seismicity induced by seasonal groundwater...

Seismicity induced by seasonal groundwater rechargeat Mt. Hood, Oregon

Martin O. Saar a;b;�, Michael Manga a;b

a Department of Earth and Planetary Science, University of California, Berkeley, CA, USAb Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

Received 13 March 2003; received in revised form 9 June 2003; accepted 18 July 2003

Abstract

Groundwater recharge at Mt. Hood, Oregon, is dominated by spring snow melt which provides a natural large-amplitude and narrow-width pore-fluid pressure signal. Time delays between this seasonal groundwater recharge andseismicity triggered by groundwater recharge can thus be used to estimate large-scale hydraulic diffusivities and thestate of stress in the crust. We approximate seasonal variations in groundwater recharge with discharge in runoff-dominated streams at high elevations. We interpolate the time series of number of earthquakes, N, seismic moment,Mo, and stream discharge, Q, and determine cross-correlation coefficients at equivalent frequency bands between Qand both N and Mo. We find statistically significant correlation coefficients at a mean time lag of about 151 days.This time lag and a mean earthquake depth of about 4.5 km are used in the solution to the pressure diffusionequation, under periodic (1 year) boundary conditions, to estimate a hydraulic diffusivity of UW1031 m2/s, ahydraulic conductivity of about KhW1037 m/s, and a permeability of about kW10315 m2. Periodic boundaryconditions also allow us to determine a critical pore-fluid pressure fraction, PP/P0W0.1, of the applied near-surfacepore-fluid pressure perturbation, P0W0.1 MPa, that has to be reached at the mean earthquake depth to causehydroseismicity. The low magnitude of PPW0.01 MPa is consistent with other studies that propose 0.019PP9 0.1MPa and suggests that the state of stress in the crust near Mt. Hood could be near critical for failure. Therefore, weconclude that, while earthquakes occur throughout the year at Mt. Hood, elevated seismicity levels along pre-existingfaults south of Mt. Hood during summer months are hydrologically induced by a reduction in effective stress.3 2003 Elsevier B.V. All rights reserved.

Keywords: hydroseismicity; groundwater; pore-£uid pressure; permeability; e¡ective stress; volcano; triggering; stress; earthquake;recharge

1. Introduction

Natural or arti¢cial changes in pore-£uid pres-

sure may trigger earthquakes, a process hereafterreferred to as hydroseismicity. Examples includehydroseismicity induced by reservoirs [1^3], by£uid injection into [4^8] or withdrawal from [9^11] aquifers or oil reservoirs, or by pore-£uidpressure changes induced by other earthquakes[12,13]. It has also been suggested that hydroseis-micity may be caused by changes in groundwater

0012-821X / 03 / $ ^ see front matter 3 2003 Elsevier B.V. All rights reserved.doi:10.1016/S0012-821X(03)00418-7

* Corresponding author. Tel. : +1-510-643-5450;Fax: +1-510-643-9980.E-mail address: [email protected] (M.O. Saar).

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recharge rates [14^16] which can be the result ofseasonal snow melt or variations in precipitation[16^19]. In this paper we use signal processingtechniques to investigate whether natural ground-water recharge variations trigger some earth-quakes in the Cascade volcanic arc, USA.

The Cascade arc is located on a tectonicallyactive, and in parts densely populated, convergentplate boundary. Thus, for both seismic and vol-canic hazard assessment it is important to discerntriggers of earthquakes as tectonic, magmatic, orhydrologic. Moreover, rapid groundwater re-charge may initiate larger (local magnitude,Ml s 3) earthquakes on critically stressed faults

[20]. More generally, understanding the causesof hydroseismicity may provide additional insightinto seismic hazards associated with reservoirimpoundment or injection of £uids into the sub-surface for example during waste £uid injection,carbon sequestration, and geothermal energyexploration. Detection of natural groundwater-re-charge-induced earthquakes also provides a base-line against which reservoir- or £uid-injection-in-duced seismicity can be measured to evaluate theactual extent of human-caused hydroseismicity.Moreover, natural hydrologic triggering of earth-quakes provides insight into the state of stress inthe crust. In addition to tectonic information, thetime lag between groundwater recharge and earth-quakes allows us to determine hydraulic proper-ties of the upper crust on spatial and temporalscales that are relevant for studies of regional hy-drogeology.

