Alon Ziv

Static stress transfer and earthquake triggering: No lower threshold in sight?

The main objective of this study is to see if a lower threshold for earthquake triggering exists. Resolving this issue is important for the understanding of earthquake mechanics and for the purpose of hazard analysis. We compute the cumulative static stress changes imposed on 63 M > 4.5 earthquakes in central California between 1969 and 1998, by adding the stress changes imposed by all previous M > 4.5 earthquakes as a function of time prior to the events. We find that 85% of the cumulative stress changes at the time of rupture are positive for stress change magnitudes of >10 kPa (>0.1 bar), and 70% are positive for stress changes of <10 kPa (< 0.1 bar) as well as <1 kPa (<0.01 bar). A comparison between these results and those obtained for synthetic catalogs, in which the timing or focal mechanisms of the earthquakes were randomized, shows that this degree of triggering is very unlikely to be found in a random catalog. Thus we conclude that no lower threshold for earthquake triggering in central California has been found. We show that the temporal distribution of stress changes that discourage failure is consistent with the theoretical prediction that the time delay increases with the magnitude of the stress change.

Stability of dike intrusion along preexisting fractures

We investigate the ability of magma to propagate along preexisting fractures oblique to the least compressive stress. Relaxation of the preexisting shear stress to zero over the portion of the fracture dilated by magma (the dike) results in slip for some distance along the closed portion of the fracture ahead of the dike tip and a stress concentration near the dike tip. This could lead to the production of new tensile cracks, oblique to the parent dike, that could capture the flow. If the shear stress resolved on the fracture plane is perpendicular to the fracture front (mode I-II), the front may deviate along its entire length; if the shear stress is parallel to the fracture front (mode I-III) the front may splay into segments. For mode I-II dikes the maximum tensile stress occurs at the dike tip and is parallel to the dike. If the effective tensile stress exceeds the rock tensile strength, then the intruding magma, rather than dilating the existing fracture, is expected to propagate into a self-generated crack analogous to the “wing cracks” observed to form at the tips of pure mode II fractures. For mode I-III dikes the maximum tensile stress lies within the plane of the dike and is oriented at some angle that depends upon the far-field boundary conditions. Even if the magma pressure exceeds the ambient normal stress, it appears to be very difficult for dikes to intrude into preexisting fractures unless one or more of the following conditions is satisfied: (1) the fracture is nearly perpendicular to the least compressive stress; (2) the resolved shear stress on the fracture is small compared to the excess magma pressure (i.e., the ratio of shear to opening of the dike walls is small); (3) the effective ambient dike-normal stress is small compared to the rock tensile strength. This indicates that it may be quite difficult for dikes emerging from midcrustal to lower crustal depths to follow faults.

Sinkhole precursors along the Dead Sea, Israel, revealed by SAR interferometry

The water level in the Dead Sea (Israel and Jordan) has been dropping at an increasing rate since the 1960s, exceeding one meter per year during the last decade. This drop has triggered the formation of sinkholes and widespread land subsidence along the Dead Sea shoreline, resulting in severe economic loss and infrastructural damage. In this study, the spatiotemporal evolution of sinkhole-related subsidence and the effect of human activities and land perturbation on sinkhole development are examined through interferometric synthetic aperture radar measurements and field surveys conducted in Israel during 2012. Interferograms are generated using COSMO-SkyMed satellite images and a high-resolution (0.5 m/pixel) elevation model obtained from LiDAR measurements. As a result of this unique combination of high-resolution data sets, millimeter-scale subsidence has been resolved in both natural and human-disturbed environments. Precursory subsidence over a period of a few months occurred before the collapse of all three sinkhole sites reported in this study. The centers of the subsiding areas migrated, possibly due to progressive dissolution and widening of the underlying cavities. Filling of newly formed sinkholes with gravel, and mud injections into drill holes, seem to enhance land subsidence, enlarge existing sinkholes, and form new sinkholes. Apart from shedding light on the mechanical process, the results of this study may pave the way for the implementation of an operational sinkhole early-warning system.

