GEOPHYSICS

Seasonal water storage, stressmodulation, and California seismicityChristopher W. Johnson,1,2* Yuning Fu,3 Roland Bürgmann1,2

Establishing what controls the timing of earthquakes is fundamental to understanding thenature of the earthquake cycle and critical to determining time-dependent earthquakehazard. Seasonal loading provides a natural laboratory to explore the crustal response to aquantifiable transient force. In California, water storage deforms the crust as snow andwater accumulates during the wet winter months.We used 9 years of global positioning system(GPS) vertical deformation time series to constrain models of monthly hydrospheric loadingand the resulting stress changes on fault planes of small earthquakes.The seasonal loadinganalysis reveals earthquakes occurring more frequently during stress conditions thatfavor earthquake rupture.We infer that California seismicity rates are modestly modulatedby natural hydrological loading cycles.

Changes in water storage and associatedsurface loads produce elastic deformationof Earth’s crust (1–3). In California, the ac-cumulation of winter snowpack in the SierraNevada, surface water in lakes and reser-

voirs, and groundwater in sedimentary basins fol-low an annual wet and dry cycle. Seasonal verticaland horizontal surface displacements reflect theelastic response of the lithosphere under hydro-spheric loads (4, 5) and have been linked to mod-ulating large-scale regional seismic activity (6–9).Seismicity may also be correlated with annualvariations in atmospheric pressure (10), surfacetemperature (11), snow accumulation (8), andcrustal pore pressure (12). Seasonal earthquakemodulation provides a natural experiment to in-vestigate the earthquake nucleation process byprobing the effects of low-amplitude stress per-turbations on active faults (13).The hydrosphere in California exhibits a strong

annual cycle following the wet and dry seasons.Time series from the continuously operating PlateBoundary Observatory and Bay Area RegionalDeformation global positioning system (GPS) net-works provide dense spatiotemporal resolutionof surface loading due to changing water storage(1, 3, 14). Seasonal vertical surface displacementpeak-to-peak amplitudes in the Sierra Nevadaand California Coast Ranges are 5 to 10mm andpeak late in the year following the dry summermonths (2). The recent drought conditions in thewestern United States amplified the observeduplift signal as Earth’s crust responds to the lossof mass (3). In the Central Valley and other sed-imentary basins, the observed seasonal verticaldisplacements are dominated by the poroelasticresponse to the head level in the local aquifersystemandpeak in the spring after thewetwintermonths (2). Stress changes in the crust from the

seasonal water loads in the Sierra Nevada, CoastRanges, and Central Valley may drive the peri-odic seismicity patterns, thus providing a physicalconnection to modulated earthquakes.In central California, periodic signals in earth-

quake catalogs indicate that 12 months and theharmonics are statistically significant and doc-ument the modulation of earthquakes at naturalloading cycles (15). Laboratory fault experimentssimulating periodic loading conditions suggest

that seismicity should more strongly correlatewith the stressing rate if the stressing periodexceeds the earthquake nucleation time (13).We expect a weaker correlation with the stressamplitude as the stressing period decreases,indicating a nucleation time exceeding the load-ing period (13). Numerical simulations predictthat the strongest correlation should occur atperiodic loading near the characteristic nucle-ation time (16). Earthquake triggering by theshort-period daily tides, which are comparablein amplitude to the seasonal loads, suggests avery weak correlation of seismicity rates withtidal stresses (17), except in regions with un-usually large tides (18). This supports the notionof earthquake nucleation times longer than thehourly tidal cycles, thereby obfuscating a detect-able earthquake response to the short-periodloading (13, 16). We might expect to find a cor-relationwith the seasonal stressing rate if earth-quake nucleation times for California faults areless than 1 year. We expect a somewhat weakercorrelationwith stress amplitude if annual periodsare shorter than the nucleation time scale.Determining the terrestrial water storage is an

inverse problem that estimates the change in thesurface mass load from the observed vertical de-formation (1). To avoid large seasonal signalsassociatedwith deforming local aquifers, we exam-ine the annual vertical displacement amplitudesand remove stations that exhibit uplift in the

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1Berkeley Seismological Laboratory, University of California,Berkeley, CA 94720, USA. 2Department of Earth and PlanetaryScience, University of California, Berkeley, CA 94720, USA.3School of Earth, Environment and Society, Bowling Green StateUniversity, Bowling Green, OH 43403, USA.*Corresponding author. Email: cwj@seismo.berkeley.edu

Fig. 1. Northern California focal mechanism catalog.The hydrological surface loading Coulombstress change (m = 0.4) is indicated by the color of the shaded focal mechanism compression quadrantfor M ≥ 2.0 events from 2006 to 2014. Events with a stress change <0.05 kPa are not shown.

