Variations In Stress Drop Research Articles

Estimation of Source Parameters of Local Earthquakes Originated in Shillong–Mikir Plateau and its Adjoining Region of Northeastern India

Abstract We estimate the source parameters (seismic moment, source radius, stress drop, and source displacement) and scaling laws for local earthquakes that occurred in the Shillong–Mikir plateau, Assam Valley, and Arunachal Himalaya in northeast India during 2001–2008. The source parameters were determined using the spectral analysis of P waves from the vertical component seismograms, after correction for attenuation. Seismic moments are observed within the range from 9.51×10 12 to ; stress drop ranges from 4×10 5 to 9×10 7 Pa for the Brune model and 7×10 5 to 1×10 8 Pa for the Madariaga model. Seismic events in this study are prominent with an average stress drop of 0.1–10 MPa. The effect of site geology may be a contributing factor for such a variation in stress drop. Source dimensions are, however, found to be smaller within the major part of the plateau. It is suggested that local earthquakes in the region are associated with a brittle shear‐failure mechanism on fault segments and/or the presence of weakened zones, and earthquakes are triggered by low deviatoric stress. Empirical relations between M w – M L and M 0 – M L are developed leading to the future prediction of calibration coefficients for the local earthquakes in the Shillong–Mikir plateau and its adjoining region. Online Material: Tables of source parameters.

The depth of pseudotachylyte formation from detailed thermochronology and constraints on coseismic stress drop variability

Pseudotachylytes are accepted as recording paleo‐seismicity in the rock record. However, the interpretation of the mechanics of faulting based on pseudotachylyte generation is often hindered because the depth at which they form is poorly constrained. Here, we use thermochronology to determine the depth at which pseudotachylytes in the Sierra Nevada, California, formed. The pseudotachylytes formed in ≤10 m long patches over a rupture surface, the rest of which comprised cataclasites that did not melt. The age of the pseudotachylytes is found to be 76.6 ± 0.3 Ma (2σ) from 40Ar/39Ar dating of pristine vein matrix. A suite of thermochronometers define the temperature‐time path of the host rock granodiorite from ∼550 to 60°C. When the pseudotachylytes formed, the ambient temperature was 110 to 160°C, implying a depth of ∼2.4 to 6.0 km under typical geothermal gradients. At these depths, the failure stress on optimally oriented faults with Byerlee friction and hydrostatic pore pressure was ≤51 MPa. Following melting, the dynamic stress acting on the fault is the melt shear resistance, which we calculate to be <0.2 MPa, suggesting that the stress drop associated with melting was complete. To conform with seismologically observed dynamic stress drops averaged over an entire rupture (1 to 10 MPa), dynamic stress drop must have varied by at least an order of magnitude between the parts of the fault that melted and those that did not. Constraining the depth of pseudotachylyte formation using thermochronology therefore provides a quantitative estimate of the degree and scale of coseismic stress heterogeneity.

EFFECT OF SOLUTION TREATMENT ON THE INVERSE DYNAMIC STRAIN AGING OF A Ni-Co BASE SUPERALLOY

Serrated flow in a Ni-Co base superalloy was investigated after subsolvus and super- solvus solution treatments at the temperatures of 400 and 450 by tensile loading at different strain rates. The results suggested that the sizes of the grain and secondaryphase of the alloy after super- solvus solution were larger than that of the alloy after subsolvus solution. The serrated flow exhibited inverse DSA behavior after two solution treatments, which was caused by the interaction between sub- stitutional solutes and mobile dislocations. The variation of critical strain of serrated flow after two solution treatments may be related to different spacing between secondaryand different densities of mobile dislocations during plastic deformation. The different densities of mobile dislocations and the diffusion controlled by grain boundary were responsible for the variation of stress drop of serrated flow after two solution treatments.

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.

Variability in earthquake stress drop and apparent stress

[1] We apply empirical Green's function coda-based analysis to four earthquake sequences in Japan that span a magnitude range of 1.8 to 6.9, to measure radiated energy, corner frequency and stress drop. We find no systematic dependence of apparent stress or stress drop on seismic moment for these sequences, and find they both are log-normally distributed; however, we identify several anomalous events - both energetic and enervated - that show sharply different spectral signatures from the rest of the population. These events indicate that much of the variation in apparent stress and stress drop is statistically significant, which may have important implications for seismic hazard analysis.

