Evaluation of the seismic moment of the April 20, 2013 Lushan earthquake

The April 20, 2013 Lushan earthquake which occurred in Sichuan, China had only moderate thrust. However, the computed seismic moments (M ₀) for the Lushan earthquake calculated by several institutions differ significantly from 0.4 × 10¹⁹ to 1.69 × 10¹⁹ Nm, up to four times difference. We evaluate ten computed M ₀s by using normal mode observations from superconducting gravimeters in Mainland China. We compute synthetic normal modes on the basis of moment tensor solutions and fit them to the observed normal modes. Comparison of our results indicates that M ₀ is the main cause for some large differences between observations and synthetics. We suggest that a moment magnitude of M _w6.6, corresponding to a M ₀ of 0.97–1.08 × 10¹⁹ Nm, characterizes the size and strength of the seismic source of the Lushan earthquake.     

Asymptotic Elastodynamic Green Function in the Kiss Singularity in Homogeneous Anisotropic Solids

The far-field asymptotic formula is derived for the elastodynamic Green function in the kiss singularity in homogeneous anisotropic solids. In contrast to standard asymptotics in regular directions the derived formula is more complex and expressed in the form of a 1-D integral. This integral is specified for the kiss singularity along the symmetry axis in transverse isotropy and along the fourfold symmetry axes in tetragonal and cubic symmetries. The shape of the slowness surface in the singularity is regular in transverse isotropy and the amplitude of the Green function is expressed by means of the Gaussian curvature of this surface in the singularity. However, the shape of the slowness surface is irregular and the Gaussian curvature is not defined in the singularity in tetragonal or cubic symmetries. In this case, the amplitude of the Green function is expressed by means of the generalized Gaussian curvature.     

Quantification of major earthquake tsunamis of the Japan Sea

The size of major tsunamigenic earthquakes which occurred in the Japan Sea is quantified on the basis of seismic and tsunamigenic source parameters. The tsunami magnitude M_t is determined from the instrumental tsunami-wave amplitudes. The M_t values thus obtained are on average 0.2 units larger than the values of moment magnitude M_w, though the M_t scale has originally been adjusted to agree with M_w. Moreover, the volume of displaced water at the source is on average 2.3 times as large as that for the Pacific events with a comparable M_w. Nevertheless, the observed height of the sea-level disturbance at the source is found consistent with the amount of crustal deformation computed for the seismic fault models. These results indicate that the tsunami source potential itself is large for M_w in comparison with the Pacific events. The large source potential is explained in terms of the effective difference both in the rigidity of the source medium and in the geometry of the fault motion. For the Japan Sea events, the M_t scale still provides the physical measure of the tsunami potential, and M_t minus 0.2 corresponds to M_w. This predicts that the maximum amplitude of tsunami waves from Japan Sea earthquakes is at least two times as large as that from Pacific earthquakes with a comparable M_w.     

Source time functions of the Gonghe,China earthquake retrieved from long-period digital waveform data using empirical Green’s function technique

