earthquakes faulting and stress in the los angeles basin since 1920 fourteen moderate sized m l 4 9 6 4 earthquakes have been reported in the los angeles basin these events are associated with both mappable surficial faults and concealed faults beneath the basin sediments to determine the style of faulting and state of stress in the basin single event focal mechanisms for 244 earthquakes of m 2 5 that have occurred during 1977 1989 have been calculated fifty nine percent of the events are strike slip and are mostly located near two of the major northwest striking right lateral strike slip faults in the basin the newport inglewood fault and the palos verdes fault the 1988 pasadena and the 1988 upland earthquakes showed left lateral strike slip on northeast striking faults numerous small earthquakes in the eastern part of the basin show left lateral strike slip faulting and form a northeast trend near yorba linda thirty two percent of the events have reverse mechanisms and are distributed along two broad zones the first the elysian park fold and thrust belt coincides with anticlines along the eastern and northern flank of the los angeles basin extending into santa monica bay the second the torrance wilmington fold and thrust belt coincides with anticlines mapped on the southwest flank of the basin and extends from offshore newport beach to the northwest into santa monica bay oblique faulting that could be inferred by the merging of strike slip and compressional tectonics does not occur in the basin instead the coexistence of zones of thrusting and large strike slip faults in the basin suggests that the thrust and strike slip movements are mostly decoupled a few normal faulting mechanisms appear to be related to faulting orthogonal to the axes of plunging anticlines the trend of the maximum horizontal stress varies from n1 w to n31 e across the basin and consistently forms high angles with the fold axes the stress field that exists along the flanks of the basin has a vertical minimum stress axis this stress field and ongoing folding and thrusting suggest that tectonic deformation is concentrated along the flanks of the deep central basin today the deformation of the basin consists of uplift and crustal thickening and lateral block movement to accommodate the north south compression across the basin

amplification of moment and strain energy release due to interaction between different size fault slip zones previous work of rudnicki and kanamori which used collinear crack solutions to examine quantitatively the effects of fault slip zone interaction on moment stress drop and strain energy release is extended by considering the effects of interaction between different size slip zones the calculations demonstrate that the presence of a large preexisting slip zone can substantially amplify the low frequency seismic signal due to slip on a nearby smaller slip zone for example if the length of the larger slip zone is l that of the smaller is l 10 and the distance between the nearest ends of the zones is l 100 the seismic moment due to slip on the larger zone induced by slip on the smaller zone is about 5 times that due to slip on an isolated zone of length l 10 furthermore because of the interaction between slip zones the moment due to slip on the smaller zone is about 2 5 times the value for an isolated zone of the same size and subjected to the same effective stress conversely estimates of stress drop based on the measured value of the moment and the total length on which slip occurs substantially underestimate the actual stress drop although the stress drop on the larger slip zone is zero the induced slip there does contribute to wo the difference between the strain energy change and the frictional work in fact it is demonstrated that wo em 2 where e is the effective stress m is the actual value of the seismic moment and is the shear modulus

stress directions in eastern north america determined to 4 5 km from borehole elongation measurements stress directions have been determined to depths of 4 5 km in eastern north america from borehole elongation measured by dipmeter calipers in 47 wells the average maximum horizontal stress directions are eastern canada n54 e 7 appalachian basin n58 e 8 and the illinois basin n89 w 5 stress directions determined for the illinois and appalachian basins are in agreement with published interpretations from hydraulic fractures and earthquake fault plane solutions new results from eastern canada and the appalachian basin show that stress directions are everywhere consistent with the midcontinent stress province these data suggest that the maximum horizontal stress does not rotate from the ene midcontinent trend to nw near the atlantic coast a directional analysis of hydraulic fractures petal centerline fractures and natural fractures from the appalachian basin shows that borehole elongation is systematically aligned perpendicular to the directions of hydraulic fractures centerline fractures and northeast striking natural fractures but is not systematically aligned with northwest striking natural fractures these observations indicate that borehole elongations provide reliable stress orientations

