Earthquake Stress Drop Research Articles

Catastrophe Theory Analysis of Rock Mass Dynamic Destabilization

In step with body Ⅱ, analytic solution and illustration of elastic energy releasing amount of rock mass dynamic destabilization are given for the first time in the form of precise and approximate catastrophe model. It is upgraded from qualitative understand to quantitative description that study on rock stability at the stage before and after earthquake and rockburst. The halting point’s position of rock mass dynamic destabilization is ascertained strictly, and it offers scientific basis for the calculation on earthquake efficiency, the study on earthquake energy magnitude released, earthquake stress drop, fault offset after earthquake and amount of elastic strain recovery of surrounding rock. The system possesses the capability of applying work to surroundings when it destabilizes, and earthquake wave energy is the work that destabilizing rock system applies to surroundings by way of destructive. The given illustration of elastic energy releasing amount implicates wealth of information, it produces credible evidence for confirming that the mathematical abstract of rock dynamic destabilization is fold catastrophe model.

Dependence of earthquake stress drop on critical slip‐weakening distance

Numerical simulations are conducted to investigate the dependence of the static stress drop of earthquakes on the critical slip‐weakening distance. A fault model in a two‐dimensional elastic medium is used, in which a locked zone (asperity) is assumed to exist between creeping zones. The presence of such a zone is commonly assumed for plate boundaries that have relatively low seismic coupling. Shear stress is concentrated at the edges of the locked zone and seismic rupture occurs when the strain energy release by rupture extension becomes sufficiently large to overcome the fracture energy. The static stress drop is calculated by taking the ratio of the average seismic slip to the length of seismic slip zone for the simulated earthquakes in the model, using various values for the normal stress applied to the fault and the characteristic slip distance of a rate‐ and state‐dependent friction law. The simulation results indicate that the static stress drop is proportional to the square root of the product of the critical slip‐weakening distance and the normal stress, when the seismic rupture starts near an edge of the locked zone. In contrast, when the seismic rupture starts near the center of the locked zone, the static stress drop increases linearly with normal stress and is independent of the critical slip‐weakening distance. These simulation results may explain the relatively small depth dependence, as well as the large scatter, in observations of the static stress drop.

Observed source parameters for dynamic rupture with non-uniform initial stress and relatively high fracture energy

We have conducted dynamic rupture propagation experiments to establish the relations between in-source stress drop, fracture energy and the resulting particle velocity during slip of an unconfined 2 m long laboratory fault at normal stresses between 4 and 8 MPa. To produce high fracture energy in the source we use a rough fault that has a large slip weakening distance. An artifact of the high fracture energy is that the nucleation zone is large such that precursory slip reduces fault strength over a large fraction of the total fault length prior to dynamic rupture, making the initial stress non-uniform. Shear stress, particle velocity, fault slip and acceleration were recorded coseismically at multiple locations along strike and at small fault-normal distances. Stress drop increases weakly with normal stress. Average slip rate depends linearly on the fault strength loss and on static stress drop, both with a nonzero intercept. A minimum fracture energy of 1.8 J/m2 and a linear slip weakening distance of 33 μm are inferred from the intercept. The large slip weakening distance also affects the average slip rate which is reduced by in-source energy dissipation from on-fault fracture energy.Because of the low normal stress and small per event slip (∼86 μm), no thermal weakening such as melting or pore fluid pressurization occurs in these experiments. Despite the relatively high fracture energy, and the very low heat production, energy partitioning during these laboratory earthquakes is very similar to typical earthquake source properties. The product of fracture energy and fault area is larger than the radiated energy. Seismic efficiency is low at ∼2%. The ratio of apparent stress to static stress drop is ∼27%, consistent with measured overshoot. The fracture efficiency is ∼33%. The static and dynamic stress drops when extrapolated to crustal stresses are 2–7.3 MPa and in the range of typical earthquake stress drops. As the relatively high fracture energy reduces the slip velocities in these experiments, the extrapolated average particle velocities for crustal stresses are 0.18–0.6 m/s. That these experiments are consistent with typical earthquake source properties suggests, albeit indirectly, that thermal weakening mechanisms such as thermal pressurization and melting which lead to near complete stress drops, dominate earthquake source properties only for exceptional events unless crustal stresses are low.

