Numerical Modeling of Transient Seismic Fields in Viscoelastic Media Based on the Laguerre Spectral Method

--The wave propagation in real media can be described within the theory of linear viscoelasticity. The presence of convolutional integral in Boltzmann's superposition principle poses the main difficulties in implementing the direct numerical methods in time domain. The paper presents a new algorithm, based on the application of the spectral Laguerre method for the approximation of temporal derivatives and convolution as applied to the problem of seismic wave propagation in the heterogeneous viscoelastic medium. Examples of the calculation of synthetic seismograms for different models of viscoelastic media are presented.     

3-D Viscoelastic FEM Modeling of Crustal Deformation in Northeast Japan

-- As a first step toward establishing a standard earthquake cycle model in Japan, we simulate the crustal deformation during the past 100 years in northeast Japan, using a 3-D FEM based on the kinematic model. Then, we compare the computed results with the observed long-term leveling data and the recent GPS data. On the whole, although the effect of the subducting PAC is dominant, coseismic deformation of the interplate earthquakes can be clearly seen in the inland. Moreover, the postseismic deformation of the earthquakes due to the viscoelastic upper mantle seriously affects the inland movements, and continues for a few decades. Our modeling, including the effects of the interplate earthquakes and the three-dimensional viscoelastic inhomogeneity, reasonably explains the observed movement. Finally, we stress that the viscoelastic effect should be taken into consideration in the analyses, even if no earthquakes occur in the analyzed period.     

Thermal-mechanical Coupling in Shear Deformation of Viscoelastic Material as a Model of Frictional Constitutive Relations

-- We propose a thermal-mechanical model of shear deformation of a viscoelastic material to describe the temperature-dependence of friction law. We consider shear deformation of one-dimensional layer composed of a Maxwell linear viscoelastic material under a constant velocity V and temperature T_w at the boundary. The strain rate due to viscous deformation depends both on temperature and shear stress. The temperature inside the layer changes owing to frictional heating and conductive cooling. Steady-state calculations show that the sign of d†^ss/dV, where †^ss is steady-state stress, changes from positive to negative as V increases, and that the threshold velocity above which the sign of d†^ss/dV is negative increases with increasing T_w. These results are in accordance with the conjecture that the downdip limit of seismogenic zones is marked by the transition in the sign of d†^ss/dV due to temperature rise with depth. We also find that the response of steady state to a step change in V is quite similar to the response of frictional slip with constitutive laws which employ state variables. These findings suggest that by further improving the present model a model of constitutive relations along faults or plate boundaries can be developed which contains temperature-dependence in a physically-sound manner.     

Calibration of the Regional Crustal Waveguide and the Retrieval of Source Parameters Using Waveform Modeling

v--vRegional crustal waveguide calibration is essential to the retrieval of source parameters and the location of smaller (M < 4.8) seismic events. This path calibration of regional seismic phases is strongly dependent on the accuracy of hypocentral locations of calibration (or master) events. This information can be difficult to obtain, especially for smaller events. Generally, explosion or quarry blast generated travel-time data with known locations and origin times are useful for developing the path calibration parameters, but in many regions such data sets are scanty or do not exist. We present a method which is useful for regional path calibration independent of such data, i.e. with earthquakes, which is applicable for events down to M_w = 4 and which has successfully been applied in India, central Asia, western Mediterranean, North Africa, Tibet and the former Soviet Union. These studies suggest that reliably determining depth is essential to establishing accurate epicentral location and origin time for events. We find that the error in source depth does not necessarily trade-off only with the origin time for events with poor azimuthal coverage, but with the horizontal location as well, thus resulting in poor epicentral locations. For example, hypocenters for some events in central Asia were found to move from their fixed-depth locations by about 20 km. Such errors in location and depth will propagate into path calibration parameters, particularly with respect to travel times. The modeling of teleseismic depth phases (pP, sP) yields accurate depths for earthquakes down to magnitude M_w = 4.7. This M_w threshold can be lowered to four if regional seismograms are used in conjunction with a calibrated velocity structure model to determine depth, with the relative amplitude of the P_nl waves to the surface waves and the interaction of regional sPmP and pPmP phases being good indicators of event depths. We also found that for deep events a seismic phase which follows an S-wave path to the surface and becomes critical, developing a head wave by S to P conversion is also indicative of depth. The detailed characteristic of this phase is controlled by the crustal waveguide. The key to calibrating regionalized crustal velocity structure is to determine depths for a set of master events by applying the above methods and then by modeling characteristic features that are recorded on the regional waveforms. The regionalization scheme can also incorporate mixed-path crustal waveguide models for cases in which seismic waves traverse two or more distinctly different crustal structures. We also demonstrate that once depths are established, we need only two-stations travel-time data to obtain reliable epicentral locations using a new adaptive grid-search technique which yields locations similar to those determined using travel-time data from local seismic networks with better azimuthal coverage.     

