Geology topics

J.C. Savage

Publications and source records attributed to J.C. Savage.

At least 19 recordsLinked to original sources

USGS2012

The uncertainty in earthquake conditional probabilities

The Working Group on California Earthquake Probabilities (WGCEP) questioned the relevance of uncertainty intervals assigned to earthquake conditional probabilities on the basis that the uncertainty in the probability estimate seemed to be greater the smaller the intrinsic breadth of the recurrence-interval distribution. I show here that this paradox depends upon a faulty measure of uncertainty in the conditional probability and that with a proper measure of uncertainty no paradox exists. I also challenge the assertion that the WGCEP probability assessment in 1988 correctly forecast the 1989 Loma Prieta earthquake by showing that posterior probability of rupture inferred after the occurrence of the earthquake from the prior WGCEP probability distribution reverts to a nearly informationless distribution.

Geophysical Research Letters↗

USGS2012

Coseismic displacements: 1992 Landers, California, earthquake

The rupture associated with the 1992 Landers earthquake ( M s = 7.5) extended along the west edge of a 60 × 50 km trilateration network that had been surveyed two months before the earthquake and was resurveyed a month after it. The coseismic displacement field within the network was calculated from the changes observed in the trilateration network supplemented by the displacements measured at four GPS stations and other less timely trilateration measurements. Stations near the rupture were displaced by as much as 3 m. The observed changes are reproduced reasonably well by dislocation modeling in which the Landers rupture is represented by 8 vertical fault segments, each extending from the surface to 9 km depth. Two additional segments represent the Big Bear and Eureka Peak faults. The average modeled right-lateral slip on the Landers rupture is about 5 m. However, the residuals for the best-fit slip distribution are about four times greater than expected from measurement error. Given that uncertainty, a broad range of slip models furnish acceptable fits to the data. The large residuals are attributed to inelastic deformation (principally sympathetic slip on numerous unmodeled faults) within the fault blocks assumed to be elastic in the model.

Geophysical Research Letters↗

USGS2012

Inferred depth of creep on the Hayward Fault, central California

A relation between creep rate at the surface trace of a fault, the depth to the bottom of the creeping zone, and the rate of stress accumulation on the fault is derived from Weertman's 1964 friction model of slip on a fault. A 5 ± 1 km depth for the creeping zone on the Hayward fault is estimated from the measured creep rate (5 mm/yr) at the fault trace and the rate of stress increase on the upper segment of the fault trace inferred from geodetic measurements across the San Francisco Bay area. Although fault creep partially accommodates the secular slip rate on the Hayward fault, a slip deficit is accumulating equivalent to a magnitude 6.6 earthquake on each 40 km segment of the fault each century. Thus, the current behavior of the fault is consistent with its seismic history, which includes two moderate earthquakes in the mid-1800's.

Journal of Geophysical Research↗

USGS2012

Interseismic deformation along the San Andreas Fault in southern California

Eight trilateration networks located along the San Andreas fault in southern California have been surveyed 8 to 19 times within a 14- to 17-year interval between 1971 and 1992. The data, measurements of distances between the same 10 to 32 pairs of geodetic monuments within a network in each of the surveys, have been corrected for coseismic offsets from nearby earthquakes calculated from dislocation models. The corrected data, a total of 2027 measurements, are displayed in the form of plots of measured distance versus time for each of the 167 lines measured. The hypothesis that the interseismic deformation is steady is tested by examining whether deviations from linear fits to the data in the plots are within the range expected for observational error. A significant deviation from steady deformation is found only for the network located neax Palmdale, California. In that network, many of the measurements made in the survey of early 1982 deviate from the trend defined by the measurements in other surveys. The deviations are not of the form (fixed proportional error) one would generally expect from systematic survey error. If the survey of early 1982 is excluded, the remaining data at Palmdale are consistent with steady deformation. Thus the apparent strain event observed near Palmdale in 1982 was transient.

Journal of Geophysical Research↗

USGS2012

Principal component analysis of interseismic deformation in southern California

Eight trilateration networks along the San Andreas fault in southern California have been surveyed repeatedly (8 to 19 times) within an approximately 15-year interval between 1971 and 1992. The data for each network were analyzed by principal component analysis to represent the observed changes in line length as a superposition of individual modes: L ij - L i = ∑ k A ik C k ( t j ), where L ij is the length of the i th line measured at the time t j , L i is the average length of the i th line, and A ik C k ( t j ) is the k th mode. Each mode is described by a common time function Ck(tj) that is evaluated only at the times t j of the surveys, and the participation of each line in that mode is described by a constant amplitude A ik for that line. For all networks the deformation is largely described by the first mode, and the first-mode time function is essentially linear in time. That is, the deformation in each of the networks appears to be steady. Two anomalies in the accumulation of deformation were observed: In the network near Palmdale a transient strain event occurred in the second mode in early 1982, and in the network within Cajon Pass, fluctuations in the accumulation of deformation somewhat greater than would be attributed to measurement error were found. Although both anomalies are formally significant given the estimated measurement error, I am not confident that either anomaly is real. The principal conclusion is that the accumulation of interseismic deformation in the southern California trilateration networks is steady within the precision of measurement.