Source Duration Scales with Magnitude Differently for Earthquakes on the San Andreas Fault and on Secondary Faults in Parkfield, California

We used a comparison of source time function pulse widths to show that a group of earthquakes on the San Andreas fault near Parkfield have a constant duration over a magnitude range of 1.4-3.7. Earthquakes on secondary faults have an increase in duration with magnitude, which is the expected relationship for the usual observation of constant stress drop. The constant duration suggests that fault area is the same regardless of magnitude and that variations in stress drop are due entirely to variations in slip. Calculated stress-drop values on secondary faults range from 0.31 to 14 MPa, and stress-drop values on the San Andreas fault range from 0.18 to 63 MPa. The observation of constant duration on the San Andreas fault is consistent with a model of a locked asperity in a creeping fault. The differences in durations between the events on the San Andreas fault and on secondary faults suggest that earthquakes on the San Andreas fault are inherently different. We speculate that faults with more cumulative displacement have earthquakes that may rupture differently. Furthermore, the differences in source properties between the two populations might be explained by differences in fault surface roughness. Online Material: Station subsets used to evaluate cross-fault seismic velocity contrasts.

Earthquake Stress Drops and Inferred Fault Strength on the Hayward Fault, East San Francisco Bay, California

We study variations in earthquake stress drop with respect to depth, faulting regime, creeping versus locked fault behavior, and wall-rock geology. We use the P -wave displacement spectra from borehole seismic recordings of M 1.0–4.2 earthquakes in the east San Francisco Bay to estimate stress drop using a stack-and-invert empirical Green’s function method. The median stress drop is 8.7 MPa, and most stress drops are in the range between 0.4 and 130 MPa. An apparent correlation between stress drop and magnitude is entirely an artifact of the limited frequency band of 4–55 Hz. There is a trend of increasing stress drop with depth, with a median stress drop of ∼5 MPa for 1–7 km depth, ∼10 MPa for 7–13 km depth, and ∼50 MPa deeper than 13 km. We use S / P amplitude ratios measured from the borehole records to better constrain the first-motion focal mechanisms. High stress drops are observed for a deep cluster of thrust-faulting earthquakes. The correlation of stress drops with depth and faulting regime implies that stress drop is related to the applied shear stress. We compare the spatial distribution of stress drops on the Hayward fault to a model of creeping versus locked behavior of the fault and find that high stress drops are concentrated around the major locked patch near Oakland. This also suggests a connection between stress drop and applied shear stress, as the locked patch may experience higher applied shear stress as a result of the difference in cumulative slip or the presence of higher-strength material. The stress drops do not directly correlate with the strength of the proposed wall-rock geology at depth, suggesting that the relationship between fault strength and the strength of the wall rock is complex.

Depth variation of coseismic stress drop explains bimodal earthquake magnitude‐frequency distribution

An essential part of seismic hazard analysis is the earthquake size‐frequency relationship, used to estimate earthquake recurrence time, and thus probability. A key feature of those distributions is their bimodal character: small to moderate magnitude earthquakes follow the Gutenberg‐Richter (GR) inverse power‐law relation while large magnitude (characteristic) earthquakes are more frequent than anticipated from GR, following approximately a gaussian distribution around the maximum magnitude limited by fault geometry. Using a numerical earthquake simulator, we show that the temperature dependence of friction behavior and therefore the depth‐variation of coseismic stress drop, derived from laboratory friction experiments, presents a simple and comprehensive explanation for the observed bimodal seismicity distribution. Characteristic earthquakes are the result of an abrupt increase in rupture width at the transition from small to large earthquakes.

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.

Earthquake scaling, fault segmentation, and structural maturity

Slip and length measurements on earthquakes suggest large stress drop variability. We analyze an extended set of slip-length measurements for large earthquakes ( M ≥ 6) to seek for the possible origin(s) of this apparent variability. We propose that such variability arises from earthquakes breaking a variable number of major fault segments. That number depends on the strength of the inter-segment zones, which itself depends on the structural maturity of the faults. We propose new D max– L parameterizations based on that idea of multiple segment-ruptures. In such parameterizations, each broken segment roughly scales as a crack, while the total multi-segment rupture does not. Stress drop on individual segments is roughly constant, only varying between 3.5 to 9 MPa. The slight variation that is still observed depends on fault structural maturity; more mature faults have lower stress drops than immature ones. The new D max– L functions that we propose reduce uncertainties with respect to available relationships. They thus provide a more solid basis to estimate seismic hazard by integrating fault properties revealed by geological studies.