appalachian stress study 1 a detailed description of in situ stress variations in devonian shales of the appalachian plateau we describe an experiment to measure variations in the state of stress within a horizontally bedded devonian shale sandstone limestone sequence in western new york a total of 75 stress measurements were made in three wells a kilometer or so apart using a wireline supported hydraulic fracturing system the stress profiles indicate that a major drop in horizontal stress level occurs in the generally massive shales this drop occurs principally across the lowermost member of a group of sand beds and corresponds to an offset in sh and sh of 3 5 and 9 mpa respectively above the sands thrust regime conditions prevail although the amount by which sh exceeds sv is undetermined since instantaneous shut in pressures isips were clipped at the level of sv due to fracture rotation below the sands the regime is strike slip with both horizontal stresses showing lateral uniformity despite substantial variations in topography the magnitude of sh in the sand beds themselves and a lower limestone remains at least as great as sv despite the decline in shale stress hence stress contrasts between these beds and neighboring shales become pronounced with depth the contrast in sh and sh between the lowermost sand and the immediately underlying shale is at least 6 and 14 5 mpa respectively sh levels in the lower strike slip regime are about 1 75 times greater than sh and are less than the value required to initiate slippage on favourably oriented frictional interfaces for the upper thrust regime and the sand and limestone beds however the inferred lower bound on sh is close to the slippage threshold for a coulomb friction coefficient of 0 6 the orientation of sh is ene with a standard deviation of 20 fracture traces were usually splayed occasionally spanning 30 of well bore no systematic correlation between mean orientation and lithology is evident significantly different orientations were obtained for adjacent tests in which almost identical islps were observed suggesting that the fractures quickly reorient themselves to propagate normal to the least principal stress direction similarly vertical traces were observed in those tests where isips apparently reflect sv suggesting that rotation to horizontal was rapid

the 1979 palmdale california strain event in retrospect although the long term 1971 1984 strain accumulation across the san andreas fault near palmdale california is simply right lateral shear at the rate of 0 20 0 01 strain a tensor shear annual measurements indicate that an anomalous contraction perpendicular to the fault accumulated in the interval 1973 1978 and was abruptly released in mid 1979 this anomaly is referred to as the 1979 palmdale strain event more frequent measurements of strain since 1979 suggest a more irregular accumulation of strain than prior to 1979 this irregularity may be due to measurement errors larger than previously estimated as a consequence of this post 1979 irregularity the 1979 strain event no longer appears as anomalous as it had in the shorter 1971 1980 record to provide independent support for existence of the 1979 palmdale strain event we review gravity measurements at palmdale by jachens 1983 and water level measurements in wells near palmdale by merifield and lamar 1981 that have previously been shown to provide a marginal correlation with the 1979 strain recovery these data taken together with the original strain observations suggest a real strain anomaly did occur near palmdale in 1979 but the evidence is not overwhelming

winter spring flushing of bass strait south eastern australia a numerical modelling study this study investigates winter spring flushing of bass strait with a two dimensional non linear depth averaged shallow water model the model is driven with a 180 day wind time series an advection diffusion scheme for several tracers is used to reveal the flushing pattern timescale of the region the study considers how external water masses flush strait waters it shows that shelf water entering the strait through the passage between king island and cape grim makes the largest contribution to strait waters results show that the central area of the strait is a stagnation area of weak currents and long flushing times 160 days the influence of external water masses on the stagnation area is estimated the findings have implications for marine ecosystems residence times air sea modifications of water mass properties and dense water formation in the region

variable rates of late quaternary strike slip on the san jacinto fault zone southern california three strike slip displacements of strata with known approximate ages have been measured at two locations on the san jacinto fault zone minimum horizontal offset between 5 7 and 8 6 km in no more than 0 73 m y northeast of anza indicates 8 12 mm yr average slip rate since late pleistocene time two measures of more recent displacement are based on trenching studies of stratigraphic offsets on the coyote creek fault in western imperial valley horizontal slip of 1 7 m has been calculated for the youngest sediment of lake cahuilla since its deposition 275 510 yr b p the corresponding slip rate is 2 8 5 0 mm yr right lateral offset of 10 9 m measured on a buried stream channel older than 5060 yr b p but younger than 6820 yr b p yields average slip rates for the intermediate time periods 400 to 6000 yr b p of 1 2 mm yr the average rates of slip for these three time intervals suggest a relatively quiescent period for the san jacinto fault zone from about 4000 b c to about 1600 a d to the extent that long term variations in seismic activity of major strike slip faults elsewhere are known fluctuations in slip rate for the san jacinto fault would not appear to be abnormal if the san jacinto and adjacent segments of the san andreas fault alternately assume dominant roles in absorbing motion between the pacific and american plates perhaps even more recently than 400 yr ago the san andreas fault south of the transverse ranges expressed most of the motion but has since become relatively inactive

