seismic moment distribution revisited i statistical results summary an accumulation of seismic moment data gathered over the previous decade justifies a new attempt at a comprehensive statistical analysis of these data herein more rigourous statistical techniques are introduced their properties investigated and these methods are employed for analysis of large modern data sets several theoretical distributions of earthquake size seismic moment frequency relations are described and compared we discuss the requirements for such distributions and introduce an upper bound or a corner moment for a distribution to have a finite energy or moment flux we derive expressions for probability density functions and statistical moments of the distributions we also describe parameter evaluation in particular how to estimate the seismic moment distribution for the largest earthquakes simulating earthquake size distributions allows for a more rigourous evaluation of distribution parameters and points to the limitations of the classical statistical analysis of earthquake data simulations suggest that several earthquakes approaching or exceeding the corner magnitude mc limit need to be registered to evaluate mc with reasonable accuracy using the harvard catalogue data we compare moment distribution parameters for various temporal spans of the catalogue for different tectonic provinces and depth ranges and for earthquakes with various focal mechanisms the statistical analysis suggests that the exponent b is universal b 0 60 0 65 for all moderate earthquakes the corner moment mc value determined by the maximum likelihood method both in subduction zones and globally is about 10 21 n m corresponding to the corner moment magnitude mc 8 0 for midoceanic earthquakes mc is apparently smaller for spreading ridges it is about 5 8 and for strike slip earthquakes on transform faults it decreases from 7 2 to 6 5 as the relative slip velocity of faults increases we investigate the seismic moment errors both random and systematic and their dependence on earthquake size the relative errors seem to decrease for larger events the influence of moment uncertainties on the parameter estimates is studied whereas the b values do not appear to be significantly influenced by the errors for the corner moment large errors can lead to substantially biased estimates we compare the harvard catalogue results with the earthquake data from instrumental catalogues in the first three quarters of the 20th century several very large earthquakes mi9 occurred around the middle of the century their magnitude values cannot be fitted by a modified gutenberg richter law with mc 8 0 8 5 among other factors this discrepancy can be explained by either substantially higher errors in the earlier magnitude values or by mc being higher for some subduction zones it is unlikely that data available presently or soon will be sufficient to determine the corner magnitude of 9 and above with reasonable precision using purely statistical methods

structure and development of the southeast newfoundland continental passive margin derived from screech transect 3 new seismic reflection data from the grand banks of newfoundland and the newfoundland basin add to the growing knowledge of the composition structure and history of this nonvolcanic margin geophysical imaging is now approaching the extent of that done previously on the conjugate margin along iberia providing a valuable database for the development of rifting models two parallel profiles over the shelf platform image deep crustal fabric representing precambrian or possibly appalachian deformation as well asmesozoic extension progressively more intense extension of continental crust is imaged oceanwards without the highly reflective detachments frequently seen on profiles off galicia a landward dipping event l is imaged sporadically and appears to be analogous to a similar event on the iberian iam9 profile the transition zone is probably exposed serpentinized mantle as interpreted off the iberian margin although there appears to be a difference in the character of ridge development and reflectivity the distinctive u reflection identified previously at the base of the newfoundland basin deep water sedimentary section and recently identified as one or more thin basalt sills is imaged on newly presented profiles that connect previously published profiles scr3 and scr2 showing that u is highly regular and continuous except where interrupted by basement highs u is also seen to have a major impact on the ability to image underlying basement a full transect beginning over completely unextended continental crust through to oceanic crust has provided a data set from which estimates of extension and the pre rifting location of the present continental edge can be made two estimates were obtained 85 km based on faulting and 120 km based on crustal thickness

deterministic seismic hazard in egypt summary the regional seismic hazard in egypt is assessed using a deterministic approach based on the computation of synthetic seismograms at a set of gridpoints located at distances of 0 2u from each other the main input for this computation are earthquake sources and structural models the earthquake sources are parametrized using focal mechanisms seismogenic areas and regional seismicity a number of deep seismic profiles have been used to define the crustal structures similar sets of gravity profiles have been used to define the density of the layers the peak displacement dmax peak velocity vmax and design ground acceleration dga are chosen and plotted to construct the seismic hazard maps there are similarities between computed and observed amplitudes of ground motion in terms of their values and spatial distributions the results obtained from the deterministic and probabilistic approaches are comparable the areas of high seismic hazard level are of great socio economic importance