Fig. 1a shows seismicity at Mt. Hood, Oregon,a Quaternary stratovolcano, for the period fromFebruary 4, 1980 through July 11, 2002. Earth-quakes occur preferentially on the southern £anksof the volcano. The o¡-axis concentration sug-gests the possibility that earthquakes are not all

Fig. 1. (a) Shaded relief map of Mt. Hood, Oregon, indicat-ing all earthquakes (pink circles and red squares) and se-lected (for criteria see text) earthquakes (red squares), streamdischarge gauging station on Salmon River (blue star), sum-mit of Mt. Hood (large white triangle), and hydrothermalSwim Warm Springs (western white diamond) and MeadowsSpring (eastern white diamond). Three (small yellow trian-gles) out of 14 relevant seismometers (Appendix A) are lo-cated within the map region. (b) Seismic moment, Mo, versusearthquake depth. (c) Histogram of earthquake depths, meanearthquake depth (4.5 km), and range of 1c standard devia-tion (2 km).

Fig. 2. Earthquake magnitude, Ml, binned in half-magnitudeincrements, versus logarithmic frequency of occurrence (Gu-tenberg^Richter relationship) for all earthquakes displayed inFig. 1. Open circles, squares, and solid circles indicate seis-micity during the summer (159week9 40, open circles) andwinter (weekv 41 or week9 14, open squares), and totalyears, respectively. Above the cut-o¡ magnitude of Ml = 1the decrease in seismicity with increasing magnitude followsapproximately the expected slope of b=31. This suggeststhat the data set is complete for Ml v 1.


M.O. Saar, M. Manga / Earth and Planetary Science Letters 214 (2003) 605^618606

caused directly by magma £ow although o¡-cen-tered magma-related seismicity can occur whenvolcanic conduits are inclined. Instead, we hy-pothesize that at least some seismicity could betriggered by seasonal groundwater recharge thatchanges pore-£uid pressures on pre-existing crit-ically stressed faults. We select a region of con-centrated o¡-axis seismicity (large open square inFig. 1a) to test this hypothesis.

2. Data and analysis

The 1980 Mount St. Helens eruption increasedmonitoring e¡orts at volcanoes in the CascadeRange. As a result, the Paci¢c Northwest SeismicNetwork has maintained short-period vertical-motion seismometers around Mt. Hood sincethe mid-1980s (Appendix A). To reduce instru-mentation bias we only use earthquakes with aminimum local magnitude of Ml = 1 (Fig. 2),above which bW31 holds in the Gutenberg^Richter [24] relationship:

log10N ¼ aþ bM l ð1Þ

where N is the number of earthquakes of magni-tude Ml and a is the production of seismicity.

Seismic moment, Mo, is approximated by[24] :

Mo ¼ 101:5ðMwþ10:73Þ ð2Þ

where we assume MwWMl due to our smallearthquake magnitudes of Ml 9 4.5.

Groundwater recharge at Mt. Hood is largelydue to spring snow melt which provides a naturalpore-£uid pressure signal of narrow temporalwidth and potentially relatively large amplitude.Groundwater recharge may be approximated byhydrographs of surface-runo¡-dominated streamsat high elevations, such as Salmon River, thatshow a peak in discharge during snow melt [22](Fig. 3). Groundwater recharge may be delayedfrom stream discharge due to £ow in the unsatu-rated zone. This possible delay is not consideredhere but may be neglected considering the uncer-tainty in earthquake depth discussed later.

Salmon River at USGS gauge 14134000 (bluestar in Fig. 1) has a 21 km2 drainage area. Gaugeelevation is 1050 m. Stream discharge for SalmonRiver is only available through September 30,1995. Thus, we determine a transfer function be-tween stream discharge of Hood River (USGSgauge 14120000) and Salmon River using aBox^Jenkins [23] method (Appendix B). Dis-

Fig. 3. Stream discharge of Salmon River, Oregon, measured at USGS gauging station 14134000 (red curve) located at an eleva-tion of 1050 m. During the estimation period, a transfer function between Hood River and Salmon River is determined using aBox^Jenkins [23] method (Appendix B). The evaluation period shows the ¢t between predicted (black) and actual (red) data. Theprediction period shows the estimated discharge for Salmon River. Intervals I and I+II are used in the analysis and are discussedin the main text.