An earthquake ofM _S=6.9 occurred at the Gonghe, Qinghai Province, China on April 26, 1990. Three larger aftershocks took place at the same region,M _S=5.5 on May 7, 1990,M _S=6.0 on Jan. 3, 1994 andM _S=5.7 on Feb. 16, 1994. The long-period recordings of the main shock from China Digital Seismograph Network (CD-SN) are deconvolved for the source time functions by the correspondent recordings of the three aftershocks as empirical Green’s functions (EGFs). No matter which aftershock is taken as EGF, the relative source time functions (RSTFs) obtained are nearly identical. The RSTFs suggest theM _S=6.9 event consists of at least two subevents with approximately equal size whose occurrence times are about 30 s apart, the first one has a duration of 12 s and a rise time of about 5 s, and the second one has a duration of 17 s and a rise time of about 8 s. Comparing the RSTFs obtained from P- and SH-phases respectively, we notice that those from SH-phases are a slightly more complex than those from P-phases, implying other finer subevents exist during the process of the main shock. It is interesting that the results from the EGF deconvolution of long-period wavform data are in good agreement with the results from the moment tensor inversion and from the EGF deconvolution of broadband waveform data. Additionally, the two larger aftershocks are deconvolved for their RSTFs. The deconvolution results show that the processes of theM _S=6.0 event on Jan. 3, 1994 and theM _S=5.7 event on Feb. 16, 1994 are quite simple, both RSTFs are single impulses. The RSTFs of theM _S=6.9 main shock obtained from different stations are noticed to be azimuthally dependent, whose shapes are a slightly different with different stations. However, the RSTFs of the two smaller aftershocks are not azimuthally dependent. The integrations of RSTFs over the processes are quite close to each other, i. e., the scalar seismic moments estimated from different stations are in good agreement. Finally the scalar seismic moments of the three aftershocks are compared. The relative scalar seismic moment of the three aftershocks deduced from the relative scalar seismic moments of theM _S=6.9 main shock are very close to those inverted directly from the EGF deconvolution. The relative scalar seismic moment of theM _S=6.9 main shock calculated using the three aftershocks as EGF are 22 (theM _S=6.0 aftershock being EGF), 26 (theM _S=5.7 aftershock being EGF) and 66 (theM _S=5.5 aftershock being EGF), respectively. Deducing from those results, the relative scalar sesimic moments of theM _S=6.0 to theM _S=5.7 events, theM _S=6.0 to theM _S=5.5 events and theM _S=5.7 to theM _S=5.5 events are 1.18, 3.00 and 2.54, respectively. The correspondent relative scalar seismic moments calculated directly from the waveform recordings are 1.15, 3.43, and 3.05.     

Use of long-period surface waves for rapid determination of earthquake-source parameters

A method for rapid retrieval of earthquake-source parameters from long-period surface waves is developed. With this method, the fault geometry and seismic moment can be determined immediately after the surface wave records have been retrieved. Hence, it may be utilized for warning of tsunamis in real time. The surface wave spectra are inverted to produce either a seismic moment tensor (linear) or a fault model (nonlinear). The method has been tested by using the IDA (International Deployment of Accelerographs) records. With these records the method works well for the events larger than M_s = 6, and is useful for investigating the nature of slow earthquakes.For events deeper than 30 km, all of the five moment tensor elements can be determined. For very shallow events (d ? 30 km) the inversion becomes ill-conditioned and two of the five source moment tensor elements become unresolvable. This difficulty is circumvented by a two-step inversion. In the first step, the unresolvable elements are constrained to be zero to yield a first approximation. In the second step, additional geological and geophysical data are incorporated to improve the first approximation. The effect of the source finiteness is also included.     

Moment tensor inversion and source rupture process of the September 27, 2003 <Emphasis Type="Italic">M</Emphasis><Subscript>S</Subscript>=7.9 earthquake occurred in the border area of China,Russia and Mongolia

We conducted moment tensor inversion and studied source rupture process for M _S=7.9 earthquake occurred in the border area of China, Russia and Mongolia on September 27 2003, by using digital teleseismic P-wave seismograms recorded by long-period seismograph stations of the global seismic network. Considering the aftershock distribution and the tectonic settings around the epicentral area, we propose that the M _S=7.9 earthquake occurred on a fault plane with the strike of 127°, the dip of 79° and the rake of 171°. The rupture process inversion result of M _S=7.9 earthquake shows that the total rupture duration is about 37 s, the scalar moment tensor is M ₀=0.97×10²⁰ N·m. Rupture mainly occurred on the shallow area with 110 km long and 30 km wide, the location in which the rupture initiated is not where the main rupture took place, and the area with slip greater than 0.5 m basically lies within 35 km deep middle-crust under the earth surface. The maximum static slip is 3.6 m. There are two distinct areas with slip larger than 2.0 m. We noticed that when the rupture propagated towards northwest and closed to the area around the M _S=7.3 hypocenter, the slip decreased rapidly, which may indicate that the rupture process was stopped by barriers. The consistence of spatial distribution of slip on the fault plane with the distribution of aftershocks also supports that the rupture is a heterogeneous process owing to the presence of barriers.     