stochastic synthesis of earthquake catalogs a model of earthquake occurrence is proposed that is based on results of statistical studies of earthquake catalogs we assume that each earthquake generates additional a probability that depends on time as t 1 this assumption together with one regarding the independence of branching events on adjacent branches of the event tree is sufficient to permit the generation of complete catalogs of earthquakes that have the same time magnitude statistical properties as real earthquake catalogs if is about 0 5 the process generates sequences that have statistical properties similar to those for shallow earthquakes many well known relations are reproduced including the magnitude frequency law omori s law of the rate of aftershock and foreshock occurrence the duration of a recorded seismic event versus its magnitude the self similarity or lack of scale of rate of earthquake occurrence in different magnitude ranges etc a value of closer to 0 8 or 0 9 seems to simulate the statistical properties of intermediate and deep shocks a formula for seismic risk prediction is proposed and the implications of the model for risk evaluation are outlined the possibilities of the determination of long term risk from real or synthetic catalogs that have the property of self similarity are dim

extensional tectonics and stratigraphy of hibernia oil field grand banks newfoundland the tectonic evolution of the grand banks involved several episodes of rifting and sequential development of the continental margin the dominant period of rifting and basin formation in the central grand banks was late callovian to aptian extensional failure of the central grand banks crust probably occurred along a shear zone that dipped gently to the west listric normal basin forming faults merge at depth with this detachment system the listric murre fault soles at 26 km 16 mi creating the very deep jeanne d arc basin cross basin transfer faults accommodated different amounts and rates of extension and resulted in the conspicuous offset pattern and funnel shaped geometry of the jeanne d arc basin the hibernia oil field is associated with one of these structural salients the stratigraphy of the jeanne d arc basin and the hibernia oil field is a direct response to this tectonic and structural framework large scale unconformity bounded sequences correspond to major plate reorganizations and zipper type opening of the atlantic ocean smaller scale adjustments to episodic extension are expressed in multiple stacking of depositional sequences the broad scale evolution of the synrift succession involved the early deposition of limestones and oil prone shales about 10 12 m y later rifting climaxed resulting in floods of coarse terrestrial material from the rift shoulders the characteristics of these depositional systems reflect a pervasive structural control affecting the distribution of facies tracts dip slip movement on basin bounding faults and c oss basin transfer fault trends were equally important a profound structural modification of the hibernia structure occurred in late barremian time when a major detachment developed within the basin fill this structural modification and associated antithetic and synthetic faulting in the hanging wall largely controlled reservoir distribution and the maturation migration and trapping of hydrocarbons

hearing thresholds of a harbor porpoise phocoena phocoena for playbacks of multiple pile driving strike sounds pile driving is presently the most common method used to attach wind turbines to the sea bed to assess the impact of pile driving sounds on harbor porpoises it is important to know at what distance these sounds can be detected using a psychophysical technique a male porpoise s hearing thresholds were obtained for series of five pile driving sounds inter pulse interval 1 2 1 3 s recorded at 100 and 800m from the pile driving site and played back in a pool the 50 detection threshold sound exposure levels sels for the first sound of the series no masking were 72 100m and 74 800m db re 1upa2s multiple sounds in succession series caused a 5db decrease in hearing threshold the mean 50 detection threshold sels for any sound in the series were 68 100m and 69 800m db re 1upa2s depending on the actual propagation conditions and background noise levels the results suggest that pile driving sounds are audible to porpoises at least at tens of kilometers from pile driving sites 2013 acoustical society of america

application of section balancing techniques to deep seismic reflection data from offshore eastern canada preliminary observations the application of section balancing techniques to the analysis of deep seismic sections requires account be taken of isostasy and ductile deformation processes structures imaged by deep seismic reflection profiling across the southern grand banks offshore eastern canada are analyzed in this way correlations of dipping events in the deep crust interpreted as shear zones with faults recognized in the shallow part of the section are tested by attempting to restore the sections to their undeformed state by reversing the displacements on the faults this process tests the geometric compatibility of the interpreted fault and the structures in its hanging wall our models suggest that the faults bounding the whale and horseshoe basins detach at the mohorovicic discontinuity in contrast the fault bounding the jeanne d arc basin detaches within the lower crust