3-D Simulation of Earthquake Generation Cycles and Evolution of Fault Constitutitve Properties

--The earthquake generation cycle consists of tectonic loading, quasi-static rupture nucleation, dynamic rupture propagation and stop, and subsequent stress redistribution and fault restrengthening. From a macroscopic point of view, the entire process of earthquake generation cycles should be consistently described by a coupled nonlinear system of a slip-response function, a fault constitutive law and a driving force. On the basis of such a general idea, we constructed a realistic 3-D simulation model for earthquake generation cycles at a transcurrent plate boundary by combining the viscoelastic slip-response function derived for a two-layered elastic-viscoelastic structure model, the slip- and time-dependent fault constitutive law that has an inherent mechanism of fault restrengthening, and the steady relative plate motion as a driving force into a single closed system. With this model we numerically simulated the earthquake generation cycles repeated in a seismogenic region on a plate interface, and examined space-time changes in shear stress, slip deficits and fault constitutive properties during one complete cycle in detail. The occurrence of unstable dynamic slip brings about decrease both in fault strength and shear stress to a constant residual level. After the arrest of dynamic slip, the breakdown strength drop j†_p of fault is restored rapidly and the process of stress accumulation resumes in the seismogenic region. On the other hand, the restoration of the critical weakening displacement D_c proceeds gradually with time through the interseismic period. The restoration of D_c can be regarded as the macroscopic manifestation of the microscopic recovery process of fractal fault surface structure. Through numerical simulation with a multi-segmented fault model, we examined the effects of viscoelastic fault-to-fault interaction. The effect of transient viscoelastic stress transfer through the asthenosphere is significant as well as the direct effect of elastic stress transfer, and it possibly explains the time lag of the sequential occurrence of large events along a plate boundary.     

Large Amplitude Folding in Finely Layered Viscoelastic Rock Structures

--We analyze folding phenomena in finely layered viscoelastic rock. Fine is meant in the sense that the thickness of each layer is considerably smaller than characteristic structural dimensions. For this purpose we derive constitutive relations and apply a computational simulation scheme (a finite-element based particle advection scheme; see Moresi et al., 2001) suitable for problems involving very large deformations of layered viscous and viscoelastic rocks. An algorithm for the time integration of the governing equations as well as details of the finite-element implementation is also given. We then consider buckling instabilities in a finite, rectangular domain. Embedded within this domain, parallel to the longer dimension we consider a stiff, layered plate. The domain is compressed along the layer axis by prescribing velocities along the sides. First, for the viscous limit we consider the response to a series of harmonic perturbations of the director orientation. The Fourier spectra of the initial folding velocity are compared for different viscosity ratios.¶Turning to the nonlinear regime we analyze viscoelastic folding histories up to 40% shortening. The effect of layering manifests itself in that appreciable buckling instabilities are obtained at much lower viscosity ratios (1:10) as is required for the buckling of isotropic plates (1:500). The wavelength induced by the initial harmonic perturbation of the director orientation seems to be persistent. In the section of the parameter space considered here elasticity seems to delay or inhibit the occurrence of a second, larger wavelength.¶Finally, in a linear instability analysis we undertake a brief excursion into the potential role of couple stresses on the folding process. The linear instability analysis also provides insight into the expected modes of deformation at the onset of instability, and the different regimes of behavior one might expect to observe.     