Comments on the generation mechanism of Seismic Electric Signals

Abstract. Recent laboratory measurements on rocks under varying pressure lead to results which strengthen a model suggested by the author for the explanation of the power law relation that interconnects the lead time of Seismic Electric Signals and earthquake stress drop. In addition, recent applications of a thermodynamic model that interrelates the defect parameters in materials of geophysical interest and their bulk properties open a new window to further advance the aforementioned explanation.

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.

Kīholo Bay, Hawai‘i, earthquake sequence of 2006: Relationship of the main shock slip with locations and source parameters of aftershocks

We study the source process of the Kīholo Bay earthquake (MW 6.7), which occurred beneath the northwest part of the Island of Hawai‘i on 15 October 2006, and static stress drops of small earthquakes that occurred in 2006 and 2007 around the main shock including aftershocks. We relocate the aftershocks to determine the fault plane from the two nodal planes. The relocated aftershocks define an E‐W trending plane that dips to the south, in good agreement with one of the nodal planes given by the Global Centroid Moment Tensor solution. Waveform inversion is performed with multiple time windows to investigate the rupture speed and the slip distribution of the main shock. Waveforms of an aftershock with MW 5.2 are used to calculate empirical Green's functions. Our results indicate that the rupture propagated unilaterally to the west with a rupture speed greater than 3.0 km/s (63% of the shear wave velocity). This westward rupture is consistent with the fact that aftershocks are distributed predominantly to the west of the main shock epicenter. Most aftershocks are located on the edge of patches with a large slip, or asperities and some also occur inside the patches. We also estimate static stress drops of 39 earthquakes (2.5 < ML < 3.5) that occurred in 2006 and 2007 near the source region of the Kīholo Bay earthquake. Static stress drops range from 0.12 to 8.6 MPa and aftershocks around large slip patches of the main shock likely to have larger stress drops.

Large Earthquake Triggering, Clustering, and the Synchronization of Faults

Large earthquakes are sometimes observed to trigger other large earthquakes on nearby faults. The magnitudes of the calculated Coulomb stress transfers presumed to cause the triggering are 10-2–10-3 of the earthquake stress drops. The earthquake stress drops and the triggering delay times are similarly small with respect to the natural recurrence time of the earthquakes. This requires that both faults be simultaneously very close to the ends of their seismic cycles. Paleoseismological data show that for the same regions prior earthquakes have occurred in clusters of ruptures of several faults separated by long quiescent periods. Both observations suggest that synchronization is occurring between faults. Theory and observations indicate that synchronization can occur between nearby faults with positive stress coupling and intrinsic slip velocities within an entrainment threshold. In the south Iceland seismic zone, the central Nevada seismic belt, and the eastern California shear zone, several synchronous clusters that apparently act independently can be recognized. This behavior is the 3D equivalent of the phase locking that results in the seismic cycle of individual faults being dominated by large characteristic earthquakes, and for synchronization of fault segments along a given fault. Rupture patterns of repeated individual earthquakes or earthquake clusters are not identical in either the 2D or 3D cases. The state of this system, which exhibits strong indications of synchrony without exact repetition, may be called fuzzy synchrony.

A possible explanation for difference in stress drop between intraplate and interplate earthquakes

It is known from observations that stress drop of intraplate earthquakes is larger than that of interplate earthquakes on average. I present a mechanical model for explaining the difference in stress drop, where an intraplate fault is assumed to be loaded uniformly, while a locked area (an asperity) on a plate boundary is nonuniformly loaded by surrounding aseismic sliding. A numerical simulation is conducted to quantitatively evaluate the difference in stress drop for different loading processes. Because the model intraplate fault is uniformly loaded, stress drop is uniform over the fault with a larger average value. In contrast, stress concentration is generated at a boundary region between locked area and aseismic sliding area for a model interplate earthquake. This stress concentration hastens earthquake occurrence, resulting in lower average stress drop. The stress drop of simulated intraplate earthquakes is several tens percent larger than that of simulated interplate earthquakes.