accuracy of modern global earthquake catalogs we compare several modem 1977 present worldwide earthquake catalogs to infer their completeness earthquake origin time and hypocenter location accuracy magnitude scalar seismic moment errors and difference between individual focal mechanism moment tensor solutions the harvard centroid moment tensor cmt us geological survey usgs mt usgs first motion fm focal mechanism pde and isc catalogs have been analyzed and compared the catalogs completeness and accuracy vary in time and depend on earthquake depth and tectonic environment we propose a new statistical method for evaluating catalog completeness and show the results for the cmt dataset a difference in frequency range of seismic waves used in earthquake processing leads to varying degrees of catalog completeness for foreshocks and aftershocks close in time earthquake origin time versus centroid time as well as hypocenter location versus centroid location can be explained well by earthquake scaling relations comparing moment magnitudes and regular earthquake magnitudes yields estimated magnitude uncertainties and shows that latter magnitudes poorly estimate earthquake size for large events moment errors reported in the cmt solutions are well correlated with the cmt gs mt magnitude difference and hence indicate magnitude uncertainty well a normalized seismic moment tensor has 4 d f and its accuracy can be represented as the non double couple non dc component value the 3 d angle phi of dc source rotation and a position of the rotation pole our results suggest that a routinely determined non dc component is in most cases only an artifact the distribution of the phi value varies over catalog time earthquake depth focal mechanism and magnitude the seismic moment errors and the value of the non dc component are indicative of the phi value for the best solutions the 3 d angle in the cmt catalog is on the order of 5 7degrees the cmt catalog is obviously the best dataset in completeness and accuracy of its detailed solutions our results specifying uncertainties and completeness of global earthquake catalogs can be used in studies of geodynamic processes tectonic deformation associated with earthquakes earthquake stress analysis and in many other applications of earthquake catalog data seismogram interpretation techniques can be reviewed and possibly revised in light of these results c 2002 elsevier science b v all rights reserved

a microearthquake survey in the abu simbel area in egypt abstract from the middle of january to the middle of march 1981 a microearthquake survey was conducted jointly by polish and egyptian seismologists in the abu simbel area about 230 km upstream from the aswan high dam a small seismic array composed of six stations and a magnetic tape digital recording system was operated during the survey altogether 63 microearthquakes at epicentral distances of up to 50 km and 12 local earthquakes at distances of up to 200 km were recorded but only 16 microearthquakes could be properly located all of them originated either directly under the high dam reservoir or close to its shores thus implying their association with its water level fluctuations it was deduced that under the abu simbel array a deep fracture zone or deep fault extending in the nne ssw direction 1 3 km wide and several kilometers deep must be present to explain the observed effects of heavy attenuation and scattering of seismic waves under the array this fracture zone might be a deep expression of the western edge of the nile valley in the abu simbel area

north grand banks basin offshore newfoundland a sedimentary epeiric basin west of the murre mercury detachment fault abstract the eastern newfoundland offshore area is geologically the best known region of the northwestern atlantic margin extensive geophysical coverage and about 140 exploratory and delineation wells have allowed structural and stratigraphic mapping of a mesozoic rift basin network that includes the south whale whale horseshoe south jeanne d arc carson bonnition jeanne d arc orphan and flemish pass basins a less explored basin not yet targeted by the oil industry and accordingly less explored has recently been discussed in the marine geoscience literature located on the bonavista platform west of the jeanne d arc basin bounding fault and defined here as the north grand banks basin this area has been described from refraction work correlated with deep seismic profiling lithoprobe east data as a possible mesozoic rift basin with hydrocarbon potential or as a palaeozoic basin detected first by gravity measurements but unconfirmed as a rift basin by reflection data this basin is only 2 km deep and contains palaeozoic and probably undeformed mesozoic sedimentary infill its hydrocarbon potential is low the mesozoic sedimentary rocks if present are probably platform carbonates and clastics formed during thermal subsidence episodes following the first two rifting stages that affected the grand banks of newfoundland the placement of the pre rift unconformity within the sedimentary successions of the north grand banks basin and the precise nature of the rocks situated above the avalon basement remain unresolved a geodynamic model involving simple shear extension in the upper crust is used to explain the evolution of newfoundland offshore sedimentary basins including the north grand banks according to this model the basin is located on the upthrown side of the murre mercury fault system that represents the upper crustal expression of a crustal penetrative detachment