Journal of Geophysical Research↗

USGS2012

Geodetic measurement of horizontal deformation across the Rio Grande rift near Socorro, New Mexico

Trilateration surveys of a geodetic network across the Rio Grande rift near Socorro, New Mexico, in 1972, 1973, 1976, and 1979 have failed to detect any significant strain accumulation. The surveys place an upper bound (95% confidence limit) of 1 mm/a (a = years) on east-west spreading cross the rift in 1972–1979. There is marginal evidence from triangulation for an episode of east-west spreading across the rift within the interval 1954–1972. The trilateration network lies on the south flank of an uplift caused by magma intrusion into a midcrustal sill during this century according to Reilinger and Oliver. The horizontal deformation induced by sill inflation is sufficiently small that continued uplift during 1972–1979 cannot be excluded by the observed absence of significant horizontal deformation.

Journal of Geophysical Research Solid Earth↗

USGS2012

Preseismic and coseismic deformation associated with the Coyote Lake, California, earthquake

The Coyote Lake earthquake ( M L = 5.9; August 6, 1979; epicenter about 100 km southeast of San Francisco) occurred on the Calaveras fault within a geodetic network that had been surveyed annually since 1972 to monitor strain accumulation. The rupture surface as defined by aftershocks is a vertical rectangle 20 km in length extending from a depth of 4 km to about 12 km. The observed deformation of the geodetic network constrains the average slip to be about 0.33 ± 0.05 m right lateral. Although the geodetic data furnished an exceptionally detailed picture of the preearthquake deformation, no significant premonitory anomaly associated with the Coyote Lake earthquake can be identified.

Journal of Geophysical Research Solid Earth↗

USGS2012

Strain accumulation across the Denali fault in the Delta River canyon, Alaska

Deformation along the Denali fault in the Delta River canyon was determined from geodetic surveys in 1941/1942, 1970, 1975, and 1979. The data were best for the 1975–1979 interval; in that period the average strain accumulation was essentially pure right lateral shear at a rate of 0.6 ± 0.1 μrad/a (a is years) (engineering shear) across a vertical plane striking N87°E. The plane of maximum shear is rotated about 30° counterclockwise from the local strike of the Denali fault but closely coincides with the strike of a major linear segment of the fault that begins 50 km farther west. The deformation between 1941/1942 and 1970 is consistent with a similar rate of strain accumulation if one removes the coseismic strain step contributed by the 1964 Alaska earthquake. The 1970–1975 deformation is poorly defined owing to uncertainties in the 1970 survey, but the strain accumulation during that period is certainly much less than during the 1975–1979 interval. The 1975–1979 strain accumulation is interpreted by means of a dislocation model which suggests that the Denali fault in the vicinity of the Delta River Canyon behaves as a leaky transform fault (i.e., a source of spreading as well as lateral slip). The block south of the Denali fault appears to be moving westward (parallel to the strike of the Denali fault west of the 147th meridian) at the rate of about 20 mm/a relative to the North American plate. Because the linear segment of the Denali fault east of the 147th meridian (along which the geodetic network is located) strikes N63°W, accommodation of the westward motion of the southern block requires some spreading within the fault zone as well as right lateral slip on the fault.

Journal of Geophysical Research Solid Earth↗

USGS2012

Geodetic strain measurements in Washington

Two new geodetic measurements of strain accumulation in the state of Washington for the interval 1972–1979 are reported. Near Seattle the average principal strain rates are 0.07 ± 0.03 μstrain/yr N 19°W and −0.13 ± 0.02 μstrain/yr N71°E, and near Richland (south central Washington) the average principal strain rates are −0.02 ± 0.01 μstrain/yr N36°W and −0.04 ± 0.01 μstrain/yr N54°E. Extension is taken as positive, and the uncertainties quoted are standard deviations. A measurement of shear strain accumulation (dilatation not determined) in the epoch 1914–1966 along the north coast of Vancouver Island by the Geodetic Survey of Canada indicates a marginally significant accumulation of right-lateral shear (0.06 ± 0.03 μrad/yr) across the plate boundary (N40°W strike). Although there are significant differences in detail, these strain measurements are roughly consistent with a crude dislocation model that represents subduction of the Juan de Fuca plate. The observed accumulation of strain implies that large, shallow, thrust earthquakes should be expected off the coast of Washington and British Columbia. However, this conclusion is not easily reconciled with either observations of elevation change along the Washington coast or the focal mechanism solutions for shallow earthquakes in Washington.

