as alignments on the boundaries between locked and creeping patches.

Spectral seismograms, magnitude spectra and source parameters of a selection of Indian plate earthquakes

Spectral seismograms of 17 earthquakes in and around the Indian sub-continent as recorded by GRA1 station of the Graefenberg array are presented and their individual and common characteristics discussed. P-wave magnitude spectra for all these earthquakes have been computed. The corner frequency, which corresponds to the frequency at the maximum value of the magnitude spectrum, is found to shift, in general, to a higher value than observed at the recording station. These magnitude spectra are used to estimate model-independent and -dependent source parameters such as seismic moment, apparent stress, stress drop and fault length. For the sake of uniform comparison, one simple omega-square type of source model has been used. No clear classification of events on the basis of source parameters is found possible. However, the model-independent apparent stress appears to have a direct proportionality with the model-dependent stress drop estimates. Also, in conformity with known observations, the highest stress drop is found for the intra-plate Latur earthquake and the lowest, for the Nicobar island arc events.