sound radiation from impact driven raked piles sound emissions from impact pile driving of raked piles present a significant azimuthal dependence in the radiated sound field due to the non axisymmetric orientation of the pile in this work the sound radiation from raked piles is modeled using a finite element method fem model of the pile and near field region the near field model of the sound field is then used as input into a normal mode model to predict the sound radiation in the far field the azimuthal dependence of the radiated sound field is shown to be accurately predicted using an equivalent axisymmetric fem model of the pile configuration thus negating the need to construct a fully three dimensional model 3d of the raked pile this is achieved by matching the radiated field from the equivalent axisymmetric pile model to a vertical array of phased point sources and then horizontally offsetting the source locations to match the incline of the raked pile the resulting sound field closely matches the numerical predictions from a fully 3d fem model of the raked pile the results of numerical modeling are compared to corresponding acoustic measurements taken on the north west shelf of western australia

earthquake activity in the aswan region egypt the november 14 1981 aswan earthquake m l 5 7 which was related to the impoundment of lake aswan was followed by an extended sequence of earthquakes and is investigated in this study earthquake data from june 1982 to late 1991 collected from the aswan network are classified into two sets on the basis of focal depth i e shallow or deeper than 10 km it is determined that a shallow seismicity is characterized by swarm activity whereas deep seismicity is characterized by a foreshock main shock aftershock sequence b the b value is equal to 0 77 and 0 99 for the shallow and deep sequences respectively and c observations clearly indicate that the temporal variations of shallow seismic activity were associated with a high rate of water level fluctuation in lake aswan a correlation with the deeper earthquake sequence however is not evident these features as well as the tomographic characteristics of the aswan region awad and mizoue this issue imply that the aswan seismic activity must be regarded as consisting of two distinct earthquake groups

loading rate impact on fracturing pattern lessons from hydrocarbon recovery lacq gas field france using scaling parameters of induced seismicity in size and space domains seismic b value and spatial correlation dimension d respectively we analyze the fracturing pattern of the gas reservoir of lacq in correlation with the production rate on the basis of previous observations and a previous model segall et al 1994 we assume that the cause of induced seismicity is a poroelastic stressing such that the production rate can be viewed as a stress rate for the rocks adjacent to the reservoir during the 20 year study period the production rate has decreased dramatically leading to a change of poroelastic stress rate from 4 5 10 3 to 1 5 10 3 mpa yr accordingly we observe a significant decrease in the size of activated fractures and a reduction of the spatial clustering of fracturing both arguing for a stress rate impact on the fracturing pattern in the gas field we interpret these changes in terms of a change in the deformation mode of stressed rocks from a more brittle to a more ductile behavior as the stress rate was decreased this hypothesis is supported by independent evidence from a number of experimental numerical and field studies the loading rate thus appears as a possible candidate to drive changes of b and d in time and space the apparent sensitivity of the earth s crust fracturing pattern to loading rate variations of much lower frequency than the tidal variations suggests that the earth s crust deformation mode itself be frequency dependent also our observations may have strong implications in contexts where the loading rate is induced by human intervention e g hydrocarbon recovery mines suggesting the possibility of adjusting the loading rate so as to shape the fracturing pattern locally according to human needs

a long lasting relaxation of seismicity at aswan reservoir egypt 1982 2001 the aswan reservoir seismicity is accepted as an example of reservoir induced seismicity with the m 5 4 event of 1981 which occurred 15 years after the reservoir impoundment started during the 1982 2001 period the aswan seismicity separates into shallow and deep seismic zones between 0 and 15 and 15 and 30 km respectively these two seismic zones behave differently over time as indicated by the seismicity rate depth migration b value and spatial clustering for the deep events the rate decreases with time the depth remains at a constant or increasing depth and the b value is lower than for the shallow events which migrate toward the surface with a close to constant seismicity rate of all the previous parameters only the seismicity rate correlates with seasonal variations of the lake level this is positive evidence for the aswan reservoir seismicity to be reservoir triggered in the 1982 2001 period clustering over time and space expresses that numerous after shock sequences are activated that is a minimum of 35 of the seismicity similarly to tectonic seismicity the observed decrease of the b value with depth is also a property suggested for natural events our results suggest that the aswan seismicity emerges both from the water level loading and the interplay between induced earth quakes themselves through numerous standard aftershock sequences this latter pro cess induces stochastic fluctuations in the seismicity patterns that inhibit a recovery of a simple seismic response to water level changes even though aftershock se quences dominate the temporal fluctuations of seismicity this does not negate the importance of influence of the reservoir in sustaining this unusual long lasting seis mic episode during the 1982 2001 period the aswan seismicity appears as a power law relaxation response to the 1981 m 5 4 shock this response being decorated by long term larger than 100 days water level changes