Comprehensive analysis of earthquake source spectra in southern California

We compute and analyze P wave spectra from earthquakes in southern California between 1989 and 2001 using a method that isolates source‐, receiver‐, and path‐dependent terms. We correct observed source spectra for attenuation using both fixed and spatially varying empirical Green's function methods. Estimated Brune‐type stress drops for over 60,000 ML = 1.5 to 3.1 earthquakes range from 0.2 to 20 MPa with no dependence on moment or local b value. Median computed stress drop increases with depth in the upper crust, from about 0.6 MPa at the surface to about 2.2 MPa at 8 km, where it levels off and remains nearly constant in the midcrust down to about 20 km. However, the results at shallow depths could also be explained as reduced rupture velocities near the surface rather than a change in stress drop. Spatially coherent variations in median stress drop are observed, with generally low values for the Imperial Valley and Northridge aftershocks and higher values for the eastern Transverse ranges and the north end of the San Jacinto fault. We find no correlation between observed stress drop and distance from the San Andreas and other major faults. Significant along‐strike variations in stress drop exist for aftershocks of the 1992 Landers earthquake, which may correlate with differences in main shock slip.

Reply to "Comment on 'Influence of Focal Mechanism in Probabilistic Seismic Hazard Analysis' by Vincenzo Convertito and Andre Herrero," by F. O. Strasser, V. Montaldo, J. Douglas, and J. J. Bommer

We thank F. O. Strasser, V. Montaldo, J. Douglas, and J. J. Bommer for the interest they have shown in our article (Convertito and Herrero, 2004). Strasser et al. (2006) present a critical comment of our work arguing that the solution proposed by Bommer et al. (2003) is a better solution. Note that the authors are nearly the same in both article and comment, except for V. Montaldo. Because this brief article is a reply, we will focus on the arguments directly concerning our article. The main objection supported by Strasser et al. (2006) is that the method we proposed is not appropriate to “style- of-faulting” correction. We completely agree with this assertion because it is simply not the scope of our article. We speak about “focal mechanism” intended as radiation pattern and nothing else. This point is clearly stated in the introduction of Convertito and Herrero (2004): “in this article we consider that the focal mechanism influence is only expressed by radiation pattern changes. In particular we do not consider any tectonic influence, stress drop variation or dynamic effects.” The style-of-faulting parameter, even if its identity is blurred (e.g., Bommer et al. , 2003), is an empirical definition of a complex set of physical conditions including the tectonic regime, the medium behavior, rock mechanics, rupture dynamics, and so on. In our opinion, the style of faulting is simply too complex to be used directly in our approach. Because the scope of our article is to show how it is possible to insert inside the main equation of probabilistic seismic-hazard analysis (psha; e.g., Cornell, 1968), simple physical parameters of the seismic source, that is, how it is possible to integrate deterministic parameters inside a probabilistic approach, we have chosen a small target, limiting ourselves only to the radiation pattern. …

Empirical relationships between aftershock area dimensions and magnitude for earthquakes in the Mediterranean Sea region

Fault dimension estimates derived from the aftershock area extent of 36 shallow depth (≤ 31 km) earthquakes that occurred in the Mediterranean Sea region have been used in order to establish empirical relationships between length, width, area and surface-wave/moment magnitude. This dataset consists of events whose aftershock sequence was recorded by a dense local or regional network and the reported location errors did not exceed on average 3–5 km. Surface-wave magnitudes for these events were obtained from the NEIC database and/or published reports, while moment magnitudes as well as focal mechanisms were available from the Harvard/USGS catalogues. Contrary to the results of some previously published studies we found no evidence in our dataset that faulting type may have an effect on the fault dimension estimates and therefore we derived relationships for the whole of the dataset. Comparisons, by means of statistical F-tests, of our relationships with other previously published regional and global relationships were performed in order to check possible similarities or differences. Most such comparisons showed relatively low significance levels (< 95%), since the differences in source dimension estimates were large mainly for magnitudes lower than 6.5, becoming smaller with increasing magnitude. Some degree of similarity, however, could be observed between our fault length relationship and the one derived from aftershock area lengths of events in Greece, while a difference was found between our regional and global fault length relationships. A calculation of the ratio defined as the fault length, derived from our relationships, to the length estimated from regional empirical relationships involving surface ruptures showed that it can take a maximum value of about 7 for small magnitudes while it approaches unity at Ms ∼ 7.2. When calculating the same ratio using instead global empirical relationships we see the maximum value not exceeding 1.8, while unity is reached at Mw ∼ 7.8, indicating the existence of a strong regional variation in the fault lengths of earthquakes occurring in the Mediterranean Sea region. Also, a relationship between the logarithms of the rupture area and seismic moment is established and it is inferred that there is some variation of stress drop as a function of seismic moment. In particular, it is observed that for magnitudes lower than 6.6 the stress drop fluctuates around 10 bar, while for larger magnitudes the stress drop reaches a value as high as 60 bar.