fractals in geology and geophysics the definition of a fractal distribution is that the number of objectsn with a characteristic size greater thanr scales with the relationn r d the frequency size distributions for islands earthquakes fragments ore deposits and oil fields often satisfy this relation fractals were originally introduced by mandelbrot to relate the length of a coastline to the length of the measuring stick this application illustrates a fundamental aspect of fractal distributions scale invariance the requirement of an object to define a scale in photographs of many geological features is one indication of the wide applicability of scale invariance to geological problems scale invariance can lead to fractal clustering geophysical spectra can also be related to fractals these are self affine fractals rather than self similar fractals examples include the earth s topography and geoid

stress induced borehole elongation a comparison between the four arm dipmeter and the borehole televiewer in the auburn geothermal well the nature and origin of borehole elongation recorded by the four arm dipmeter calipers is studied utilizing information obtained from hydraulic fracturing stress measurements and borehole televiewer data taken in a well located in auburn new york a preferred orientation n10 w s10 e 10 and a less prominant e w orientation of borehole elongation was observed on two runs of the dipmeter comparisons of borehole geometry determined using the televiewer and the dipmeter show that both tools give the same orientation of borehole elongtion provided that the zone of elongation is longer than 30 cm comparisons of dipmeter caliper data with orientation of in situ stress and natural fractures obtained from hydrofracturing tests and televiewer data show that the n10 w s10 e borehole elongations 1 are axisymmetric 2 are aligned with the minimum horizontal stress sh and 3 are not associated with natural fractures intersecting the well these elongations are interpreted as stress induced well bore breakouts the e w elongation direction is characterized by an asymmetric borehole cross section in thinly bedded rocks and is not caused by breakouts this asymmetric geometry can be discriminated from breakouts using the oriented electric measurements provided by the dipmeter this study demonstrates that the dipmeter can be used to determine the orientation of sh by mapping breakouts confirming the results of earlier less detailed studies and provides a firm basis for mapping regional stress patterns using existing dipmeter data

estimation of maximum horizontal principal stress magnitude from stress induced well bore breakouts in the cajon pass scientific research borehole in this paper we utilize the mechanical properties of core samples detailed observations of stress induced well bore breakouts and estimates of the magnitude of shmin from hydraulic fracturing experiments to construct a vertical profile of the maximum horizontal principal stress shmax to 3 5 km depth in the cajon pass borehole as in essentially all other boreholes the hydraulic fracturing stress measurements in the cajon pass borehole yielded appreciably more and more reliable data on the magnitude of the least principal horizontal stress shmin than the maximum principal horizontal stress shmax to utilize the breakout observations to constrain the magnitude of shmax a brittle failure criterion was used that is based on the effective strain energy concept this failure criterion also allows us to account for the polyaxial stress around the borehole and to incorporate the role of pore fluid pressure on rock strength in various ways a comparison of the shmax profile estimated from the breakouts with estimates of shmax obtained from the hydraulic fracturing tests indicates that they compare fairly well for the case when the effect of pore pressure on hydraulic fracture initiation is negligible the overall stress state to a depth of 3 5 km in the well corresponds to a normal strike slip faulting regime the shmax profile indicates several marked decreases in stress magnitude associated with major fault zones an observation consistent with the shmin profile obtained from hydraulic fracturing tests

tomographic evidence for localized lithospheric shear along the altyn tagh fault seismic tomography across the altyn tagh fault at the north edge of the tibetan plateau reveals a low p wave velocity anomaly below the fault down to 140 kilometers this anomaly probably reflects strike slip shear in the lithosphere slip partitioning may also induce a wedge of crust from the tarim basin to plunge into the mantle

source parameters of the 1980 mammoth lakes california earthquake sequence from the more than 1500 mammoth lakes earthquakes recorded on three component digital seismographs spudich et al 1981 150 were used in an analysis of the locations mechanism and source parameters a composite fault plane solution of nine earthquakes 3 9 m 5 1 defines a right lateral strike slip mechanism on a steeply dipping nearly east west plane striking s75 e or left lateral strike slip on a nearly north south plane striking n10 e vertical cross sections of well located aftershocks indicate possibly three east west planes that coincide with the locations of the four largest earthquakes with ml 6 0 using the spectral analysis of s waves brune 1970 source parameters for 67 earthquakes were determined forty eight had magnitudes greater than or equal to 3 0 seismic moments ranged from 9 20 1018 dyn cm to 2 33 1024 dyn cm earthquakes with seismic moment greater than about 1 0 1021 dyn cm had nearly constant stress drops 50 bars earthquakes with seismic moment less than about 1 0 1021 dyn cm had stress drops that apparently decrease as seismic moment decreases