mechanical behavior of western alpine structures inferred from statistical analysis of seismicity 1 two seismic arcs 150 km and 120 km long located in the western alps 50 km apart from each other are characterized by different statistical patterns in energy and space domains for the two arcs we found power law distributions in energy domain with a lower b value and fall off for large events for the easternmost arc only and roughly similar spatial damage by comparing the shape and the statistical parameters of these distributions with those provided by numerical models of rock damage we suggest a relatively more brittle behavior for one area with respect to the other we discuss the implications of the observed distributions in terms of tectonics and of mechanics of faulting we suggest three candidates to drive the relative changes in seismicity distribution between the two arcs the earthquake depth the host rock composition and the inherited fracturing patterns

mainshocks are aftershocks of conditional foreshocks how do foreshock statistical properties emerge from aftershock laws 1 the inverse omori law for foreshocks discovered in the 1970s states that the rate of earthquakes prior to a mainshock increases on average as a power law 1 tc t p of the time to the mainshock occurring at tc here we show that this law results from the direct omori law for aftershocks describing the power law decay 1 t tc p of seismicity after an earthquake provided that any earthquake can trigger its suit of aftershocks in this picture the seismic activity at any time is the sum of the spontaneous tectonic loading and of the activity triggered by all preceding events weighted by their corresponding omori law the inverse omori law then emerges as the expected in a statistical sense trajectory of seismicity conditioned on the fact that it leads to the burst of seismic activity accompanying the mainshock in particular we predict and verify by numerical simulations on the epidemic type aftershock sequence etas model that p is always smaller than or equal to p and a function of p of the b value of the gutenberg richter law gr and of a parameter quantifying the number of direct aftershocks as a function of the magnitude of the mainshock the often documented apparent decrease of the b value of the gr law at the approach to the mainshock results straightforwardly from the conditioning of the path of seismic activity culminating at the mainshock however we predict that the gr law is not modified simply by a change of b value but that a more accurate statement is that the gr law gets an additive or deviatoric power law contribution with exponent smaller than b and with an amplitude growing as a power law of the time to the mainshock in the space domain we predict that the phenomenon of aftershock diffusion must have its mirror process reflected into an inward migration of foreshocks toward the mainshock in this model foreshock sequences are special aftershock sequences which are modified by the condition to end up in a burst of seismicity associated with the mainshock foreshocks are not just statistical creatures but are genuine forerunners of large shocks as shown by the large prediction gains obtained using several of their qualifiers

second order moment of central california seismicity 1969 1982 the second order moment cross correlation function of earthquakes in the u s geological survey central california catalog between 1969 and 1982 was calculated with respect to a magnitude threshold m 4 0 over interevent distances up to 80 km and interevent times up to 320 days the statistical procedure results in a representation of the spatial temporal structure of the catalog associated with m 4 0 earthquakes and is capable of revealing patterns too weak to be detected in the space time distribution of seismicity for individual earthquake sequences a method is introduced for identifying aftershocks based on a physical two parameter model of the earthquake interaction process the results show that the aftershock process dominates the second order moment and may even obscure the statistical expression of a precursory process a concentration of foreshocks within 15 km and 3 days of m 4 0 main shocks exhibits an apparent migration toward the main shock loci with velocity 2 6 5 3 km d this concentration may be related to an observed tendency for m 4 0 events to cluster auto correlate over this interevent range with the identified aftershocks removed the residual catalog is poissonion in space and time when two m 4 0 earthquakes occur within 80 km and 40 days of each other aftershock productivity appears to be relatively enhanced in the earlier sequence this suggests that aftershock populations are not solely dependent on their main shocks and that unusually productive aftershock sequences may be predictors of future moderate earthquakes