On the Expected Relationships among Apparent Stress, Static Stress Drop, Effective Shear Fracture Energy, and Efficiency

We consider expected relationships between apparent stress τ a and static stress drop Δ τ s using a standard energy balance and find τ a = Δ τ s(0.5 – ξ ), where ξ is stress overshoot. A simple implementation of this balance is to assume overshoot is constant; then apparent stress should vary linearly with stress drop, consistent with spectral theories (Brune, 1970) and dynamic crack models (Madariaga, 1976). Normalizing this expression by the static stress drop defines an efficiency η sw = τ a/Δ τ s as follows from Savage and Wood (1971). We use this measure of efficiency to analyze data from one of a number of observational studies that find apparent stress to increase with seismic moment, namely earthquakes recorded in the Cajon Pass borehole by Abercrombie (1995). Increases in apparent stress with event size could reflect an increase in seismic efficiency; however, η sw for the Cajon earthquakes shows no such increase and is approximately constant over the entire moment range. Thus, apparent stress and stress drop co-vary, as expected from the energy balance at constant overshoot. The median value of η sw for the Cajon earthquakes is four times lower than η sw for laboratory events. Thus, these Cajon-recorded earthquakes have relatively low and approximately constant efficiency. As the energy balance requires η sw = 0.5 – ξ , overshoot can be estimated directly from the Savage–Wood efficiency; overshoot is positive for Cajon Pass earthquakes. Variations in apparent stress with seismic moment for these earthquakes result primarily from systematic variations in static stress drop with seismic moment and do not require a relative decrease in sliding resistance with increasing event size (dynamic weakening). Based on the comparison of field and lab determinations of the Savage–Wood efficiency, we suggest the criterion η sw > 0.3 as a test for dynamic weakening in excess of that seen in the lab.

Mechanical controls on fault geometry

Faults inevitably become non-planar because of how they grow and how they are affected during slip by mechanical heterogeneities inherent in the earth. Some faults acquire a non-planar geometry because of non-uniform tectonic deformation or because they grow by the linkage of originally discontinuous structures. However, even faults that are originally planar are unlikely to remain so. Elastic analyses show that as a fault slips, it rotates with the surrounding rock. It rotates uniformly and remains planar if: (a) the shear stress drop along the fault is uniform, (b) the rock surrounding the fault is uniform and isotropic, and (c) the far-field stress state is uniform. Variation in stress drop or in fault strength, heterogeneity in host-rock stiffness, and interaction with other faults cause non-uniform rotation along a fault that slips, and the fault geometry deforms. Mechanical and geometrical heterogeneities are inherent in the earth, so all natural faults will tend to become non-planar to some degree as they slip, even if they were initially planar. Information on fault shape can illuminate the mechanics of faulting, and, in conjunction with slip data, help locate contacts between rock bodies of different elastic moduli. In uniform isotropic rocks, fault curvature is proportional to the rate at which the stress drop varies as a function of position along a fault, whereas the slip profile reflects a weighted average of the stress drop.

The Complex Rupture Process of the 1996 Deep Flores, Indonesia Earthquake (Mw 7.9) from teleseismic P‐waves

From an analysis of broadband teleseismic P‐waveforms we resolve the complex rupture characteristics of the 17 June 1996, Flores earthquake (Mw 7.9, depth 590 km). This earthquake was unusual because of its large rupture length and the variation in rupture velocity and stress drop. The 20 s rupture propagated westward at 2–3 km/s to a distance of 20–30 km, and eastward at 4 km/s over 75 km. Average static stress drop was about 15 MPa, but the stress drop during the episode of main moment release was a factor of four higher. The oblique normal faulting mechanism is consistent with the stress expected as the slab descends along a highly curved trench. Significant rupture complexity is also reported for the deep 1994 Mw 7.7 Fiji and Mw 8.2 Bolivia earthquakes and is evident in the source‐time functions of many smaller earthquakes at depths &gt;300 km. Thus source complexity of deep earthquakes appears no less common than for shallow earthquakes, and requires the existence of significant heterogeneity in the physical properties that control deep earthquake rupture.