Interplate Earthquake Fault Slip During Periodic Earthquake Cycles in a Viscoelastic Medium at a Subduction Zone

--A 2-D finite-element-method (FEM) numerical experiment of earthquake cycles at a subduction zone is performed to investigate the effect of viscoelasticity of the earth on great interplate earthquake fault slip. We construct a 2-D viscoelastic FEM model of northeast Japan, which consists of an elastic upper crust and a viscoelastic mantle wedge under gravitation overlying the subducting elastic Pacific plate. Instead of the dislocation model prescribing an amount of slip on a plate interface, we define an earthquake cycle, in which the plate interface down to a depth is locked during an interseismic period and unlocked during coseismic and postseismic periods by changing the friction on the boundary with the master-slave method. This earthquake cycle with steady plate subduction is periodically repeated to calculate the resultant earthquake fault slip.¶As simulated in a previous study (Wang, 1995), the amount of fault slip at the first earthquake cycle is smaller than the total relative plate motion. This small amount of fault slip in the viscoelastic medium was considered to be one factor explaining the small seismic coupling observed at several subduction zones. Our simulation, however, shows that the fault slip grows with an increasing number of repeated earthquake cycles and reaches an amount comparable to the total relative plate motion after more than ten earthquake cycles. This new finding indicates that the viscoelasticity of the earth is not the main factor in explaining the observed small seismic coupling. In comparison with a simple one-degree-of-freedom experiment, we demonstrate that the increase of the fault slip occurs in the transient state from the relaxed initial state to the stressed equilibrium state due to the intermittent plate loading in a viscoelastic medium.     

Direct Assessment of Wood’s Metal Wettability on Quartz

--A tensiometric method (Wilhelmy plate) is used to study Wood's metal dynamic wettability on specially prepared surfaces of quartz single crystals at low velocities of immersion (2 to 16 wm/s). After correction for buoyancy, the force exerted on the plate by the molten metal is used to derive the unit work of wetting n cos Š where n is the Wood's metal surface tension and Š is the interfacial contact angle. Tests at different temperatures (85, 120 and 200°C) show that below 120°C, viscosity effects cannot be neglected. At an immersion/emersion rate of 2 wm/s, n cos Š is in the range 0.417-0.444 N/m at 120°C, and 0.432-0.458 N/m at 200°C. These figures allow the conversion of injection pressures into capillary diameters during Wood's metal injection tests. The method is promising since it may be used in porous materials to check the sensitivity of the unit work of wetting n cos Š to parameters such as roughness and mineralogy, which are known to vary in a wide range within the pores and cracks of rocks.     

Physical Modeling Results on Modified Pseudo-depth Sections in Exploration of Highly Resistive Targets – II

-- This work extends the results that Apparao et al. (1997a) obtained for a vertical resistive sheet to the case of inclined resistive sheet models for different electrode arrays. It is found that the depth of investigation (DI) remains the same as that for the vertical target. Using this DI, modified pseudo-depth sections have been constructed over sheet models at different inclinations. It is noted that, for the Wenner array, the maximum anomaly contours fall directly over the target cross section. For dipole-dipole and three-electrode arrays, these contours fall on the up-dip side of the dipping target, with the maximum anomaly contour matching the depth level of the top of the target. It is also observed that the target cross section is at a distance of about 0.33L (L/3) from the maximum anomaly value/contour position for the three-electrode array and 0.25L (L/4) for the dipole-dipole system. These features are identifiable in the individual profiles and may help field geophysicists in the recognition and location of dipping target bodies.     

3-D HLEM Modeling of Tropical Weathering: A Trial from a Granitic Area of N-W Rajasthan, India

--In a sand-covered granite terrain of northwestern Rajasthan, India, a five-frequency HLEM survey along a 10-km traverse line generated several clear and strong anomalies. Subjected to a joint constrained 1-D layered earth inversion, the IP and OP frequency soundings at each point of observation yields either no solution or one which is inconsistent with the adjacent point. On the other hand, a 3-D model fitting of these anomalies with a tabular body in a layered host leads to a more meaningful interpretation, suggesting the presence of (1) pockets of weathered conductive material and (2) resistive intruding dykes, embedded in a semi-weathered layer, as the cause of the observed anomalies. The locations of weathered pockets are probably determined by pre-existing weak structures such as joints, fractures and faults, which facilitated movement of groundwater and hence weathering. Thus covered features deep in the bedrock such as intrusives, joints, fractures and faults, which are not directly detectable by the HLEM method, being under a more conductive overburden, are indirectly detected through their imprints left in the overlying weathering profile.     