M.O. Saar, M. Manga / Earth and Planetary Science Letters 214 (2003) 605^618 607

charge at Hood River is available until September30, 2001 and is convolved with the transfer func-tion to extend the discharge data to that date(Fig. 3).

For this analysis we distinguish two time inter-vals. Interval I has a lower bound on October 1,1986, i.e., at the beginning of the water year whenmost seismometers had been installed. The upperbound of interval I is set to the last availabledischarge date for Salmon River, September 30,1995. Interval II starts on October 1, 1995 andends when discharge measurements at Hood Riv-er were discontinued on September 30, 2001 (Fig.3). Therefore, our analysis focuses on interval I,to allow evaluation of the best-constrained data,and on the combined interval I+II, to investigatethe longest possible time series.

Fig. 4a,b shows histograms for stream dis-charge, Q, number of earthquakes, N, and seismicmoment, Mo, binned monthly for intervals I andI+II, respectively. Elevated levels of stream dis-charge exist from November through June witha peak in May due to snow melt. Number ofearthquakes and total seismic moment show apeak during September and October for both in-tervals I and I+II. In addition, interval I+IIshows seismicity in January and February. Forinterval I, the time lag between peak stream dis-charge, a proxy for groundwater recharge, andseismicity is about 5 months. To test whether Q,

N, and Mo have yearly periodicity, we determinetheir power spectra which indeed show dominantperiods of about one year (Fig. 5) for both inter-vals I and I+II.

Rather than using monthly binned data aver-aged over all years from Fig. 4 to determine cross-correlation coe⁄cients, we use the actual time se-ries at a resolution of one day. Seismicity isbinned to yield daily number of earthquakes, N,and total daily seismic moment, Mo. Next, weapply moving least-squares polynomial ¢ts (Ap-pendix C) of order 9 5 to Q, N, and Mo (Fig.6), resulting in the interpolated time series de-noted Q, N, and Mo, respectively. This type ofinterpolation ensures that the data are optimallymatched in a least-squares sense and that laterdetermination of cross-correlation coe⁄cients be-tween time series is based on equivalent frequencybands. Moreover, interpolation of N and Mo pro-vides evenly spaced data allowing for standardspectral analysis techniques. For better temporalcomparison, the interpolated data from Fig. 6(black curves) are shown normalized by their re-spective maximum values in Fig. 7.

For a lead channel f and a lag channel g, thenormalized cross- (fgg) and auto- (f= g) correla-tion coe⁄cients, xfg(t), at a time lag of t, aregiven by:

319x fgðtÞ ¼P fgðtÞffiffiffiffiffiffiffiffiffiffiffiffiffi

P ff ð0Þp ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

P ggð0Þp 91 ð3Þ

Fig. 4. Monthly binned histograms showing cumulative meandaily stream discharge (bold solid line), cumulative numberof earthquakes (thin solid line), and cumulative seismic mo-ment (thin dashed line) for (a) interval I and (b) intervalI+II.

Fig. 5. Period content of time series. Ten-day running aver-age power spectra, normalized by their respective maximumpower, of stream discharge, Q (bold solid line), number ofearthquakes, N (thin solid line), and seismic moment, Mo

(thin dashed line). Dominant periods around one year occurfor both interval I (a) and interval I+II (b).



where:

P fg ¼Z r

3r

f ðd Þ gðtþ d Þdd ð4Þ

The normalization ensures that perfect correla-tion, no correlation, and perfect anticorrelationare indicated by values of 1, 0, and 31, respec-tively.

We determine normalized unbiased cross-corre-lation coe⁄cients, xQN and xQMo

(Fig. 8) for thetime series. Cross-correlations show statisticallysigni¢cant peaks at 151 days that are distinctfrom 99% con¢dence intervals for random earth-quake distributions (Appendix D).