Journal of Geophysical Research Solid Earth↗

USGS2012

Strain accumulation in southern California, 1973-1980

Frequent surveys of seven trilateration networks in southern California over the interval 1973–1980 suggest that a regional increment in strain may have occurred in 1978–1979. Prior to 1978 and after late 1979 the strain accumulation has been predominantly a uniaxial north-south compression. This secular trend was interrupted sometime in 1978–1979 by an increment in both north-south and east-west extension in five of the seven networks. The onset of this change appears to have occurred first in the networks farthest south. The changes occurred without any unusual seismicity within the networks, but the overall seismicity in southern California was unusually low prior to and has been unusually high since the occurrence. The average principal strain rates for the seven networks in the 1973–1980 interval are 0.17 μstrain/yr north-south contraction and 0.08 μstrain/yr east-west extension. Although the observed increment in strain could be related to unidentified systematic error in the measuring system, a careful review of the measurements and comparisons with three other measuring systems reveal no appreciable cumulative systematic error.

Journal of Geophysical Research Solid Earth↗

USGS2012

Local gravity anomalies produced by dislocation sources

Rundle (1978) and Walsh and Rice (1979) have shown that the change in the vertical component of gravity is proportional to uplift for a spherical source of dilatation and for slip on an infinitely long dip-slip fault. In the first case, no free air gravity anomaly is produced and in the second case no Bouguer gravity anomaly. Gravity anomalies due to other dislocation sources in three dimensions are as follows: For strike-slip faulting the ratio of the gravity change to uplift depends upon position; however, the gravity change contours are roughly similar to those corresponding to a zero free air gravity anomaly. Nor is the ratio constant for dip-slip faulting except for the two special cases of dip slip on a vertical fault and horizontal slip on a horizontal fault, neither of which produce a Bouguer anomaly. The Bouguer anomaly produced by an open horizontal crack is the same as would be produced had the material within the crack been mined out without deforming the solid. If the horizontal crack were filled with material of density equal to the host rock (a good approximation to sill formation), no Bouguer anomaly is produced. For cracks of other inclinations the ratio of gravity change to uplift is not constant. Thus, dilatancy, in general, does not correspond to the absence of a free air anomaly, as might be suggested by the special case of a spherical source of dilatation. For two-dimensional models a cylindrical source of dilatation produces no free air gravity anomaly, dip-slip faulting produces no Bouguer anomaly, and open cracks produce a Bouguer anomaly equal to that which would be produced had the material within the crack been mined out without deforming the solid. A two-dimensional crack filled with material of density equal to that of the host rock would produce no Bouguer anomaly. Jachens et al. (1983) have reported temporal changes in gravity, elevation, and area strain along the San Andreas fault in southern California such that the Bouguer anomaly apparently remains unchanged and the uplift-to-strain ratio is about −100 km. Several dislocation mechanisms are proposed that fulfill these constraints, but these mechanisms appear to be rather contrived and are not regarded as satisfactory explanations.

Journal of Geophysical Research Solid Earth↗

USGS2012

Deformation in the Yakataga seismic gap, Southern Alaska, 1980-1986

A 60-by-40-km trilateration network in the Yakataga seismic gap was surveyed in 1980, 1982, 1984, and 1986 with precise electro-optical distance-measuring equipment to measure strain accumulation. The overall deformation is roughly approximated by a 0.24±0.03 µstrain/yr N32°W±2.4° uniaxial contraction that is uniform in time. However, the spatial distribution of deformation shows some concentration of convergence in the neighborhood of the Chugach-St. Elias fault and of right-lateral shear across the Contact fault. A simple dislocation model of the plate interaction in the Yakataga gap fits the observed deformation reasonably well but seems to require that the motion of the Pacific plate relative to the North American plate be directed more nearly N36°W than N15°W, the generally accepted direction of relative motion for this location. However, the direction of plate motion inferred from the dislocation model depends upon details of the interaction at the plate boundary that may not have been modeled accurately. A nearby but smaller trilateration network at Icy Bay was surveyed in 1982, 1984, and 1986. This network spans the southwest corner of the rupture zone of the 1979 St. Elias earthquake. The deformation at Icy Bay consists of left-lateral shear across a northeast trending zone. The relation of this deformation to strain accumulation in the Yakataga gap, postseismic relaxation associated with the 1979 earthquake, or rebound from the unloading associated with the rapid recession of the Guyot glacier is not understood.