hearing thresholds of two harbor seals phoca vitulina for playbacks of multiple pile driving strike sounds pile driving which creates high amplitude sounds with potentially negative impacts on the marine environment is used to attach wind turbines to the sea bed to quantify the distance at which pile driving sounds can be detected by harbor seals unmasked hearing thresholds were obtained for series of five pile driving sounds recorded at 100 and 800 m from a pile driving location the played back spectra resembled the spectra of sounds recorded under certain conditions 10 50 km from an offshore pile driving site the lower the received level the later within the series of sounds the harbor seals responded the mean 50 detection threshold sound exposure levels for any sound in the series were 40 seal 01 100 m 39 seal 01 800 m 43 seal 02 100 m and 43 seal 02 800 m db re 1 pa2s add 9 db for sound pressure level db re 1 pa the mean 50 detection thresholds based on detection of only the first sound of the series were ca 5 db higher detection at sea depends on the actual propagation conditions and on the degree of masking of the sounds by ambient noise but the present study suggests that pile driving sounds are audible to harbor seals up to hundreds of kilometers from pile driving sites

a systematic test of the hypothesis that the b value varies with depth in california we spatially map the shallow to deep b value ratio in the crust in california previous studies of the frequency magnitude distribution as a function of depth for selected crustal regions indicated that b decreases from b 1 1 in the 0 5 km depth range to b 0 8 in the depth range 7 15 km our detailed mapping confirms that this pattern can be established at the 99 significance level for about 32 of the entire seismically active crust about 2 of the crust displays the opposite b gradient one such area is the san francisco bay area we speculate that differences in stress levels are the main factor controlling the depth dependency of b these results confirm that the b value should not always be considered a constant in studies such as seismic hazard estimations

brittle ductile transition and associated seismicity experimental and numerical studies and relationship with the b value the acoustic emission ae and the mechanical behavior of granite samples during triaxial compression tests have been analyzed the size of ae events displays power law distributions conforming to the gutenberg richter law observed for earthquakes which is characterized by the b value as the confining pressure increases the macroscopic behavior becomes more ductile for all different stages of the rock mechanical behavior linear nonlinear prepeak nonlinear postpeak shearing there is a systematic decrease of the b value with increasing confining pressure a numerical model based on progressive elastic damage and the finite element method allows simulations of the main experimental observations on ae and of a wide range of macroscopic behaviors from brittleness to ductility the model reproduces a decrease in the b value that appears to be related to the type of macroscopic behavior brittle ductile rather than to the confining pressure both experimental and numerical results suggest a relationship between the b value and the brittle ductile transition moreover these results are consistent with recent earthquake observations and give new insight into the behavior of the earth s crust

depth dependence of earthquake frequency magnitude distributions in california implications for rupture initiation statistics of earthquakes in california show linear frequency magnitude relationships in the range of m2 0 to m5 5 for various data sets assuming gutenberg richter distributions there is a systematic decrease in b value with increasing depth of earthquakes we find consistent results for various data sets from northern and southern california that both include and exclude the larger aftershock sequences we suggest that at shallow depth 0 to 6 km conditions with more heterogeneous material properties and lower lithospheric stress prevail rupture initiations are more likely to stop before growing into large earthquakes producing relatively more smaller earthquakes and consequently higher b values these ideas help to explain the depth dependent observations of foreshocks in the western united states the higher occurrence rate of foreshocks preceding shallow earthquakes can be interpreted in terms of rupture initiations that are stopped before growing into the mainshock at greater depth 9 15 km any rupture initiation is more likely to continue growing into a larger event so there are fewer foreshocks if one assumes that frequency magnitude statistics can be used to estimate probabilities of a small rupture initiation growing into a larger earthquake then a small m2 rupture initiation at 9 to 12 km depth is 18 times more likely to grow into a m5 5 or larger event compared to the same small rupture initiation at 0 to 3 km

importance of direct and indirect triggered seismicity in the etas model of seismicity 1 using the simple etas branching model of seismicity which assumes that each earthquake can trigger other earthquakes we quantify the role played by the cascade of triggered seismicity in controlling the rate of aftershock decay as well as the overall level of seismicity in the presence of a constant external seismicity source we show that in this model the fraction of earthquakes in the population that are aftershocks is equal to the fraction of aftershocks that are indirectly triggered and is given by the average number of triggered events per earthquake previous observations that a significant fraction of earthquakes are triggered earthquakes therefore imply that most aftershocks are indirectly triggered by the mainshock