To reduce possible dominance by a year withexceptionally high seismicity, we also determinemoving normalized unbiased cross-correlation co-

e⁄cients, x fg, on overlapping segments withineach time series (Appendix D). The segment widthis 3 years with 30 days shift after each cross-cor-relation calculation resulting in 75 and 109 seg-ments for intervals I and I+II, respectively. Foreach segment 20 repetitions are performed so thata total of over 1000 and 2000 iterations are usedto determine the con¢dence intervals for intervalsI and I+II, respectively (Appendix D). Fig. 9shows statistically signi¢cant moving cross-corre-lation coe⁄cients for x QN and x QMo

that arealways distinct from the 90%, and in three quar-ters of the cases even from the 99%, con¢dencelimits for random earthquake distributions. Re-sults from all segments are averaged for each

Fig. 6. Original (gray) and interpolated (black) time series of(a) seismic moment, (b) number of earthquakes, and (c)stream discharge of Salmon River at Mt. Hood. Stream dis-charge includes predicted data from Fig. 3 for interval II. In-terpolation is performed using a moving least-squares poly-nomial ¢t method of order 9 5 per segment as described inthe text and in Appendix C. This ensures that the data areoptimally matched in a least-squares sense and that the seriescan be compared at equivalent frequency bands (Fig. 7).

Fig. 7. Interpolated time series from Fig. 6, normalized byeach series’ absolute maximum value. Local maxima of num-ber of earthquakes (thin solid line) and seismic moment (thindashed line) typically follow local maxima of stream dis-charge (bold solid line) after a time lag of about 151 days.

Fig. 8. Time lag versus unbiased normalized cross-correlationcoe⁄cients xQN (bold solid line) and xQMo

(bold dashedline) for interval I. Thin horizontal lines indicate the respec-tive upper bounds of the 99% con¢dence intervals of 1000cross-correlations for randomly assigned phases for each lagchannel (Appendix D). Lower bounds are comparable to thenegative of the upper bounds. Both curves suggest a time lagof about 151 days.



time lag (bold lines in Fig. 9). For both x QN andx QMo

a maximum is reached for a time lag ofabout yW151 days.

3. Discussion

In the following we describe processes that cancause hydroseismicity and provide a model thatallows us to determine both hydraulic di¡usivity,U, and critical pressure change, PP. From U wethen estimate hydraulic conductivity, Kh, and per-meability, k. Throughout the discussion we com-pare our results with other studies.

3.1. Causes of hydroseismicity

Principal mechanisms involved in triggering hy-droseismicity may be explained by combiningconcepts from linear poroelasticity [25] with theCoulomb failure criterion:

d s ¼ d 0 þ Wc0n ð5Þ

where ds, d0, W are the fault’s shear strength, co-hesion, and coe⁄cient of friction, respectively,and cPn is the e¡ective normal stress across thefault. Throughout this paper compressive stressesare positive. cPn clamps the fault requiring largershear stresses, d, to induce failure (Fig. 10) and isgiven (Appendix E) by the e¡ective principalstress tensor:

c0 ¼ c3KPN ij ð6Þ

where cc is the (regular) principal stress tensor, Pis the pore-£uid pressure, Nij is the Kroneckerdelta, and K is the Biot^Willis coe⁄cient, de¢nedas:

K ¼ 13K=K s ð7Þ

Here, K and Ks are the bulk moduli (incompres-sibilities) of the bulk rock matrix and the solid‘grains’, respectively [25]. Deformation can leadto failure, when the shear stress, d (AppendixE), exceeds the material’s shear strength, ds, in

Fig. 9. Time lag versus the mean of the unbiased normalizedmoving cross-correlation coe⁄cients x QN (bold solid line)and x QMo

(bold dashed line). Thin horizontal lines indicatethe respective upper bounds of the 99% (black) and 90%(white) con¢dence intervals of over 2000 cross-correlationsfor randomly assigned phases for each lag channel (AppendixD). Lower bounds are comparable to the negative of theupper bounds. Vertical lines at maximum coe⁄cient valuesindicate mean (center line) and meanV1c standard deviation(outer lines) for the respective time lags determined from 75(a) and 109 (b) moving windows of 3-year width. The fourmean time lags and respective standard errors are (in days):(a) 157V 2.7 (solid line), 152V 2.1 (dashed line); (b) 155V 4.1(solid line), 139V 3.9 (dashed line), resulting in a total meanand standard error of 151V 6.6 days.