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winter and subsidence in the summer. This in-cludes many stations located in the Central Valleyof California, where large volumes of groundwaterare pumped seasonally for agricultural purposesand the GPS peak amplitude is anticorrelated withthe Sierra Nevada and Coast Ranges modulation(2). The data from the remaining 661 GPS sitesare averaged to monthly time series of verticalmotions from January 2006 to December 2014.Changes in elevation are mapped to a surfacemass load using Green’s functions for a sphericalgravitatingEarthmodel (19). The inversionmeth-od (14, 20) estimates surface mass loads on a0.25° by 0.25° grid from32°N to 42.5°N and 125°Wto 115°W (movie S1). Knowing the time-dependenthydrological surface loads, we can calculate themonthly stress variations at seismogenic (8 km)depth in a stratified spherical elastic Earth (9).There are competing effects of other sources ofseasonal forcing—i.e., atmosphere, temperature,and tides—that could further change the state ofstress on the fault (10, 11, 21) but are generallysmaller in amplitude during the annual water-loading cycle (20). Our focus is seasonal forcing,and the long-term trend is removed from thestress time series (20).Our analysis attempts to provide the best hy-

drologically induced stress-change estimate byselecting the most plausible failure plane fortectonically driven earthquakes. Detailed inves-tigations of focal mechanisms in California re-veal a heterogeneous stress field and variationsin faulting style (22, 23) that need to be con-sidered when investigating the effect of appliedstress transients on fault activity. Plate boundarydeformation in central California involves right-lateral strike-slip faulting along the San AndreasFault (SAF) system and distributed regional short-ening in fold and thrust belts of the Coast Ranges(24, 25). To fully capture the complex fault struc-tures in California, we examine a declustered (26)catalog of focal mechanisms [magnitude (M) ≥ 2.0,N = 3,689] in the region 34.5°N to 41.5°N and124.5°W to 117°W between January 2006 andDecember 2014 (fig. S1) (20). The focal plane geom-etry is calculated using first-motion data recordedby theNorthernCaliforniaEarthquakeDataCenter(Fig. 1). We exclude events from two geothermaland volcanic centers where variation in the seis-micity ismainly a response to large-volume fluidinjection (27) or the upwelling of volcanic fluids(28). The focal mechanism nodal plane selectionprocess is nontrivial; while shear-stress changesare identical on the two orthogonal planes, normalstresses generally are not. We address ambiguityin the focal mechanism geometry by selecting thepreferred plane using a geometric approach. Forthe strike-slip mechanisms, we select the planethat is best aligned with the SAF (325°) for a ge-ometry consistentwith the tectonic environment.For thenormalandreversemechanisms,weassumeAndersonian geometry and select the plane witha dip angle closer to 30° for reverse events and60° for normal events. Using the preferred focalgeometry, the shear, normal, and Coulomb (m =0.4) stress is calculated for each earthquake(Fig. 1).