Journal of Geophysical Research Solid Earth↗

USGS2012

Absence of strain accumulation in the Shumagin seismic gap, Alaska, 1980-1987

Measurements of the deformation of a trilateration network in the Shumagin seismic gap in the interval 1980–1987 failed to detect any significant strain accumulation (observed extension rate in the direction of plate convergence 0.00±0.03 μstrain/yr). Dislocation models of the subduction process and measurements at a comparable network at a known seismic subduction zone (Nankai Trough, Japan) suggest that a rate of the order of −0.2 μstrain/yr should have been observed if the main thrust zone beneath the Shumagin Islands were locked. The simplest explanation of the observed absence of strain accumulation in the Shumagin seismic gap is that the main thrust zone beneath the Shumagin Islands is not presently locked. Other possible explanations depend upon very particular circumstances.

Journal of Geophysical Research Solid Earth↗

USGS2012

Principal component analysis of geodetically measured deformation in Long Valley caldera, eastern California, 1983-1987

Typical geodetic measurements of deformation consist of repeated surveys of a particular geodetic network. Such deformation data can be interpreted as a consequence of one or more self-coherent sources by means of principal component analysis. A self-coherent source is defined as any source that produces deformation that is time and space separable. Principal component analysis then gives the time and space factors that characterize the deformation attributed to each self-coherent source. Geodetic measurements of deformation at Long Valley caldera provide two examples of the application of principal component analysis. A 40-line trilateration network surrounding the caldera was surveyed in midsummer 1983, 1984, 1985, 1986, and 1987. Principal component analysis indicates that the observed deformation can be represented by a single coherent source. The time dependence for that source displays a rapid rate of deformation in 1983–1984 followed by less rapid but uniform rate in the 1984–1987 interval. The spatial factor seems consistent with expansion of a magma chamber beneath the caldera plus some shallow right-lateral slip on a vertical fault in the south moat of the caldera. An independent principal component analysis of the 1982, 1983, 1984, 1985, 1986, and 1987 leveling across the caldera requires two self-coherent sources to explain the deformation. The deformation pattern produced by the larger of these two sources appears to be roughly consistent with that found from the trilateration data. The deformation due to the second source is a nearly uniform tilt in the uplift profile. Presumably, that tilt is simply an artifact of systematic error in the leveling.

Journal of Geophysical Research Solid Earth↗

USGS2012

Equivalent strike-slip earthquake cycles in half-space and lithosphere-asthenosphere earth models

By virtue of the images used in the dislocation solution, the deformation at the free surface produced throughout the earthquake cycle by slippage on a long strike-slip fault in an Earth model consisting of an elastic plate (lithosphere) overlying a viscoelastic half-space (asthenosphere) can be duplicated by prescribed slip on a vertical fault embedded in an elastic half-space. For the case in which each earthquake ruptures the entire lithosphere (thickness H ), the half-space equivalent slip rate is as follows: Depth interval 0- H , slip identical to that in lithosphere-asthenosphere model (i.e., abrupt coseismic slip and no subsequent slip); depth interval (2 n −1) H to (2 n +1)H ( n = 1,2,…), slip rate uniform in space and dependent upon time as F n ( t ) exp (− t /τ a ) where F n is a ( n - 1) degree polynomial in t , τ a is twice the asthenosphere relaxation time (η/μ), and t is measured from the instant after the preceding earthquake. The slip rate averaged over the seismic cycle in each depth interval equals the secular rate of relative plate motion. For reasonable values of τ a , slip rates below 5 H do not vary much from that mean value and can be treated as constant. Thus the surface deformation due to the earthquake cycle in the lithosphere-asthenosphere model can be calculated very simply from the half-space model with time-dependent slip in the two depth intervals H −3 H and 3 H −5 H , and uniform slip at a rate equal to the secular relative plate velocity below depth 5 H . Inversion of 1973–1988 geodetic measurements of deformation across the segment of the San Andreas fault in the Transverse Ranges north of Los Angeles for the half-space equivalent slip distribution suggests no significant slip on the fault above 30 km and a uniform slip rate of 36 mm/yr below 30 km. One equivalent lithosphere-asthenosphere model would have a 30-km thick lithosphere and an asthenosphere relaxation time greater than 33 years, but other models are possible.

