Codependent histories of the San Andreas and San Jacinto fault zones from inversion of fault displacement rates

Department of Geosciences, Pennsylvania State University, 542 Deike Building, University Park,Pennsylvania 16082, USAABSTRACTThe displacement histories of the San Jacinto and southernmost San Andreas fault zonesare constrained by offset data with ages in the range of 5 Ma to 5 ka. Apparent discrep-ancies between long- and short-term average displacement rates can be reconciled with atime-variable rate model. In this model, the displacement rate on the San Andreas decel-erated from ;35 mm/yr at 1.5 Ma to as low as 9 6 4 mm/yr by 90 ka. Over this sametime period, the rate on the San Jacinto fault zone accelerated from an initial value ofzero to a rate of 26 6 4 mm/yr. The data also imply that the rate of the San Andreasfault accelerated since ca. 90 ka, from ;9 mm/yr to the modern rate of 27 6 4 mm/yr,whereas the San Jacinto decelerated from 26 6 4 mm/yr to the modern rate of 8 6 4mm/yr. The time scale of these changes is signiﬁcantly longer than the earthquake cycle,but shorter than time scales characteristic of lithospheric-scale dynamics. The emergenceof the San Jacinto fault zone ca. 1.5 Ma coincided with the development of a majorrestraining bend in the San Andreas fault zone, suggesting that the formation of newsubparallel faults could be driven by conditions that inhibit displacement on preexistingfaults.Keywords: fault displacement rates, lithospheric rheology, continental dynamics, crustaldeformation.INTRODUCTIONContinental plate boundary zones are oftencharacterized by systems of faults spanningbroadly deforming regions (Fig. 1). Determin-ing how these faults accommodate relativeplate motions and the nature of their spatialand temporal interactions remains an elusivegoal. In particular, whether fault-displacementrates are constant or time variable—and if so,on what time scales—is difﬁcult to ascertainbecause most geologically determined dis-placement rates represent averages since theage of an offset geologic or geomorphic fea-ture. In the case of time-varying rates, this av-eraging effect can lead to apparently inconsis-tent estimates depending on the ages of theoffset markers.The partitioning of Paciﬁc–North Ameri-ca relative plate motion among the manynorthwest-oriented dextral strike-slip faults insouthern California has been the subject of in-tensive research for decades (Table 1). In thelatitude band 328Nto348N, ;70% of the totalrelative motion between these plates is accom-modated by the San Jacinto and southernmostSan Andreas faults (Fig. 1). Together theytransfer ;35 mm/yr of motion from the Im-perial to the Mojave segment of the San An-dreas fault (north of the San Jacinto–San An-dreas intersection). Previous studies havetended to concentrate either on displacementrates of individual faults or on the steady-statepartitioning of deformation between faults.However, these data can also be used to assesswhether the rate of deformation is conservedbetween these two fault zones over time, as iswidely accepted.Here we apply a technique that allows us touse time-averaged estimates of displacementrate to infer the time history of instantaneousdisplacement rates on the San Andreas andSan Jacinto fault zones. This history allows usto investigate interactions between these twofault zones and, in particular, to assess wheth-er they act in a coupled manner. As we show,interactions between these faults could haveimportant implications for geodynamics, bear-ing on issues such as the relative strengths ofupper mantle and lower- and upper-crustal lay-ers, and the degree to which the deformationﬁeld within the upper crust is coupled to thatwithin the upper mantle. Investigations suchas ours, which use data representing signiﬁ-cantly different periods of time, may thus pro-vide a new approach to investigating somelong-standing problems in geodynamics.DATATable 1 summarizes the geologic, geomor-phic, and geodetic observations constrainingaverage displacement rates on these two faultsover a diverse range of time scales. Each ratelisted in Table 1 represents an average over aﬁnite interval of time. The duration of eachaveraging interval is determined by the age ofa measured offset marker, such as a distinctiverock unit, a geomorphic feature, or a geodeticmonument. With the exception of the geodeticinferences, the averaging intervals are quitelong relative to the earthquake cycle, which ison the order of hundreds of years for the SanAndreas and San Jacinto fault zones. Becausethese data record averages over long periodsof time, they should be insensitive to temporalirregularities in earthquake recurrence.Age-dependent variation in the rate data isappreciable for both faults (Table 1). For theSan Andreas, rate estimates range from ashigh as 30 mm/yr to as low as 14 mm/yr.Rates for the San Jacinto fault zone also varyby nearly a factor of two; long-term averagesare signiﬁcantly larger than estimates repre-senting shorter, more recent, intervals. In or-der to compare the different observations andto constrain the history of fault displacements,we need to consider the uncertainty in eachdatum. In the geologic literature, error bars donot typically represent statistical measures ofuncertainty (e.g., standard deviations of a nor-mal distribution), but rather they usually rep-resent upper and lower bounds on possibledisplacement rates, based on complex age andoffset relationships among various markersacross the faults. Error estimates often resultin asymmetric plus-or-minus ranges. Our anal-yses of these data are based on more tradi-tional statistical measures of uncertainty. Wehave thus had to make some assumptionsabout how best to represent the reported errorbounds in terms of Gaussian error distribu-tions. Table 1 lists the standard deviations thatwe chose to best represent the allowable slipranges derived from geologic observations. Inall cases we conservatively chose error distri-butions with 95% conﬁdence regions coincid-ing roughly with the absolute bounds reportedin the literature.ANALYSIS AND RESULTSTo explore the history of displacement rateson the San Andreas and San Jacinto faultzones implied by the averages of Table 1, weemployed the theory of smoothing splines(e.g., Matthews and Segall, 1993). The basicgoal is to use the rate averages, which repre-