If slight changes in static stress influence thetiming of earthquakes, either promoting or dis-couraging nucleation, then earthquakes will oc-cur more often during slip-encouraging loadingconditions. We quantify the percent excess seis-micity (NEx) using 0.5 and 6.0 kPa/year stressintervals centered on zero for the resolved stressamplitude and stressing rate, respectively (20).The focal mechanisms are separated into pop-ulations of dip-slip events containing the reverse,normal, and oblique earthquakes (N = 2345) andstrike-slip (N = 1344) events (Fig. 2 and figs. S2and S3). Figure 2 shows the results for the shear-stress amplitude and rate for thedip-slip and strike-slip events. A positive trend of 22.5 ± 18.2 NEx/kPa(at 95% confidence) between –1.1 and 1.6 kPa isobserved for the shear-stress amplitude of thestrike-slip events, indicating a seismic responseto the peak shear amplitude. The dip-slip eventsexhibit a response to the shear stressing ratewith a positive trend of 12.5 ± 5.9NEx/kPa/year,ranging from –11.8 to 26.7 kPa/year. Excess eventsare not observed for the strike-slip events froman increase in the shear stressing rate, and, sim-ilarly, the dip-slip events do not show excess seis-micity as the shear stress amplitude increases.Interestingly, in all tests performed, the excessseismicity is ~0% for the near-zero stress interval.We repeat the analysis for a series of sensitivitytests (20) and assess our assumptions regardingmagnitude cutoff threshold, focal plane ambiguity,and the error in the focal plane solutions (figs. S4to S6). The population of M ≥ 2.3 (N = 1861)events indicate similar results for the strike-slip

events (N = 762) but no significant trend for thepopulation of dip-slip events (N = 1099) (fig. S4).The NEx values indicate that earthquakes areoccurring at different times of the shear-stresscycle for different fault types, suggesting that thestrike-slip events aremechanically different fromthe dip-slip population.The dominant faults in California belong to

the northwest-striking SAF system consistingmostly of right-lateral strike-slip and off-fault dip-slip structures. Excess dip-slip events are resolv-able during times of peak stressing rate, whichagrees with laboratory and numerical modeling(13, 16) if the nucleation time is less than 1 year.This follows aCoulomb failure threshold–triggeringmodel that predicts slip to occur with no lag timeat the highest stressing rates. However, the pop-ulation of strike-slip earthquakes indicates ex-cess events when the peak stress amplitude isgreatest (Fig. 2). This could either suggest thatthe nucleation time is longer for the strike-slippopulation of events or that there is an increasedtime lag from the peak stressing rate due tohigher tectonic loading rates (16). The strike-slipfaults associated with the central SAF system areaccumulating strain at rates 8 to 10 times as highas the dip-slip faults (24), consistent with thetime-lag scenario.The results do not indicate a trendwith changes

in the normal stress, independent of fault type(figs. S2 and S3). Themajor SAF system of strike-slip faults are postulated to be frictionally weak(29), and we expected a reduced sensitivity tonormal-stress changes. Laboratory measurements,

Johnson et al., Science 356, 1161–1164 (2017) 16 June 2017 2 of 4

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Fig. 2. Percent excess seismicity for shear-stress amplitude and shear stressing rate. (A) Dip-slipevents NEx values for shear-stress amplitude. (B) Strike-slip events NEx values for shear-stress amplitude.(C) Dip-slip events NEx values for shear stressing rate. (D) Strike-slip events NEx values for shear stressingrate. Bin interval is 0.5 kPa for shear-stress amplitude and 6.0 kPa/year for shear stressing rate. Theerror bars show the ±2 SD from bootstrapping. The minimum and maximum stress and stressing rateare shown numerically for the outer bins. The slope of the best-fit line is shown in the top left of eachpanel with the 2-SD error. The chi-square value is shown for the goodness of fit of the best-fit line.

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heat flow, and regional principal stress-orientationdata all support friction values between 0.1 and 0.2on the major strike-slip faults (29, 30). Our resultssupport the weak-fault hypothesis for faults inCalifornia. However, we cannot assume that allfaults in California are inherently weak due tovarying geology and the overall maturity of dif-ferent fault strands. If we perform the analysisand select the fault plane with maximum ten-sion, we do find a positive trend with the faultunclamping stress, but cannot say with confidencethat the plane selected is the correct failure planeand that a true response to the fault unclampingis occurring.We calculated seasonal stress time series using

the Uniform California Earthquake Rupture Fore-cast model geometry (UCERF3) (31), a multiyearcommunity effort that provides earthquake rup-ture probabilities on California faults. For eachfault location, we fit a seasonalmodel to the stresstime series and obtain model coefficients to cal-culate an average annual stress cycle. We assumethat this represents the monthly stress changefor the past 230 years. Figure 3 shows the annualpeak-to-peak Coulomb stress amplitude on faultsthroughout northern California [see fig. S7 forthe corresponding shear, normal, and Coulomb(friction values m = 0.1 and m = 0.7) stresses]. Thechange in Coulomb stress is <1 kPa onmost strike-