Optimized Seismic Threshold Monitoring – Part 2: Teleseismic Processing

v--vThis second paper (Part 2) pertaining to optimized site-specific threshold monitoring addresses the application of the method to regions covered by a teleseismic or a combined regional-teleseismic network. In the first paper (Part 1) we developed the method for the general case, and demonstrated its application to an area well-covered by a regional network (the Novaya Zemlya nuclear test site). In the present paper, we apply the method to the Indian and Pakistani nuclear test sites, and show results during the periods of nuclear testing by these two countries in May 1998. Since the coverage by regional stations in these areas is poor, an optimized approach requires the use of selected, high-quality stations at teleseismic distances.¶To optimize the threshold monitoring of these test sites, we use as calibration events either one of the nuclear explosions or a nearby earthquake. From analysis of the calibration events we derive values for array beamforming steering delays, filter bands, short-term averages (STA) lengths, phase travel times (P waves), and amplitude-magnitude relationships for each station. By applying these parameters, we obtain a monitoring capability of both test sites ranging from m_b 2.8-3.0 using teleseismic stations only. When including the nearby Nilore station to monitor the Indian tests, we show that the threshold can be reduced by about 0.4 magnitude units. In particular, we demonstrate that the Indian tests on 13 May, 1998, which were not detected by any known seismic station, must have corresponded to a magnitude (m_b) of less than 2.4.¶We also discuss the effect of a nearby aftershock sequence on the monitoring capability for the Pakistani test sites. Such an aftershock sequence occurred in fact on the day of the last Pakistani test (30 May, 1998), following a large (m_b 5.5) earthquake in Afghanistan located about 1100 km from the test site. We show that the threshold monitoring technique has sufficient resolution to suppress the signals from these interfering aftershocks without significantly affecting the true peak of the nuclear explosion on the threshold trace.     

Converted T Phases Recorded on Hawaii from Polynesian Nuclear Tests: A Preliminary Report

v--vWe present a preliminary study of T waves from Polynesian nuclear tests at Mururoa, recorded on digital stations of the Hawaii Volcano Observatory network, following their conversion to seismic waves at the southern shore of the Island of Hawaii, and subsequent propagation to the recording stations. We show that seismograms are composed of several packets, which can be interpreted as resulting from TMP and TMS conversions, and which feature distinct spectral characteristics. As the distance from the shoreline to the station increases, the relative importance of the several wave packets changes; a prominent shadow for TMP is found at 8-12 km from the shore. This pattern is affected by the local crustal structure; in a favorable case, propagation in deep, low-attenuation layers resulted in a clear record as far as 76 km from the shoreline. While these results are generally robust, they can be moderately affected by a change of location of the source inside Mururoa Atoll.     

A Hidden Markov Model Based Tool for Geophysical Data Exploration

--Unsupervised learning techniques provide a way of investigating scientific data based on automated generation of statistical models. Because these techniques are not dependent on a priori information, they provide an unbiased method for separating data into distinct types. Thus they can be used as an objective method by which to identify data as belonging to previously known classes or to find previously unknown or rare classes and subclasses of data. Hidden Markov model based unsupervised learning methods are particularly applicable to geophysical systems because time relationships between classes, or states of the system, are included in the model. We have applied a modified version of hidden Markov models which employ a deterministic annealing technique to scientific analysis of seismicity and GPS data from the southern California region. Preliminary results indicate that the technique can isolate distinct classes of earthquakes from seismicity data.     

The Skin Effect of the Anelastic Earth

--Assuming that the rheology of the earth's crust is defined by stress-strain relations containing a memory mechanism, it is seen that the stress field and the maximum shear stress (mss), caused by elongated mountain ranges, are limited mostly to the crust. In a geological, relatively short time, where relaxation is reached, the mss assumes the depth distribution (2~x)exp(-2~x) where x is the depth h measured in units of wavelength w of the mountain range; the mss reaches its maximum value, of about 1/3 the surface load, at the depth x = 1/2~ (x = h/w). Contrary to the case of the perfectly elastic earth model, where the mss at the surface is about 0.25 the maximum surface load, in the case of the anelastic earth model the mss is asymptotically nil at the surface and for depths larger than w, the mss is less than 1.2% the maximum surface load. It is seen that the relaxation of the medium causes a rotation of the planes of the mss in a layer near the surface and that, in the case when the surface load is applied periodically, there is a phase shift between the surface load and the stress at depth which is less than four days when the period is one year; it is smaller for shorter periods. It is also seen that the creation of reservoirs lasting a finite time causes a small variation of the mss in the crust which, when the reservoir is removed, leaves a residual mss with maximum at the surface and decreasing exponentially with depth; for a load lasting one year it takes 250 days to reduce to 40% the stress at depth. As a consequence of the residual mss, caused by the load of the topography, after earthquakes the local mss will not drop to zero; this decreases the time required by tectonic forces to release the next earthquake and increases the rate of seismicity.     