Physical size of tsunamigenic earthquakes of the northwestern Pacific

The new scale M_t of tsunami magnitude is a reliable measure of the seismic moment of a tsunamigenic earthquake as well as the overall strength of a tsunami source. This M_t scale was originally defined by Abe (1979) in terms of maximum tsunami amplitudes at large distances from the source. A method is developed whereby it is possible to determine M_t at small distances on the basis of the regional tsunami data obtained at 30 tide stations in Japan. The relation between log H, maximum amplitude (m) and log Δ, a distance of not less than 100 km away from the source (km) is found to be linear, with a slope close to 1.0. Using three tsunamigenic earthquakes with known moment magnitudes M_w, for calibration, the relation, M_t = log H + log Δ + D, is obtained, where D is 5.80 for single-amplitude (crest or trough) data and 5.55 for double-amplitude (crest-to-trough) data. Using a number of tsunami amplitude data, M_t is assigned to 80 tsunamigenic earthquakes that occurred in the northwestern Pacific, mostly in Japan, during the period from 1894 to 1981. The M_t values are found to be essentially equivalent to M_w for 25 events with known M_w. The 1952 Kamchatka earthquake has the largest M_t, 9.0. Of all the 80 events listed, at least seven unusual earthquakes which generated disproportionately-large tsunamis for their surface-wave magnitude M_s are identified from the relation. From the viewpoint of tsunami hazard reduction, the present results provide a quantitative basis for predicting maximum tsunami amplitudes at a particular site.     

Analytic expressions for the velocity sensitivity to the elastic moduli for the most general anisotropic media

For non‐linear kinematic inversion of elastic anisotropy parameters and related investigations of the sensitivity of seismic data, the derivatives of the wavespeed (phase velocity and group velocity) with respect to the individual elastic moduli are required. This paper presents two analytic methods, called the eigenvalue and eigenvector methods, to compute the derivatives of the wavespeeds for wave propagation in a general anisotropic medium, which may be defined by up to 21 density‐normalized elastic moduli. The first method employs a simple and compact form of the eigenvalue (phase velocity) and a general form of the group velocity, and directly yields general expressions of the derivatives for the three wave modes (qP, qS₁, qS₂). The second method applies simple eigenvector solutions of the three wave modes and leads to other general forms of the derivatives. These analytic formulae show that the derivatives are, in general, functions of the 21 elastic moduli as well as the wave propagation direction, and they reflect the sensitivity of the wavespeeds to the individual elastic moduli. Meanwhile, we give results of numerical investigations with some examples for particular simplified forms of anisotropy. They show that the eigenvalue method is suitable for the qP‐, qS₁‐ and qS₂‐wave computations and mitigates the singularity problem for the two quasi‐shear waves. The eigenvector method is preferable to the eigenvalue method for the group velocity and the derivative of the phase velocity because it involves simpler expressions and independent computations, but for the derivative of the group velocity the derivative of the eigenvector is required. Both methods tackle the singularity problem and are applicable to any degree of seismic anisotropy for all three wave modes.     

The temporal series of the New Guinea 29 April 1996 aftershock sequence

The aim of our search is the analysis of aftershock temporal series following a mainshock with magnitude M ≥ 7.0. Investigating aftershock behavior may find the key to explain better the mechanism of seismicity as a whole.In particular, the purpose of this work is to highlight some methodological aspects related to the observation of possible anomalies in the temporal decay. The data concerning the temporal series, checked according to completeness criteria, come from the NEIC-USGS data bank. Here we carefully analyze the New Guinea 29 April 1996 seismic sequence.The observed temporal series of the shocks per day can be considered as a sum of a deterministic contribution (the aftershock decay power law, n(t) = K·(t + c)^−p + K₁) and of a stochastic contribution (the random fluctuations around a mean value represented by the above mentioned power law). If the decay can be modeled as a non-stationary Poissonian process where the intensity function is equal to n(t) = K·(t + c)^−p + K₁, the number of aftershocks in a small time interval Δt is the mean value n(t)·Δt, with a standard deviation .     