stress orientation profile to 3 5 km depth near the san andreas fault at cajon pass california a detailed profile of the orientation of the apparent maximum horizontal compressive stress was constructed over the depth interval 1 75 3 46 km in the cajon pass drill hole located 4 2 km from the san andreas fault in southern california the profile is based on the analysis of stress induced well bore breakouts and consists of 32 616 orientation determinations at a basic sampling interval of 4 cm the azimuth of the apparent maximum horizontal compressive stress around the borehole is 057 s d 19 depth dependent variations in breakout azimuths from a few degrees to as much as 100 occur over depth intervals of several centimeters to hundreds of meters in the borehole with wavelengths showing a self similar distribution over a range of depth intervals the variations in breakout orientation at depth seem to reflect stress fluctuations associated with active faults penetrated by the drill hole assuming linear elastic behavior perturbations in stress magnitude and orientation were computed for predrilling slip on these faults fault stress drops limited to the ambient shear stress i e up to total stress drop along with occasional local extreme stress drops and geometrical complications can explain the variations in breakout orientations in the drill hole the penetrative stress inhomogeneity may suggest that the average orientation of borehole breakouts in cajon pass which indicates left lateral shear on planes parallel to the san andreas fault may not be representative of the state of stress near the fault at depth in this region rather the stress orientation profile indicates the superposition of numerous local stress perturbations on an average stress field which is characterized by an absence of appreciable right lateral shear on planes parallel to the san andreas combining these observations with the highly variable stress state in shallow boreholes in the western mojave desert it is suggested that the heterogeneous stress field in this region representing a spectrum of seismic events may extend over substantial distances across and along the san andreas fault zone if the average measured breakout orientation in cajon pass is representative of the state of stress near the san andreas in this region then substantial left lateral shear stress is resolved on planes parallel to the fault in contradiction to the sense of its long term motion we use an elastic dislocation model to compute the net stress change near the cajon pass drill site since just prior to the large 1812 earthquake taking into account coseismic slip in major earthquakes and aseismic accumulation of slip on the san andreas and san jacinto faults the model suggests that the net change in fault parallel shear stress during the current earthquake cycle in the cajon pass area is nearly negligible the difference between the measured and computed results requires that additional left lateral shear stress be superimposed on a generally fault normal maximum horizontal compressive stress the results suggest that during the great fort tejon earthquake of 1857 left lateral shear stress parallel to the san andreas fault in the region of cajon pass may have played a role in terminating the southeastward extent of the rupture propagation

irregular recurrence of large earthquakes along the san andreas fault evidence from trees old trees growing along the san andreas fault near wrightwood california record in their annual ring width patterns the effects of a major earthquake in the fall or winter of 1812 to 1813 paleoseismic data and historical information indicate that this event was the san juan capistrano earthquake of 8 december 1812 with a magnitude of 7 5 the discovery that at least 12 kilometers of the mojave segment of the san andreas fault ruptured in 1812 only 44 years before the great january 1857 rupture demonstrates that intervals between large earthquakes on this part of the fault are highly variable this variability increases the uncertainty of forecasting destructive earthquakes on the basis of past behavior and accentuates the need for a more fundamental knowledge of san andreas fault dynamics