Sedimentary Basins and the Blockage of Lg Wave Propagation in the Continents

v--vThe phenomenon of "Lg blockage," where Lg is strongly attenuated by crustal heterogeneities, poses a serious problem to CTBT monitoring because Lg is an important seismic phase for discrimination. This paper examines blockage in three continental regions where the Lg blockages may be caused by large, enclosed sedimentary basins along the propagation path. The Barents Sea Basin blocks Lg propagation across the Barents Sea from the Russian nuclear test sites at Novaya Zemlya to Scandinavian stations. Also, "early Lg" waves are observed in Sn codas on NORSAR, NORESS, and ARCESS recordings of Novaya Zemlya explosions where direct Lg is blocked. Early Lg waves may have resulted from Sn-to-Lg mode conversion at the contact between the Barents Basin and the Kola Peninsula. The Northern and Southern Caspian Sea Basins also block Lg waves from PNEs and earthquakes, perhaps due to thick, low-velocity, low-Q sediments replacing the granitic layer rocks in the crust. Lg blockage has also been observed in the Western Mediterranean/Levantine Basin due to low-Q sediments and crustal thinning. A "basin capture" model is proposed to explain Lg blockage in sedimentary basins. In this model, shear waves that reverberate in the crust and constitute the Lg wave train are captured, delayed, and attenuated by thick, low-velocity sediments that replace the "granitic" layer rocks of the upper crust along part of the propagation path. Sn waves, which propagate below the basin, would not be blocked and in fact, the blocked Lg waves may be diverted downward into Sn waves by the low velocity sediments in the basin.     

Regional Seismic Wavefield Computation on a 3-D Heterogeneous Earth Model by Means of Coupled Traveling Wave Synthesis

-- I present a new algorithm for calculating seismic wave propagation through a three-dimensional heterogeneous medium using the framework of mode coupling theory originally developed to perform very low frequency (f < ~0.01т.05 Hz) seismic wavefield computation. It is a Greens function approach for multiple scattering within a defined volume and employs a truncated traveling wave basis set using the locked mode approximation. Interactions between incident and scattered wavefields are prescribed by mode coupling theory and account for the coupling among surface waves, body waves, and evanescent waves. The described algorithm is, in principle, applicable to global and regional wave propagation problems, but I focus on higher frequency (typically f S ~0.25 Hz) applications at regional and local distances where the locked mode approximation is best utilized and which involve wavefields strongly shaped by propagation through a highly heterogeneous crust. Synthetic examples are shown for P-SV-wave propagation through a semi-ellipsoidal basin and SH-wave propagation through a fault zone.     

A Method to Remove Electromagnetic Coupling from Induced Polarization Data for an "Exponential" Earth Model

--The electromagnetic (EM) coupling effect in induced polarization (IP) data is an important problem. In many works it has been computed only considering homogeneous or layered earth models with discretely uniform conductivity. In this study, an algorithm has been developed to compute the EM coupling effect in IP data measured on the earth, whose conductivity varies (increases or decreases) exponentially with depth. The EM coupling effects for Percent Frequency Effect (PFE) and phase data are computed for a dipole-dipole array with different separations, however the method can be applied to any electrode array. The results obtained for the cases of increasing and decreasing conductivity as a function of depth indicate that the EM coupling effect strongly depends on the subsurface resistivity and the dipole length. Here an "exponential" earth model is considered to remove EM coupling from the IP data in frequency and phase domain. For this purpose, first, the region of pseudo-section is divided into segments, and within each segment a typical average apparent resistivity („_a) curve is constructed. An exponential conductivity model is fitted to average „_a data. The conductivity model is then used to compute EM responses. Next the data are corrected for the EM coupling contribution. This decoupling process is applied to field data from a galenite-pyrite mineralization area at the Dolluk site, in western Turkey. The results from the decoupling method developed here are compared with other techniques.     