Long-term earthquake prediction in the circum-pacific convergent belt

Investigation of the time-dependent seismicity in 274 seismogenic regions of the entire continental fracture system indicates that strong shallow earthquakes in each region exhibit short as well as intermediate term time clustering (duration extending to several years) which follow a power-law time distribution. Mainshocks, however (interevent times of the order of decades), show a quasiperiodic behaviour and follow the ‘regional time and magnitude predictable seismicity model’. This model is expressed by the following formulas $$\begin{gathered} \log T_t = 0.19 M_{\min } + 0.33 M_p - 0.39 \log m_0 + q \hfill \\ M_f = 0.73 M_{\min } - 0.28 M_p + 0.40 \log m_0 + m \hfill \\ \end{gathered} $$ which relate the interevent time,T _t (in years), and the surface wave magnitude,M _f , of the following mainshock: with the magnitude,M _min, of the smallest mainshock considered, the magnitude,M _p , of the preceded mainshock and the moment rate,m ₀ (in dyn.cm.yr^?1), in a seismogenic region. The values of the parametersq andm vary from area to area. The basic properties of this model are described and problems related to its physical significance are discussed. The first of these relations, in combination with the hypothesis that the ratioT/T _t , whereT is the observed interevent time, follows a lognormal distribution, has been used to calculate the probability for the occurrence of the next very large mainshock (M _s ≥7.0) during the decade 1993–2002 in each of the 141 seismogenic regions in which the circum-Pacific convergent belt has been separated. The second of these relations has been used to estimate the magnitude of the expected mainshock in each of the regions.     

One Solution of the Forward Problem of DC Resistivity Well Logging by the Method of Volume Integral Equations with Allowance for Induced Polarization

For theoretically studying the intensity of the influence exerted by the polarization of the rocks on the results of direct current (DC) well logging, a solution is suggested for the direct inner problem of the DC electric logging in the polarizable model of plane-layered medium containing a heterogeneity by the example of the three-layer model of the hosting medium. Initially, the solution is presented in the form of a traditional vector volume-integral equation of the second kind (IE2) for the electric current density vector. The vector IE2 is solved by the modified iteration–dissipation method. By the transformations, the initial IE2 is reduced to the equation with the contraction integral operator for an axisymmetric model of electrical well-logging of the three-layer polarizable medium intersected by an infinitely long circular cylinder. The latter simulates the borehole with a zone of penetration where the sought vector consists of the radial J_r and J_z axial (relative to the cylinder’s axis) components. The decomposition of the obtained vector IE2 into scalar components and the discretization in the coordinates r and z lead to a heterogeneous system of linear algebraic equations with a block matrix of the coefficients representing 2x2 matrices whose elements are the triple integrals of the mixed derivatives of the second-order Green’s function with respect to the parameters r, z, r', and z'. With the use of the analytical transformations and standard integrals, the integrals over the areas of the partition cells and azimuthal coordinate are reduced to single integrals (with respect to the variable t = cos ? on the interval [?1, 1]) calculated by the Gauss method for numerical integration. For estimating the effective coefficient of polarization of the complex medium, it is suggested to use the Siegel–Komarov formula.     

Source parameters of the Gonghe,Qinghai Province,China,earthquake from inversion of digital broadband waveform data

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Earthquake doublets in the Solomon Islands

Large, shallow, thrust earthquakes in the Solomon Islands region tend to occur in closely related pairs. Two recent sequences are July 14, 1971 (M_S = 7.9) and July 26, 1971 M(_S = 7.9) and 14^h37^m, July 20, 1975 (M_S = 7.9) and 19^h54^m, July 20, 1975 (M_S = 7.7). The mechanism of these seismic doublets has important bearing on the triggering mechanism of earthquakes in subduction zones. Detailed analysis of the seismic body waves and surface waves were performed on the 1971, 1974, and 1975 doublets, providing a better understanding of: (1) the mechanics of seismic triggering, (2) the state of stress on the fault plane, and (3) the nature of subduction between the Pacific and Indian plates. The results indicate that although the geometry of the subduction zone in the Solomon Islands is complicated by the presence of several sub-plates, the slip direction of the Indian plate with respect to the Pacific plate is relatively uniform over the entire region. The large seismic moments of the 1971 sequence (1.2 · 10²⁸ and 1.8 · 10²⁸ dyne cm) indicate that these events directly represent the underthrusting of the Indian and Solomon plates beneath the Pacific plate. The body waves from these doublets, recorded on the WWSSN long-period seismograms, are remarkably impulsive and simple compared with those from events of comparable seismic moment in other subduction zones. In addition, the source dimensions of the body waves are 30–70 km in length, substantially smaller than the overall rupture surfaces radiating the surface waves which are 100–300 km in length. These facts suggest the existence of relatively large, isolated high-stress zones on the fault plane. This type of stress distribution is distinct from other regions which have more heterogeneous stress distribution on the fault plane, and this is proposed as the principal characteristic of this region responsible for the occurrence of the doublets and for the apparent efficiency of triggering in the Solomon trench. Prior to the 1971 sequence, similar sequences have occurred in the same area in 1919–1920 and 1945–1946. From the amount of slip (1.3 m) determined for the 1971 sequence and the apparent recurrence interval of 25 years, a seismic slip rate of 5 cm yr^?1 is determined. This value is a significant portion of the convergence rate between the Indian and Pacific plates indicating that the plate motion here is taken up largely by seismic slip.     