Fig. 10. Relationship between stresses: (a) pore-£uid pressureis P= 0 so that the e¡ective stress is cP=c ; (b) pore-£uidpressure is Pg0 (the £uid-¢lled gap is drawn only for illus-trative purposes) and thus cP=c3KPNij as described in thetext; (c) Mohr circle with Mohr^Coulomb failure envelope(diagonal line). For explanation see main text.



Eq. 5, for a given e¡ective normal stress cPn. Be-cause cPn and d depend on both orientation of thefault within a stress ¢eld and on the magnitude ofthe stresses (Eqs. E1 and E2), failure can be trig-gered by changes in both a and cP (Fig. 10). Thelatter mechanism may induce earthquakes bycausing: (1) an increase in cP1, (2) a decrease incP3, or (3) an equal decrease in all e¡ective prin-cipal stresses, for example due to an increase in P(Eq. 6). The ¢rst two mechanisms cause failure byincreasing the e¡ective di¡erential stress, cP13cP3,and thus shear stress, d, in Eq. E2. The thirdmechanism induces failure by decreasing the e¡ec-tive strength of the material caused by a decreasein cPn which unclamps the fault and moves theMohr circle closer to the Mohr^Coulomb failureenvelope, while leaving d unchanged (Fig. 10).

Fluctuations in pore-£uid pressure, P, denotedPP, on faults due to an increase in cP1 (e.g., by theweight of a ¢lling reservoir that contracts the porespace) occur immediately. In contrast, a local in-crease in hydrostatic pore-£uid pressure, Ph =bwgh, (e.g., by groundwater recharge, reservoirimpoundment, or injection of £uids at depth),may trigger earthquakes after a time lag, y, thatis related to pressure di¡usion to the fault. Here,bw is the density of water, g is acceleration due to

the Earth’s gravity, and h is the height of thewater column above the point of interest. Reser-voirs exhibit both processes and thus typicallycause earthquakes both concurrent with, and de-layed from, their ¢lling [2,6]. In this paper we areinterested in seismicity induced by groundwaterrecharge and are thus focusing on earthquakesdelayed from recharge by pore-£uid pressure dif-fusion. Here, the load of the additional ground-water is small and thus triggered seismicity due toa (small) increase in cP1 is neglected. Nonetheless,because only the connected pore space is £uid-¢lled, relatively high hydrostatic pore-£uid pres-sure changes, PP, may be reached that may besu⁄cient to induce earthquakes.

3.2. Analytic model

We can approximate the e¡ect of seasonalgroundwater recharge with periodic yearly (i=1 year) pore-£uid pressure variations of amplitudeP0 at the surface (z= 0 m) as:

P0ðt; z ¼ 0Þ ¼ P0cos2Zti

� �ð8Þ

Pore-£uid pressure evolution below the watertable is governed by the (pressure) di¡usion equa-tion. In a one-dimensional half-space the di¡usionequation is given by:

UD

2P0

D z2¼ dP0

dtð9Þ

where the hydraulic di¡usivity:

U ¼ Kh

Ss¼ gk

XSsð10Þ

is assumed constant. Here, Kh, Ss, k, and X are thehydraulic conductivity, speci¢c storage, perme-ability, and kinematic viscosity, respectively. Thesolution to Eq. 9, with the boundary conditiongiven by Eq. 8 is [26] :

P0

P0¼ exp 3z

ffiffiffiffiffiffiffiffiZ

iU

r� �cos

2Zti

3zffiffiffiffiffiffiffiffiZ

iU

r� �ð11Þ

and is graphed in Fig. 11 for i= 1 year and hy-draulic di¡usivity U= 0.3 m2/s as determined laterin Eqs. 13 and 14 for the study region. The ex-ponential term in Eq. 11 describes the decrease in

Fig. 11. Periodic pore-£uid pressure £uctuations, PP/P0, atvarious depths, z (in km), for hydraulic di¡usivity U=0.3m2/s and surface pressure perturbation periodicity i=1 year.With increasing depth, the amplitude of the pore-£uid pres-sure perturbation decreases and the phase lag increases. At adepth of 4.5 km, approximately 10% of the original pressureamplitude, P0, remains and the delay of the peak is about151 days (dashed line), i.e., a phase lag of about 0.8 Z.



the time-dependent pressure amplitude withdepth, z, to PP/P0 = 1/e at a characteristic lengthscale (skin depth) of:

zc ¼ffiffiffiffiffiffiffiffiiU

Z

rð12Þ

The cosine term in Eq. 11 describes the periodicvariations of the pressure signal as a function ofboth depth, z, and time, t. In addition, both termsin Eq. 11 are a function of U and i.