crustal deformation in great california earthquake cycles periodic crustal deformation associated with repeated strike slip earthquakes is computed for the following model a depth l h extending downward from the earth s surface at a transform boundary between uniform elastic lithospheric plates of thickness h is locked between earthquakes it slips an amount consistent with remote plate velocity vpl after each lapse of earthquake cycle time tcy lower portions of the fault zone at the boundary slip continuously so as to maintain constant resistive shear stress the plates are coupled at their base to a maxwellian viscoelastic asthenosphere through which steady deep seated mantle motions compatible with plate velocity are transmitted to the surface plates the coupling is described approximately through a generalized elsasser model we argue that the model gives a more realistic physical description of tectonic loading including the time dependence of deep slip and crustal stress buildup throughout the earthquake cycle than do simpler kinematic models in which loading is represented as imposed uniform dislocation slip on the fault below the locked zone parameters of the model are chosen to fit seismic and geologic constraints and the apparent time dependence of surface strain rates along presently locked traces of the 1857 and 1906 san andreas ruptures we fix vpl 35 mm yr tcy 160 years and l 9 11 km based on earthquake nucleation depths the geodetic data are then found to be described reasonably within the context of a model that is locally uniform along strike and symmetric about a single san andreas fault strand by lithosphere thickness h 20 30 km and elsasser relaxation time tr 10 16 years we therefore suggest that the asthenosphere appropriate to describe crustal deformation on the earthquake cycle time scale lies in the lower crust and perhaps crust mantle transition zone and has an effective viscosity between about 2 1018 and 1019 pa s depending on the thickness assigned to the asthenospheric layer predictions based on the chosen set of parameters are also consistent with data on variations of contemporary surface strain and displacement rates as a function of distance from the 1857 and 1906 rupture traces although the fit is degraded by asymmetry relative to the fault and by slip on adjacent fault strands

slip along the san andreas fault associated with the great 1857 earthquake historical records indicate that several meters of lateral slip along the san andreas fault accompanied the great 1857 earthquake in central and southern california these records together with dendrochronological evidence suggest that the rupture occurred along 360 to 400 km of the fault including several tens of kilometers of the currently creeping reach in central california geomorphic expressions of late holocene right lateral offsets are abundant along the 1857 rupture along 300 kilometers of the 1857 rupture between cholame and wrightwood the youngest discernible offset ranges from 3 to 9 1 2 meters dormancy of the fault since 1857 almost certainly indicates that this latest offset was created in 1857 fault slip apparently associated with the 1857 earthquake varies in a broadly systematic way along the trace of the fault it is relatively uniform along each of several long segments but changes rather abruptly in value between these segments this nonuniform displacement pattern may imply that some segments of the fault rupture more frequently or experience a slower long term slip rate than others the 1857 offsets indicate a seismic moment m o between 5 3 and 8 7 10 27 dyne cm assuming a 10 to 15 km depth of rupture and relatively uniform slip as a function of depth a comparison with the rupture length average slip value and tectonic setting of the california earthquake of 1906 m s 8 1 4 indicates a value of m 8 1 4 for the 1857 event

effect of borehole deviation on breakout orientations well bore breakouts are zones of spalling and fracture that form on opposite sides of a well bore and tend to change the cross sectional shape of the borehole from circular to roughly elliptical in vertical holes drilled in areas where one principal stress sv is vertical breakouts tend to form at opposite ends of the borehole diameter parallel to the least compressive horizontal principal stress direction sh this paper uses an analytical elastic solution for stress at the wall of a borehole to analyze the rotation of breakout orientations away from the direction of sh as the borehole deviates from the direction of the vertical principal stress the calculated orientations of breakouts in deviated boreholes depend on the type of faulting regime in which the well was drilled i e normal strike slip or thrust on the deviation angle o of the borehole axis from vertical on the angle between the horizontal projection of the borehole axis and the direction of sh and on the relative magnitudes of the three principal stresses sh sh the greatest compressive horizontal stress and sv in the strike slip faulting regime regardless of the values of sv sh and sh a borehole must deviate at least 35 from vertical before the horizontal projection of the breakout orientation differs by more than 10 from sh in the normal and thrust faulting regimes however the borehole deviation angle ocrit required to rotate projected breakout orientations by 10 from sh approaches zero as the value of sh approaches that of sh in the thrust faulting regime only about 3 of all combinations of sv sh and sh will produce ocrit values less than 10 while about 12 of all such combinations will yield ocrit 10 in the normal faulting regime about 12 and 33 of such combinations will yield ocrit 20 in the thrust and normal faulting regimes respectively careful study of changes in breakout orientation as a function of borehole deviation may improve the resolution of inferred stress directions when studying breakouts in deviated boreholes in these two faulting regimes

strain rate profile across the elsinore san jacinto and san andreas faults near palm springs california 1973 81 a profile of the strain accumulation rate along a line trending n50 e across the subparallel elsinore san jacinto and san andreas faults near palm springs california has been constructed from trilateration surveys in the 1973 81 interval the strain accumulation is principally right lateral shear across a vertical plane parallel to fault strike n40 w the strain rate profile for that component exhibits two clearly resolved maxima one centered on the san jacinto fault max 0 35 0 02 rad a and the other on the san andreas fault max 0 40 0 02 rad a no maximum is associated with the elsinore fault this result clearly implies that slip at depth on both the san andreas and san jacinto faults is loading the shallower sections of these faults and that eventually rupture can be expected on both