Sensitivity of the strong ground motion time histories to a finite source model: A case study for the January 12, 2010 Haiti earthquake (Mw=7.0)

We analyze the waveforms generated by the January 12, 2010 Haiti earthquake (M_w=7.0) for its source characteristics. A 60 to 25 km source model is retrieved by the Kikuchi and Kanamori finite source inversion technique that uses broadband teleseismic body wave records. The derived rupture model points out unilateral rupture propagation commenced at the eastern side of the fault plane where the major seismic moment release occurred. The rupture front propagated westward and terminated at a site where the largest aftershocks occurred. Our estimates yield a seismic moment of M_o=8.17×10¹⁹ N m released on a 60 km-long fault plane. A patch at the eastern side of the ruptured fault plane inferred as a region of maximum moment release.     

Effects of multiple scattering on coda waves in three-dimensional medium

The contribution of multiple scattering to the coda waves for three-dimensional elastic medium is investigated by extending the computational procedures developed earlier for the two-dimensional medium. It is shown that the effects of multiple scattering start to become important at a shorter lapse time,t _c = 0.65(n ₀σu)^?1, than in the two-dimensional case (t _c = 0.8(n ₀σu)^?1).     

Analysis of foreshock sequence of the 1975 Haicheng earthquake ofM S 7.3

The “earthquake nucleation” is discussed in this paper. The acceleration is a property of the nucleation phase and is a necessary condition of earthquake instability too. If the acceleration property of this nucleating process is described by the equation dΘ/dt=C/(t _f?t) ⁿ , the process can be summarized briefly that the rate of cumulative seismic release is proportional to the inverse power of the remaining time to failure. Based on this principle, the foreshock sequence of the 1975 Haicheng earthquake withM _S7.3, was analysed backward. It is stated clearly that the time-to-failure and magnitude of the mainshock can be predicted successfully if the coefficientr ² attains to the maximum. In the estimation of mainshock time, the error can generally be less than, or far less than, one-half the remaining time between the time of the last used data point and the mainshock.     

Long-term earthquake prediction in the Marmara region based on the regional time- and magnitude-predictable model

In order to estimate the recurrence intervals for large earthquakes that occurred in the Marmara region, this region, limited with the coordinates of 39°–42°N, 25°–32°E, has been separated into seven seismogenic sources on the basis of certain seismological criteria, and regional time- and magnitude-predictable model has been applied for these sources. Considering the interevent time between successive mainshocks, the following two predictive relations were computed: log T _t = 0.26 M _min + 0.06 M _p –0.56 log M ₀ + 13.79 and M _f = 0.63 M _min ? 0.07 M _p + 0.43 log M ₀ ? 7.56. Multiple correlation coefficient and standard deviation have been computed as 0.53 and 0.35 for the first relation and 0.66 and 0.39 for the second relation, respectively. On the basis of these relations and using the occurrence time and magnitude of the last mainshocks in each seismogenic source, the probabilities of occurrence P(Δt) of the next mainshocks during the next five decades and the magnitude of the expected mainshocks were determined.     