The actual pore-£uid pressure at depth isP=Ph+PP, i.e., the hydrostatic pore-£uid pressurewith superimposed periodic pore-£uid pressure£uctuations, PP (Fig. 12). The argument in thecosine in Eq. 11 is expected to be zero (or a multi-ple of 2Z) so that the cosine reaches its maximum,one, during failure (e.g., point C in Fig. 12). Itmay be reasonable to assume that if a criticalpore-£uid pressure, Pc, had been reached beforethe cosine maximum (e.g., point B in Fig. 12) thenfailure should have occurred at shallower depthswhere a cosine maximum reaches the same criticalpore-£uid pressure, Pc, earlier in time (e.g., pointA in Fig. 12). Here we assume that the subsurfacehas a pervasive system of at least one fault alongwhich failure can occur at any depth given appro-priate stress conditions. Thus, from the conditionthat the argument of the cosine term in Eq. 11 hasto be zero, we can determine U from:

U ¼ i z2

4Zt2ð13Þ

3.3. Hydraulic di¡usivity

In our case the proposed period of pressureperturbation is i= 1 year and the time lag, y,between groundwater recharge and seismicity atMt. Hood is y= t= 151 with a standard error ofV 7 days (Fig. 9). Earthquake phase data forearthquake relocation were not readily available.Thus, we could not resolve whether the 1c stan-dard deviation in the earthquake depth distribu-tion, z= 4.5 V 2 km (Fig. 1c), re£ects error in de-termining earthquake locations. Hurwitz et al.[27] suggest that ice caps on many Cascade Rangevolcanoes may restrict recharge on their summitsand uppermost £anks and that the water table

below stratovolcanoes may thus be relativelydeep. Consequently, pore-£uid pressure di¡usiondistances to mean seismic depths may be shorterthan the 4.5 km assumed here, while relativelyslow £ow through the unsaturated zone abovethe water table could delay £uctuations of watertable levels. Furthermore, isotopic contents ofwater discharged for example at hydrothermalMeadows Spring suggest a recharge elevation of2700^2900 m, i.e., about 600 m below the summitof Mt. Hood [28]. However, lowering of the watertable not only reduces the available di¡usion time,t, in the saturated zone but also decreases thedi¡usion depth, z, to the earthquakes. Lower val-ues of t and z in Eq. 13 tend to cancel each other.In addition, earthquake depths are determinedrelative to a horizontal plane that is approxi-mately at the mean elevation (V1 km) of therelevant seismometers in the region. As a result,z and t assumed here are probably both somewhat

Fig. 12. Hydrostatic pressure, Ph, (at depths from 0 to 3 km)with superimposed (for better visibility) 10-fold exaggeratedperiodic pore-£uid pressure £uctuations, P=Ph+10PP, versustime for U= 0.3 m2/s and periodicity of i=1 year. The crit-ical pore-£uid pressure for failure should be reached at themaximum of the cosine term and a minimum possible depth(point A) as explained in the main text. At a depth of 3 km,the peak of the pressure perturbation is delayed (with respectto the surface) by 100 days (vertical line). Thus, at the meanearthquake depth of about 4.5 km the peak is delayed bythe determined time lag of about 151 days. The upper halvesof the sinusoids are ¢lled to better visualize the decrease inamplitude and increase in phase lag of the pore-£uid pressureperturbation with increasing depth.



smaller than may be expected. Due to the largeuncertainty in earthquake depth ( V 2 km) alreadyconsidered and due to the cancelling e¡ects ofreducing both z and t, we neglect the e¡ects ofwater table reduction by a possible 0.5^1 km rel-ative to the surface.