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.

Statistics of Earthquake Stress Drops on a Heterogeneous Fault in an Elastic Half-Space

We investigate properties of earthquake stress drops in simulations of evolving seismicity and stress field on a heterogeneous fault. The model consists of an inherently discrete strike-slip fault surrounded by a 3D elastic half-space. We consider various spatial distributions of frictional properties and analyze results generated by 150–300 model years. In all cases, the self-organized heterogeneous initial stress distributions at the times of earthquake failure lead to stress drops that are systematically lower than those predicted for a homogeneous process. In particular, the large system-sized events have stress drops that are consistently ∼25% of predictions based on the average fault strength. The type and amount of assumed spatial heterogeneity on the fault affect the stress-drop statistics of small earthquakes ( M L <5) more than those of the larger events. This produces a decrease in the range of stress drops as the earthquake magnitudes increase. The results can resolve the discrepancy between traditional estimates of stress drops and seismological observations. The general tendency for low stress drops of large events provides a rationale for reducing the statistical estimates of potential ground motion associated with large earthquakes.

Determination of the pore fluid pressure ratio at seismogenic megathrusts in subduction zones: Implications for strength of asperities and Andean‐type mountain building

We construct the differential stress profile across the fore arc in a subduction zone from the force balance between the shear stress, τ, at seismogenic megathrust and the lithostatic pressure. We assume that τ is written by μ (1 − λ) σn, where λ is the pore fluid pressure ratio, μ is the coefficient of static friction, and σn is the normal stress. Given a density structure of the fore‐arc wedge, we determine λ by comparing calculated fore‐arc stresses with observed ones, as 0.95–0.98 in Shikoku, Miyagi, Peru, north Chile, and south Chile and 0.90–0.93 in south Vancouver Island and Washington. The parameter τ averaged over the seismogenic megathrust is of the order of ∼10 MPa. Stress drops of great earthquakes in these zones occupy 14–87% and not a constant fraction of τ. They, on the other hand, increase linearly with 1 − λ. We propose a simple fault model in which the area of asperities as a fraction of the total fault area is proportional to 1 − λ. Variation of fractional area of asperities thus may explain the observed correlation and the regional variation of λ. Assuming that the differential stress at summit of the Andean mountains is zero, not at the coast as observed at present, we determine λ to be 0.84 in north Chile in the mountain building stage. Such a smaller value of λ, along with λ &lt; ∼0.4 in collision zones previously obtained and &gt;∼0.9 in subduction zones, would suggest that variation of λ controls the tectonic style of the Earth.

Constant Stress Drop from Small to Great Earthquakes in Magnitude-Area Scaling

Abstract Earthquakes span a tremendous range of scales, more than 5 orders of magnitude in length. Are earthquakes fundamentally the same across this huge range of scales, or are the great earthquakes somehow different from the small ones? We show that a robust scaling law seen in small earthquakes, with stress drops being independent of earthquake size, indeed holds for great earthquakes as well. The simplest hypothesis, that earthquake stress drops are constant from the smallest to the largest events, combined with a more thorough treatment of the geometrical effects of the finite seismogenic layer depth gives a new magnitude-area scaling that matches the data well and matches the data better over the whole magnitude range than the currently used scaling laws, which have nonconstant stress-drop scaling. This has significant implications for earthquake physics and for seismic hazard estimates.