Real‐Time Back Azimuth for Earthquake Early Warning

Abstract The incentive to speed up real‐time location has motivated previous researchers to go beyond standard location procedures and use not only P ‐wave arrival at some network stations but also its nonarrival at others. In addition to being sensitive to velocity model and picking uncertainties, this approach is also highly dependent on time delays due to unknowns network latencies, processing, and packet size. Thus, seeking ways to add independent real‐time constraints on earthquake location are important for earthquake early warning applications. In this study, we assess the robustness of three independent real‐time back‐azimuth (BAZ) determination schemes, using offline records of southern California earthquakes. We find that BAZ values computed by the three methods provide equivalent levels of accuracy. By sending the three BAZ estimates to a screening module that checks for coherency and signal‐to‐noise ratio criteria, we show that accurate BAZ estimates are obtainable in real time, with a standard deviation of 13°. Through examination of two earthquake scenarios that use offline data, we show that the inclusion of BAZ estimates into real‐time location schemes improves the performance of real‐time hypocenter determination, by cutting the time it takes to obtain well‐constrained hypocenters.

P‐Wave Attenuation with Implications for Earthquake Early Warning

Several widely implemented and tested earthquake early warning algorithms employ empirical equations that relate earthquake magnitudes with ground‐motion peak amplitudes and hypocentral distances. This approach is effective to the extent that the offline dataset available for setting the fitting coefficients in those equations is of sufficient quality and quantity. However, to address the problem of having a limited dataset, it is instructive to gain physical understanding of the main factors controlling the P ‐wave attenuation. In this study, theoretical expressions are derived that relate the root mean square (rms) of the P ‐wave displacement d rms and velocity v rms to the seismic moment, stress drop, and hypocentral distance.nnThe theoretical attenuation laws are then validated against observed attenuation, using earthquake data from southern California and Japan. Good agreement is found between observed and predicted ground motions. The similar ground‐motion attenuation in California and Japan suggests that the attenuation laws are similarly applicable for the two regions and implies that they may also be implemented in other regions without having to go through a lengthy calibration phase.nnBecause d rms is more strongly dependent on the seismic moment than v rms, use of the attenuation law for d rms yields better magnitude prediction than that of v rms. It is shown that the d rms‐to‐ v rms ratio is proportional to the characteristic length of the rupture and that the stress drop is a function of the seismic moment and the cube of d rms/ v rms. This result paves the way for a new stress‐drop determination scheme that is totally independent of previously used approaches. Finally, it is shown that the rms of the ground motions are proportional to their peak values.

The Relation between Ground Acceleration and Earthquake Source Parameters: Theory and Observations

Abstract A simple relation between the root mean square (rms) of the ground acceleration and earthquake spectral (or source) parameters is introduced: in which Ω 0 is the low‐frequency displacement spectral plateau, f 0 is the corner frequency, κ is an attenuation parameter, and T is the data interval. This result uses the omega‐square model for far‐field radiation and accounts for site‐specific attenuation. The main advantage of the new relation with respect to that of Hanks (1979) is that it relaxes the simplifying assumption that the spectral corner frequency is much smaller than the maximum corner frequency resulting from attenuation, and that the spectrum may be approximated as being perfectly flat between the two frequencies. The newly proposed relation is tested using a composite dataset of earthquake records from Japan, California, Mexico, and Taiwan. Excellent agreement is found between observed and predicted ground acceleration for any combination of corner frequencies. Thus, use of the above relation enables the extrapolation of ground‐motion prediction equation inferred from the frequent small‐magnitude earthquakes to the rare large magnitudes. This capacity is extremely useful near slow‐slip plate boundaries, where the seismic moment release rates are low.