Simulation of the Influence of Rate- and State-dependent Friction on the Macroscopic Behavior of Complex Fault Zones with the Lattice Solid Model

-- In order to understand the earthquake nucleation process, we need to understand the effective frictional behavior of faults with complex geometry and fault gouge zones. One important aspect of this is the interaction between the friction law governing the behavior of the fault on the microscopic level and the resulting macroscopic behavior of the fault zone. Numerical simulations offer a possibility to investigate the behavior of faults on many different scales and thus provide a means to gain insight into fault zone dynamics on scales which are not accessible to laboratory experiments. Numerical experiments have been performed to investigate the influence of the geometric configuration of faults with a rate- and state-dependent friction at the particle contacts on the effective frictional behavior of these faults. The numerical experiments are designed to be similar to laboratory experiments by Dieterich and Kilgore (1994) in which a slide-hold-slide cycle was performed between two blocks of material and the resulting peak friction was plotted vs. holding time. Simulations with a flat fault without a fault gouge have been performed to verify the implementation. These have shown close agreement with comparable laboratory experiments. The simulations performed with a fault containing fault gouge have demonstrated a strong dependence of the critical slip distance D_c on the roughness of the fault surfaces and are in qualitative agreement with laboratory experiments.     

Earthquake Hazard Parameters in Crete Island and its Surrounding Area Inferred from Bayes Statistics: An Integration of Morphology of the Seismically Active Structures and Seismological Data

-- The study addresses the evaluation of earthquake hazard parameters such as maximum regional magnitude (M_max) and the slope of Gutenberg-Richter law # (where b=# log e) for the Hellenic Wadati-Benioff zone and the overriding lithospheric plate in the area of Crete and its surroundings. The seismicity of the area is divided in a cellular (1.0° 2 1.0°) manner allowing analysis of the localized earthquake hazard parameters and graphical representation of their spatial variation. Our approach incorporates the recently updated earthquake catalogue for Greece and the adjacent areas, the consideration of the morphology of the deep seismically active structures in the studied area and use of a probabilistic procedure for estimating the earthquake hazard parameters.¶One of the main inconsistencies in the earthquake hazard assessment is the estimation of the maximum magnitude and the related uncertaint y. The Bayesian approach, applied in the present, is a straightforward technique for evaluating the earthquake hazard parameters and is based on the following assumptions: Poissonian character of seismic events flow, a frequency-magnitude law of Gutenberg-Richter's type with cutoff maximal value for estimated parameter and a seismic catalogue, having a rather sizeable number of events (i.e., 50 events at least per cell). For five cells in which the number of events is less than 50, an effort is made to produce synthetic data. The re-assessed parameters obtained from the synthetic data show no significant difference and the real data (of the five cells) are finally taken into account although the estimated uncertainty is high.¶For four random cells we constructed hazard curves showing the probabilities that a certain magnitude M will be exceeded in one year and the return periods (in years) that are expected for a given magnitude. These are particularly useful for the mapping of earthquake hazard in regions of either low or high seismic activity, as is Crete and the adjacent area.¶The obtained results show that the W and E parts of both subducting and overriding plates differ in the spatial distribution of all the estimated earthquake hazard parameters. The M_max distribution indicates strong coupling between the western portions of the interacting plates (M_max > 6.3) to the south of 36°N. The smaller values of M_max (M_max < 6.3) estimated in the SE part of the studied area indicate weak coupling between the eastern portions of the subducting and overriding plates.¶Values of b > 1.0 are found to the south and east of Crete for the Wadati-Benioff zone, and over the central part of the island and the area to the northeast of it (cell 11) for the continental wedge, which suggests nonuniform stress field and/or heterogeneous material.     

Relocation of Swarm Events in the June 1987 Earthquake Sequence from the Lake Aswan Area in Egypt

--We have examined the digital waveform data and relocated a number of events within the June 1987 earthquake swarm, which occurred beneath the northern part of Lake Aswan, 70 km southwest of the Aswan High Dam in Egypt. This swarm occurred between June 17th and 19th with a maximum magnitude event of "M_L"=3.5.¶Cross correlation between a chosen master and the analyzed events has been carried out on seismograms from stations of the Aswan network. The cross correlation demonstrates the presence of a difference in both the P wave ((t_p) and the S wave ((t_s) arrival times at each station in the network relative to the arrival times of the master event at the same stations. (t_p ranges between т.15 and 0.11 second, while (t_s ranges between т.17 and 0.11 second.¶The primary interpretation is that the se time differences represent an error in the manually picking arrival times. Then, (t_p and (t_s values for each event result from a change in the hypocentral parameters from those of the master event, assuming the P- and S-wave velocity distribution remains constant during the swarm activity. This interpretation enables us to determine the relative distribution of hypocenters with respect to the hypocentral location of the master event. We present the results from a swarm of 9 events demonstrating they originate from a nearly unique location, rather than the zone identified from the preliminary locations which used manually picked onset times.