utilization of observations of well bore failure to constrain the orientation and magnitude of crustal stresses application to continental deep sea drilling project and ocean drilling program boreholes

hydraulic fracturing in situ stress measurements to 2 1 km depth at cajon pass california stress measurements to 2 1 km reveal stress changes with depth that cannot be explained by an elastic response to uniform crustal strain the data at about 1 km depth suggest that the stress is limited by the frictional strength of rock and is perturbed at greater depths by faults which intersect the borehole the stress data indicate that there is little or no right lateral shear stress acting on planes parallel to the san andreas fault

regional patterns of tectonic stress in europe nearly 1500 stress orientation determinations are now available for europe the data come from earthquake focal mechanisms overcoring measurements well bore breakouts hydraulic fracturing measurements and young fault slip studies and sample the stress field from the surface to seismogenic depths three distinct regional patterns of maximum compressive horizontal stress shmax orientation can be defined from these data a consistent nw to nnw shmax stress orientation in western europe a wnw ese shmax orientation in scandinavia similar to western europe but with a larger variability of shmax orientations and a consistent e w shmax orientation and n s extension in the aegean sea and western anatolia the different stress fields can be attributed to plate driving forces acting on the boundaries of the eurasian plate locally modified by lithospheric properties in different regions on average the orientation of maximum stress in western europe is subparallel to the direction of relative plate motion between africa and europe and is rotated 17 clockwise from the direction of absolute plate motion the uniformly oriented stress field in western europe coincides with thin to medium lithospheric thickness approximately 50 90 km and high heat flow values 80 m w m2 in western europe a predominance of strike slip focal mechanisms implies that the intermediate principal stress is vertical the more irregular horizontal stress orientations in scandinavia coincide with thick continental lithosphere 110 170 km and low heat flow 50 m w m2 the cold thick lithosphere in this region may result in lower mean stresses associated with far field tectonic forces and allow the stress field to be more easily perturbed by local effects such as deglaciation flexure and topography the stress field of the aegean sea and western anatolia is consistent with n s extension in a back arc setting behind the hellenic trench subduction zone the stress field is influenced in places by regional geologic structures e g in the western alps where shmax directions show a slight tendency toward a radial stress pattern not all major geologic structures however appear to affect the shmax orientation e g in the vicinity of the rhine rift system horizontal stress orientations are continuous

effects of fault interaction on moment stress drop and strain energy release solutions for collinear shear cracks are used to examine quantitatively the effects of fault slip zone interaction on determinations of moment stress drop and static energy release two models the barrier model and the asperity model are considered in the asperity model the actual distribution of strengths on a fault plane is idealized as a combination of two limiting cases areas which slip freely at a uniform value of a residual friction stress and unbroken ligaments or asperities across which slip occurs only at the time of a seismic event in the barrier model slip zones separated by unbroken ligaments barriers are introduced into a uniformly stressed medium to approximate the nonuniform fault propagation proposed by das and aki the strain energy change due to introducing collinear slip zones or due to breaking the asperities between them is shown to be given by the usual formula for an isolated slip zone with the stress drop replaced by the effective stress significant interaction between slip zones occurs only if the length of the asperity is less than half the length of the slip zones for the case of two collinear slip zones fracture of the asperity between them is shown to cause a large moment primarily because of the additional displacement which is induced on the adjacent slip zones for example if the asperity length is 0 05l where l is the length of each adjacent slip zone then fracture of the asperity causes a moment almost 1 8 times the moment caused by introducing a slip zone of length l for two collinear slip zones the local stress drop due to fracture of the separating asperity is shown to become unbounded as the asperity length goes to zero but in the same limit the stress drop averaged over the entire fault length is approximately equal to the apparent stress drop inferred for an isolated fault of the same moment and total fault length this apparent stress drop is approximately equal within a factor of 2 or 3 to the effective stress and hence can be used in the usual formula to give a good estimate of the strain energy change for the barrier model numerical results are given for the ratio of the stress drop calculated on the assumption of an isolated slip zone to the true stress drop for example in the case of two collinear slip zones of length l separated by a barrier of length 0 2l this ratio is 0 5 whereas for a barrier length equal to that of the adjacent slip zones the ratio is 0 24 stress drop estimates become worse with increasing number of fault segments