Journal of Geophysical Research↗

USGS2010

Postseismic relaxation following the 1994 M w 6.7 Northridge earthquake, southern California

We have reexamined the postearthquake deformation of a 65 km long linear array of 11 geodetic monuments extending north–south across the rupture (reverse slip on a blind thrust dipping 40°S–20°W) associated with the 1994 M w 6.7 Northridge earthquake. That array was surveyed frequently in the interval from 4 to 2650 days after the earthquake. The velocity of each of the monuments over the interval 100–2650 days postearthquake appears to be constant. Moreover, the profile of those velocities along the length of the array is very similar to a preearthquake velocity profile for a nearby, similarly oriented array. We take this to indicate that significant postseismic relaxation is evident only in the first 100 days postseismic and that the subsequent linear trend is typical of the interseismic interval. The postseismic relaxation (postseismic displacement less displacement that would have occurred at the preseismic velocity) is found to be almost wholly parallel (N70°W) to the nearby (40 km) San Andreas Fault with only negligible relaxation in the direction of coseismic slip (N20°E) on the Northridge rupture. We suggest that the N70°W relaxation is caused by aseismic, right-lateral slip at depth on the San Andreas Fault, excess slip presumably triggered by the Northridge rupture. Finally, using the Dieterich (1994) stress-seismicity relation, we show that return to the preseismic deformation rate within 100 days following the earthquake could be consistent with the cumulative number of M > 2.5 earthquakes observed following the main shock.

California↗

USGS2009

Postseismic relaxation following the 1992 M7.3 Landers and 1999 M7.1 Hector Mine earthquakes, southern California

Postseismic relaxation (measured postseismic deformation less the deformation that would have occurred at the preseismic rate) has been monitored at the same 10 monuments over ???6 years following both the 1992 Landers and the 1999 Hector Mine earthquakes. For both earthquakes the displacement components of the observed relaxation are well described by ?? i + ?? i f 1 (t), where ?? i and ?? i are constants peculiar to each component at each monument, t is the time after the earthquake, and f 1 (t) is a temporal function common to all components and all monuments for that earthquake. The temporal fanction f 1 (t) can be approximated by bt + c log e (1 + t /??), where ?? = 38.7 ?? 15.2 days and 25.6 ?? 7.7 days for the Landers and Hector Mine relaxations, respectively. Because the estimated values of ?? do not differ significantly, the transient term log e (1 + t/??) in the temporal function may be the same for both earthquakes. The asymptotic (t ??? ???) relaxation rates ?? i b are only a few mm/a and do not appear to be significantly different following the two earthquakes. The asymptotic deformation rates appear to be slightly greater than the preseismic deformation rates, but the preseismic rates were not measured directly. Thus, the deformations of the Landers array measured over the first 5.6 years following the Landers earthquake and over the first 6.4 years following the Hector Mine earthquake are generally consistent with a simple model in which the transient postearthquake relaxation depends upon time as log e (1 + t/??) with ?? = 28 ?? 5 days and the asymptotic postseismic speeds of the monuments exceed the preseismic speeds by at most only a few millimeters per annum.

Journal of Geophysical Research B: Solid Earth↗

USGS2008

Postearthquake relaxation after the 2004 M6 Parkfield, California, earthquake and rate-and-state friction

An unusually complete set of measurements (including rapid rate GPS over the first 10 days) of postseismic deformation is available at 12 continuous GPS stations located close to the epicenter of the 2004 M6.0 Parkfield earthquake. The principal component modes for the relaxation of the ensemble of those 12 GPS stations were determined. The first mode alone furnishes an adequate approximation to the data. Thus, the relaxation at all stations can be represented by the product of a common temporal function and distinct amplitudes for each component (north or east) of relaxation at each station. The distribution in space of the amplitudes indicates that the relaxation is dominantly strike slip. The temporal function, which spans times from about 5 min to 900 days postearthquake, can be fit by a superposition of three creep terms, each of the form ??l loge(1 + t/??l), with characteristic times ??, = 4.06, 0.11, and 0.0001 days. It seems likely that what is actually involved is a broad spectrum of characteristic times, the individual components of which arise from afterslip on different fault patches. Perfettini and Avouac (2004) have shown that an individual creep term can be explained by the spring-slider model with rate-dependent (no state variable) friction. The observed temporal function can also be explained using a single spring-slider model (i.e., single fault patch) that includes rate-and-state-dependent friction, a single-state variable, and either of the two commonly used (aging and slip) state evolution laws. In the latter fits, the rate-and-state friction parameter b is negative.

Journal of Geophysical Research B: Solid Earth↗