Rupture process of the 19 August 1992 Susamyr, Kyrgyzstan, earthquake

The Susamyr earthquake of August 19, 1992 in Kyrgyzstan is one of the largest events (M_s = 7.4, M_b = 6.8) of this century in this region of Central Asia. We used broadband and long period digital data from IRIS and GEOSCOPE networks to investigate the source parameters, and their space-time distribution by modeling both body and surface waves. The seismic moment (M₀ = 6.8 × 10¹⁹ N m) and the focal mechanism were determined from frequency-time analysis (FTAN) of the fundamental mode of long period surface waves (100–250 s). Then, the second order integral moments of the moment-rate release were estimated from the amplitude spectra of intermediate period surface waves(40–70 s). From these moments we determined a source duration of 11–13 s, major and minor axes of the source of 30 km and 10–22 km, respectively; and an instant centroid velocity of 1.2 km/s. Finally, we performed a waveform inversion of P and SH waves at periods from 5–60 s. We found a source duration of 18–20 s, longer than the integral estimate from surface wave amplitudes. All the other focal parameters inverted from body waves are similar to those obtained by surface waves ( = 87° ± 6°, = 49° ± 6°, = 105° ± 3°, h = 14 ± 2 km, and M₀ = 5.8 ± 0.7 × 10¹⁹ N m). The initial rupture of this shallow earthquake was located at the south-west border of Susamyr depression in the western part of northern Tien Shan. A finite source analysis along the strike suggests a westward propagation of the rupture. The main shock of this event was preceded 2 s earlier by small foreshock. The main event was almost immediately followed by a very strong series of aftershocks. Our surface and body wave inversion results agree with the general seismotectonic features of the region.     

Time-frequency analysis of seismic excitation and estimates of attenuation parameters for the Friuli (Italy) local earthquakes

Stochastic modelling is applied to the analysis of local earthquake recordings, which are usually extremely rich in random incident-wave trains that are chaotically superimposed because of scattering effects in the Earth's crust. The presence in the seismic signal of effects connected with the scale of inhomogeneity in the lithosphere cannot be deterministically described in detail. The application of a stochastic second-order autoregressive model to accelerometric records for the higher magnitude (M_L ? 6) Friuli earthquakes and to short-period seismometric records for the aftershocks of the strong earthquake of 6 May 1976 has allowed inferences to be drawn about the spectral properties of seismic signals and the propagation mechanisms of seismic waves. These inferences are based on an extremely small number of parameters of a mathematical model suitable for simultaneously describing the random sequence of scattered wave trains in the time and frequency domains. Useful physical information has been obtained about the dynamic characteristic correlation times and the predominant frequency of the seismic signals; moreover, the strength, σ²_e(t), of the innovation of the stochastic process fitting the real digital data set has been estimated. From the envelopes of σ²_e(t), the quantity heuristically used in the stochastic approach to describe seismic excitation, the·mean free-path between successive scatterings (l), or the equivalent diffusivity coefficient (d) and turbidity (g), and their dependence on seismic wave frequency have been investigated. For Friuli, using seismometric data at an epicentral distance of ～ 20 km and earthquakes with a magnitude just under 2, mean free-path estimates obtained by means of autoregressive parameters vary from ～ 5 km for the strong interaction model to ～ 30 km for the single scattering model. Furthermore, by means of accelerometric records for the strongest earthquakes in Friuli during May and September 1976, the dependence for the maximum of the seismic excitation on the epicentral distance R was estimated as (σ²_e)_max ～ R^?ν (with ν 1.94 ± 0.13), which is in good agreement with results obtained for the same region using standard methods by means of acceleration peaks versus R. Lastly, stochastic modelling provides a method of estimating change versus time for the predominant frequency and characteristic correlation time of narrow band digital recordings. These two parameters were computed by means of autoregressive parameters in different physical situations and were found to be functions of the earthquake source, the instrumentation frequency response, and the Earth's filtering effects.     

The time of occurrence and the magnitude of the largest aftershock over India

Summary The time of occurrence and the magnitude of the largest aftershock in relation to the main shock have been studied for India and its neighbourhood based on the USCGS data during the years 1963–1971. It is found that the largest aftershock occurs within 2 hours after the main shock in about 50% of the cases and frequency of occurrencen(t) of the largest aftershocks decreases hyper-bolically with the intervalt after the main event and could be represented by a law of the formn(t)=At ^–h whereA andh are constants. The probability of occurrence of the largest aftershock within 2 hours of the main shock is found to be higher over island are regions of the world. The difference (M ₀–M ₁) of the magnitude of the largest aftershockM ₁ to that of the main shockM ₀ as a measure of aftershock activity does not show any marked regional variation over India and its neighbourhood, as was reported by Mogifor Japan. Examination of the values ofM ₁/M ₀ and the constantb in Gutenberg-Richter's frequency magnitude relationship reveals a range of variation in both; high values ofM ₁/M ₀ have been found to be associated with high values ofb in many tectonic earthquakes and thus not, restricted to reservoir associated seismic activity.