Intraplate and interplate earthquakes in Chilean subduction zone: A theoretical and observational comparison

During the last decade, efforts to improve our knowledge of great Chilean earthquakes have shown that not all of the major destructive events have occurred in the contact between the Nazca and south American plates (interplate earthquakes). Waveform analysis of records from the Ms = 8.0, 1950 Antofagasta and the Ms = 7.8, 1939 Chillán earthquakes have shown that these large events are tensional, rupturing along nearly vertical, intermediate depth, fault planes within the subducting slab (intraplate events). Previous studies found that other earthquakes in Chile, like Santiago 1945 (Ms = 7.1), La Ligua 1965 (Ms = 7.1), Tal-tal 1965 (Ms = 6.9), Tocopilla 1970 (Ms = 6.5), and Tarapacá 2005 (Mw = 7.8) were also of tensional type. In the present work, we analyze theoretical and observational evidence comparing interplate and intraplate earthquakes. We found clear differences in the source characteristics between these two kinds of events, with intermediate depth, intraplate earthquakes presenting larger corner frequencies and greater seismic energy release than interplate events (for a given seismic moment). This is also reflected in the higher averaged apparent stress drop for intraplate earthquakes ( σ a ∼ 90 bar) compared to interplate events ( σ a ∼ 30 bar). From theoretical computations, we found that the rupture velocity has a minor effect on the resulting displacements; while directivity and changes in the static stress drop produced notable (and similar) results. We believe that the differences found in the data might be due to changes in the static stress drop, the effect of directivity, or both. Regardless of the cause of the observed differences in the apparent stress drop, these results should be taken into consideration into the assessment of the Seismic Hazard in Chile.

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.

Power law relationship between parameters of earthquakes and precursory electrical phenomena

Abstract. A number of Seismic Electric signals data have been accumulated during the last two decades that also includes the signals observed before the magnitude 6 class earthquakes that occurred in Greece very recently i.e., the first two months of 2008. Using all the available data we investigate whether a possible interconnection exists between the lead time of Seismic Electric Signals and the stress drop of subsequent earthquakes. We show that for "non thrust" earthquakes a power law relation emerges with an exponent value around 0.29, the possible physical meaning of which is discussed. This value is very close to the range of critical exponents that govern the fracture processes and is also comparable with the value of the slope, found much earlier by the VAN group, in the linear relation between the logarithm of the SES amplitude and the earthquake magnitude.

Slip-Length Scaling in Large Earthquakes: The Role of Deep-Penetrating Slip below the Seismogenic Layer

Coseismic slip is observed to increase with earthquake rupture length for lengths far beyond the length scale set by the seismogenic layer. The observation, when interpreted within the realm of static dislocation theory and the imposed limit that slip be confined to the seismogenic layer, implies that earthquake stress drop increases as a function of rupture length for large earthquakes and, hence, that large earthquakes differ from small earthquakes. Here, a three-dimensional elastodynamic model is applied to show that the observed increase in coseismic slip with rupture length may be satisfied while maintaining a constant stress drop across the entire spectrum of earthquake sizes when slip is allowed to penetrate below the seismogenic layer into an underlying zone characterized by velocity-strengthening behavior. Is this deep coseismic slip happening during large earthquakes? We point to a number of additional associated features of the model behavior that are potentially observable in the Earth. These include the predictions that a substantial fraction, on the order of one-third of the total coseismic moment, is due to slip below the seismogenic layer and that slip below the seismogenic layer should be characterized by long rise times and a dearth of high-frequency motion.

Scaling Relations of Strike-Slip Earthquakes with Different Slip-Rate-Dependent Properties at Depth

Abstract Empirical observations suggest that earthquake stress drop is generally constant. To investigate the effect of rupture width on earthquake scaling relations, we analyze synthetic seismicity produced by a 3D vertical strike-slip fault model using two different profiles of frictional slip-rate behavior below the seismogenic zone. Within the rate-and-state framework, a relatively abrupt transition of the a – b profile from velocity weakening to strengthening at the base of the seismogenic crust produces increasing slip and stress drop with increasing event size. Choosing a smoother transition allows large earthquakes to propagate deeper, leading to similar slip-length scaling but constant stress-drop scaling. Our numerical experiments support the idea that the maintenance of constant stress drop across the entire range of observed earthquake magnitudes may be achieved by allowing coseismic slip to rupture to depths below the seismogenic layer.