Real‐Time Moment Magnitude and Stress Drop with Implications for Real‐Time Shaking Prediction

Abstract Despite the potentially dramatic effect of the stress drop on ground‐motion intensity, currently available earthquake early warning systems that deliver peak ground‐motion predictions do not account for the effect of this parameter. To address this issue, a new evolutionary algorithm for determining stress drop and moment magnitude in real time is described. It consists of two distinct modules: one processes data recorded by individual stations and another computes event‐average stress drops and moment magnitudes. To speed up the analysis, the real‐time algorithm deviates from standard procedures of stress‐drop determination in several ways. Because these time‐saving measures come at the price of accuracy, a quality‐control parameter is introduced, which quantifies the discrepancy between the observed and modeled ground motion. The results of implementing the algorithm offline using KiK‐borehole data from Japan are presented. It is shown that it is possible to recover the moment magnitudes and the stress drops in real time. Two example timelines of seismic moment and stress drop are presented. These show that the source parameters of small‐to‐moderate earthquakes may be estimated quite accurately within 5 to 10xa0s since the first trigger, whereas those of larger magnitudes (i.e., M w >6) take 20–30xa0s. Finally, ground‐motion prediction equations for the velocity’s root mean square and peak ground velocity are presented. Once the epicenter, seismic moment, and stress drop are determined using a few stations nearest to the epicenter, their values can be input into those equations to get the ground‐motion intensity at sites further away from it.

The Relation Between Ground Motion, Earthquake Source Parameters, and Attenuation: Implications for Source Parameter Inversion and Ground Motion Prediction Equations

Theoretical equations relating the root-mean-square (rms) of the far-field ground motions with earthquake source parameters and attenuation are derived for Brune’s omega-squared model that is subject to attenuation. This set of model-based predictions paves the way for a completely new approach for earthquake source parameter inversion and forms the basis for new physics-based ground motion prediction equations (GMPEs). The equations for ground displacement, velocity, and acceleration constitute a set of three independent equations with three unknowns: the seismic moment, the stress drop, and the attenuation parameter. These are used for source parameter inversion that circumvents the time-to-frequency transformation. Initially, the two source parameters and the attenuation constant are solved simultaneously for each seismogram. Sometimes, however, this one-step inversion results in ambiguous solutions. Under such circumstances, the procedure proceeds to a two-step approach, in which a station-specific attenuation parameter is first determined by averaging the set of attenuation parameters obtained from seismograms whose one-step inversion yields well-constrained solutions. Subsequently, the two source parameters are solved using the averaged attenuation parameter. It is concluded that the new scheme is more stable than a frequency domain method, resulting in considerably less within-event source parameter variability. The above results together with rms-to-peak ground motion relations are combined to give first-order GMPEs for acceleration, velocity, and displacement. In contrast to empirically based GMPEs, the ones introduced here are extremely simple and readily implementable, even in low-seismicity regions, where the earthquake catalog lacks strong ground motion records.

Array‐Based Earthquake Location for Regional Earthquake Early Warning: Case Studies from the Dead Sea TransformArray‐Based Earthquake Location for Regional Earthquake Early Warning

Constraining earthquake locations with as few stations as possible is crucial for earthquake early warning. In this study, a new real-time array-based location algorithm is introduced that consists of two modules. The first is a single standalone array module that monitors waveform slowness and back azimuth in a continuous manner and identifies Pand S-phase arrivals. The second is a multiarray module that intersects multiple back-azimuth estimates and surfaces of equal differential arrivals of the P phase. Initial location estimates are issued either by the standalone module, after the S-phase arrival to the first array, or by the multiple arrays module after the P phase arrives to a second array. Location estimates are subsequently updated with data made available by additional arrays. This approach is validated with 10 earthquakes recorded by small-aperture arrays deployed along the Dead Sea Transform. Use of real-time array methodology is particularly suited to environments with sparse network and/or unfavorable source–station configurations.

Reconditioning fault slip inversions via InSAR data discretization

A major difficulty in inverting geodetic data for fault slip distribution is that measurement errors are mapped from the data space onto the solution space. The amplitude of this mapping is sensitive to the condition number of the inverse problem, i.e., the ratio between the largest and smallest singular value of the forward matrix. Thus, unless the problem is well-conditioned, slip inversions cannot reveal the actual fault slip distribution. In this study, we describe a new iterative algorithm that optimizes the condition of the slip inversion through discretization of InSAR data. We present a numerical example that demonstrates the effectiveness of our approach. We show that the condition number of the reconditioned data sets are not only much smaller than those of uniformly spaced data sets with the same dimension but are also much smaller than non-uniformly spaced data sets, with data density that increases towards the model fault.