slip faults in the SAF system. The stress cycles onoblique and dip-slip faults in the eastern CoastRanges and flanking the Sierra Nevada are lar-ger. On many faults the peak slip-encouragingshear and normal stresses are out of phase by 30to 180 days (fig. S8). We assess the timing of his-toric seismicity from 1781 to 2012 for M ≥ 5.5earthquakes (N = 137) and only consider eventsnot identified as foreshock or aftershocks (32).We assumed that the UCERF3 geometry of thenearest fault location is representative of the his-toric event to evaluate the stress for the monththe earthquake occurred. Our simplified treat-ment of the historical seismicity records suggeststhat more events occur during times of slip-encouraging failure conditionswith a trend of 14.5 ±9.6 NEx/kPa for the Coulomb (m = 0.4) stress change(Fig. 4). The more recent earthquakes occurringduring the instrumental era (1932 to 2012) pro-duce similar results, with more events duringperiods of inferred positive Coulomb seasonalstress changes (fig. S9). Although the geometryand hydrological stress conditions of large earth-quakes are less well known, the historic catalogssuggest that large earthquakes might also betriggerable from low-amplitude seasonal stresschanges. We infer that annual hydrospheric load-ing is a contributing factor in the modulation ofmicroseismic earthquakes in California.

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−124˚ −123˚ −122˚ −121˚ −120˚ −119˚ −118˚35˚

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Fig. 3. Northern California faults in the UCERF3 fault model shown with the annual peak-to-peakCoulomb stress change from hydrological loading.

Fig. 4. Percent excess seismicity from 1781 to2012 for M ≥ 5.5 events (N = 137), using theUCERF3 historic seismic records and theaverage monthly annual stress estimated fromthe closest fault–model geometry.The errorbars show the ±2 SD from bootstrapping. Theminimum and maximum extent of stress valuesis shown numerically for the outer bins. The slopeof the best-fit line is shown in the top left ofeach panel with the 2-SD error. The chi-squarevalue is shown for the goodness of fit of thebest-fit line.

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ACKNOWLEDGMENTS

Funding for this project was provided by the U.S. Geological SurveyNational Earthquake Hazards Reduction Program (G15AP00106) andthe Southern California Earthquake Center. This material is based onwork supported by the National Science Foundation Graduate ResearchFellowship under grant number DGE1106400 for C.W.J. GPS data were

collected by the Plate Boundary Observatory operated by UNAVCOfor EarthScope (www.earthscope.org) and supported by NationalScience Foundation grant no. EAR-0350028 and EAR-0732947. Thedata were processed using the GIPSY OASIS II software providedby the Jet Propulsion Laboratory. Waveform data, metadata,or data products for this study were accessed through the NorthernCalifornia Earthquake Data Center (NCEDC), doi:10.7932/NCEDC.The monthly water-loading estimates and earthquake catalogwith the calculated stresses are all available in the supplementarymaterials.

SUPPLEMENTARY MATERIALS

www.sciencemag.org/content/356/6343/1161/suppl/DC1Materials and MethodsFigs. S1 to S9Movie S1References (33–53)

22 September 2016; resubmitted 9 December 2016Accepted 23 May 201710.1126/science.aak9547

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Seasonal water storage, stress modulation, and California seismicityChristopher W. Johnson, Yuning Fu and Roland Bürgmann

DOI: 10.1126/science.aak9547 (6343), 1161-1164.356Science 

, this issue p. 1161Sciencehydrological loading cycle modulates microseismicity in California.years. Slight changes in stress did indeed influence the timing of earthquakes, which confirms that the annualwhether this is indeed the case by combining detailed earthquake records with high-resolution GPS data from the past 9

askedet al.the alternating wet and dry cycles in earthquake-prone California should affect the earthquake rate. Johnson Earthquakes can be triggered by changes in crustal stress, such as variations in fluid pore pressure. As a result,

Saving earthquakes for the wet season

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