Possible relationship between Seismic Electric Signals (SES) lead time and earthquake stress drop

Stress drop values for fourteen large earthquakes with MW ≥ 5.4 which occurred in Greece during the period 1983–2007 are available. All these earthquakes were preceded by Seismic Electric Signals (SES). An attempt has been made to investigate possible correlation between their stress drop values and the corresponding SES lead times. For the stress drop, we considered the Brune stress drop, ΔσB, estimated from far field body wave displacement source spectra and ΔσSB derived from the strong motion acceleration response spectra. The results show a relation may exist between Brune stress drop, ΔσB, and lead time which implies that earthquakes with higher stress drop values are preceded by SES with shorter lead time.

An Analysis of the Mw 4.7 Jabalpur, India, Earthquake of 16 October 2000: Toward Ground-Motion Estimation in the Region from Future Events

With the aim of ground-motion estimation in the region of Jabalpur, India, which suffered serious damage during the 21 May 1997 earthquake ( M w 5.8), we analyze an event that occurred on 16 October 2000. This earthquake was recorded by broadband seismic stations of Jabalpur (jpbl, Δ = 45 km) and Rewa (rewa, Δ = 173 km), and a few other stations at regional distances. Seismic phases constrain the depth of the focus to 27 km. Regional centroid moment tensor inversion of long- period waves at farther stations (Δ > 250 km) yields a focal mechanism with one of the nodal planes characterized by: strike φ = 57°, dip δ = 43°, and rake λ = 22°. A similar focal mechanism is obtained from the inversion of filtered JBPL and rewa data. Compared with the earthquake of 2000, the 1997 event was deeper (36 km) and the corresponding nodal plane ( φ = 61°, δ = 64°, and λ = 74°) involved less strike-slip component. The seismic moment obtained from S -wave spectra is 1.36 × 10 16 N m ( M w 4.7). Within the framework of the ω 2 -source model, the high-frequency level of the source spectrum of the 2000 event requires Δ σ = 42 MPa. The same Δ σ was estimated for the 1997 earthquake, suggesting that the stress drop of subcrustal earthquakes in the Jabalpur region may, in general, be high. We simulate ground motions at JBLP site assuming a ω 2 -source model and Δ σ = 42 MPa and using the random vibration theory (rvt) and the empirical Green’s function technique. The predicted attenuation curves from rvt fit observed peak ground acceleration (pga) and peak ground velocity (pgv) data from the events of 2000 and 1997 (45 R 2 and 4.5 cm/sec, respectively, in the epicentral region during the 1997 Jabalpur earthquake. The corresponding values for the proposed maximum credible earthquake in the Jabalpur area ( M w 6.5, h = 30 km, Δ = 20 km) are 235 cm/sec 2 and 13 cm/sec, respectively. The simulated ground motions at JBPL, with Δ σ = 42 MPa, along with the transfer functions now available from an extensive microzonation study of the area, may be used to predict ground motions in the Jabalpur area during future earthquakes.

"Did You Feel It?" Intensity Data: A Surprisingly Good Measure of Earthquake Ground Motion

The U.S. Geological Survey is tapping a vast new source of engineering seismology data through its “Did You Feel It?” (DYFI) program, which collects online citizen responses to earthquakes. To date, more than 750,000 responses have been compiled in the United States alone. The DYFI data make up in quantity what they may lack in scientific quality and offer the potential to resolve longstanding issues in earthquake ground-motion science. Such issues have been difficult to address due to the paucity of instrumental ground-motion data in regions of low seismicity. In particular, DYFI data provide strong evidence that earthquake stress drops, which control the strength of high-frequency ground shaking, are higher in the central and eastern United States (CEUS) than in California. Higher earthquake stress drops, coupled with lower attenuation of shaking with distance, result in stronger overall shaking over a wider area and thus more potential damage for CEUS earthquakes in comparison to those of equal magnitude in California—a fact also definitively captured with these new DYFI data and maps.