Modeling seismicity clustering and fault weakness due to high pore pressures

An earthquake model that couples shear stress and zones of high pore pressure produces many features of observed seismicity patterns and geodetic observations. The model shows earthquake clustering, repeated events, large spatial and temporal variations in stress drop, complex slip distributions, and a power law distribution of sizefrequency. This dynamical model tracks the evolution of the stress state in a 2D fault plane of discrete rectangular dislocations subjected to heterogeneous increases in pore pressure and embedded in a 3D elastic solid. The source of increasing pore pressure can include a time-dependent porosity reduction mechanism or fluid sources from dehydration reactions. Increased fluid pressure within the fault plane reduces the effective confining stress until cells slip by simple frictional sliding. Changes in the fault plane shear stresses associated with a slipped cell are calculated using the solution for a rectangular dislocation in an elastic solid, and pore pressures are redistributed using a cellular automaton model of migrating fluid pressures. The frictional resistance of the system is shown to evolve non-linearly from a uniform shear stress on a strong fault, to a strongly heterogeneous shear stress distribution on a weak fault. Features of the non-linear temporal response of the system frictional resistance are discussed in terms of calculated seismicity patterns and increased seismicity clustering.

Earthquake locations using single‐station deep borehole recordings: Implications for microseismicity on the San Andreas fault in southern California

We have located and estimated source parameters of 109 earthquakes (0 to 5 M) using seismograms recorded at 2.5 km depth in the Cajon Pass borehole, southern California. The borehole is about 4 km from the San Andreas fault, at the boundary between the locked, almost aseismic Mojave and San Bernardino segments, where the San Jacinto fault approaches the San Andreas. This area is of interest both on account of its tectonic complexity and its high potential seismic hazard. The clear, relatively unattenuated downhole recordings are rotated to determine the incoming azimuth of the P wave, and the delay time between the P and S arrivals is used to estimate the hypocentral distance. The difference between the hypocenters located this way and the Southern California Seismic Network (SCSN) locations of the same earthquakes increases with hypocentral distance from the borehole. Of the earthquakes within 20 km of the borehole, 95% are within 1–2 km of the SCSN epicenters and all are within 5 km of the SCSN depths. All but three of the 58 earthquakes located here which the SCSN did not record were within 20 km of the borehole and so the location errors are similar to those of SCSN A and B quality events. Most of the small earthquakes occurred within the relatively active San Jacinto fault zone, but at least eight are located close to or within the San Andreas fault zone. The stress drops for these events range from 0.1 to 18 MPa. These earthquakes appear similar to the other events in this study suggesting that the San Andreas fault is similar to other faults at the scale of these small earthquakes. The variation in stress drop and slip orientation of these small earthquakes suggests that larger scale heterogeneity continues to these small scales. Also, the location of these small earthquakes in major established fault zones implies that earthquake source dimensions are not geometrically controlled by fault zone width.

Rupture histories of eastern North American earthquakes

Abstract Digital, worldwide records of P and SH waves are used to invert for rupture histories of the recent, larger, eastern North American earthquakes. The data include a broad bandwidth to facilitate recovery of both source details and total moment. The following events are studied- 9 January 1982 New Brunswick; 5 October and 23 December 1985 Nahanni; 25 November 1988 Saguenay; and 25 December 1989 Ungava earthquakes. We employ a finite-fault, waveform inversion scheme that discretizes the slip history as a function of position on the fault. This formulation allows estimation of rise time and slip velocity, in addition to the spatial distribution of slip. Static stress drops averaged over the entire rupture surface range from a few tens of bars to just over 100 bars and are similar to values estimated for western United States earthquakes. Estimates of stress drop for spatially limited asperities are in the range of a few hundred bars, with the value for the Saguenay earthquake asperity being the largest (approaching 1 kbar). The variation in stress drop is considerable, but no evidence is seen for a scaling relation in which stress drop increases with moment. Maximum slip velocities on the fault also have a wide range (from 50 cm/sec to perhaps greater then 200 cm/sec), with the Saguenay and 5 October Nahanni earthquakes lying at the upper end of this range. Of the events studied, the Saguenay earthquake is unique in terms of its greater depth, spatially concentrated source, and large asperity stress drop.

Contrasts between source parameters of M 5.5 earthquakes in northern Baja California and southern California

SUMMARY Earthquake source processes are determined for four historic events that occurred in Baja California between 1915 and 1954. These results are combined with previous studies of recent and historic seismicity to compare earthquake processes along the San Jacinto, Imperial-Cerro Prieto and northern Baja fault systems of southern California and northern Mexico. Observed regional differences in rupture complexity, fault rupture lengths and aftershock/foreshock activity appear to be related to variations in heat flow and total fault offset. There appear to be no systematic variations in stress drop (as measured from far-field observations) between earthquakes along the Imperial-Cerro Prieto fault zone and those within the Peninsular Ranges of northern Baja California. Slip rates estimated from historical seismicity between 1915 and 1992 fall ? 1.5 cm yr−1 short of the estimated relative plate motion between the Pacific plate and North America for this region.