Using i= 1 year, tW151 days, and zW4.5 kmin Eq. 13 yields a hydraulic di¡usivity of:

U ¼ 0:30 � 0:22 m2=s ð14Þ

This value of U agrees with other crustal hydraulicdi¡usivities compiled by Talwani and Acree [1]and is in the upper range for fractured igneousrocks [29]. Gao et al. [30] suggest a value ashigh as 1 m2/s for some fractured volcanic sys-tems.

3.4. Critical pore-£uid pressure change

The step-function characteristics of a pore-£uidpressure increase due to initial reservoir impound-ment and its error function solution [1,31] do notallow for evaluation of the critical value of PP/P0

at which failure occurs [1]. In contrast, the addi-tional temporal information provided here by theperiodicity of the surface pressure perturbation inthe case of seasonal groundwater recharge allowsfor estimation of critical PP/P0. Because failure islikely to occur when the cosine term in Eq. 11 isone, we can determine PP/P0 for the above calcu-lated value of U= 0.3 m2/s at a mean depth ofabout 49 z9 4.5 km and period i= 1 year as:

P0

P0¼ exp 3z

ffiffiffiffiffiffiffiffiZ

iU

r� �W0:1 ð15Þ

Thus, about 10% of the estimated amplitude ofnear-surface pressure variations appears to be suf-¢cient to trigger hydroseismicity at Mt. Hood.

Average annual precipitation in the (Oregon)Cascades, and particularly at Mt. Hood, is about3 m [32] of which approximately 50% in¢ltratesthe ground [33,34] mostly during spring snowmelt. This leads to in¢ltration rates of about 1.5m/year concentrated during a few months. Lava£ows in the region typically have near-surface po-rosities of about 15% [35] that decrease withdepth. Thus, groundwater levels may £uctuate an-nually by approximately 10 m resulting in season-

al £uid pressure variations that may exceedP0 = 0.1 MPa. Therefore, according to Eq. 15,the critical pore-£uid pressure increase at depthzW4.5 km may be as low as PPW0.01 MPa,and possibly lower, at Mt. Hood.

While several studies mentioned in Section 1, aswell as this paper, suggest that some earthquakesare triggered by pore-£uid pressure perturbations,the necessary critical pore-£uid pressure increase,PP, is uncertain [1]. However, it is often arguedthat many faults are near critically stressed [36].Therefore, small stress changes invoked by a vari-ety of di¡erent mechanisms may be su⁄cient tocause seismicity on some pre-existing faults. Ex-amples include earthquake triggering by solidEarth and ocean tides [37^39], seasonal modula-tions of seismicity by the load of snow [40], pre-cipitation- and snow melt-induced seismicity[16,19] and general £uid-driven seismicity [41].Lockner and Beeler [42] conduct laboratory stud-ies of rock failure along pre-existing faults in-duced by periodic axial stress changes superim-posed on a con¢ning pressure of 50 MPa. They¢nd a transition from weak to strong correlationbetween periodic stress and failure at an ampli-tude of 0.05^0.1 MPa shear stress. Roelo¡s [6,29]suggests that an increase of PPW0.1 MPa cancause reservoir-induced seismicity. Similarly, pos-sible triggering of earthquakes by static stresschanges of about 0.1 MPa and less has been pro-posed by King et al. [43] and Stein et al. [44^46]

Harris [47] summarizes the work of several au-thors and states that ‘‘It appears that static stresschanges as low as 0.01 MPa (0.1 bar) can a¡ectthe locations of aftershocks’’.

The examples cited previously as well as ourresults suggest that the necessary stress changefor earthquake initiation on pre-existing faultsmay be as low as 0.01^0.1 MPa which is only afraction of the coseismic stress drop. Therefore,Harris [47] points out that Coulomb stresschanges are said to ‘enhance’ the occurrence ofan earthquake, as opposed to generating it. Wesupport this view and suggest that pore-£uid pres-sure changes due to groundwater recharge at Mt.Hood increase the probability of seasonal earth-quake occurrences.

Heki [40] states that seasonal seismicity is not



expected if the rate of secular (long-term) regionalstress increase is much larger than the annualsuperimposed disturbance. For the case of theCascades subduction zone, and assuming the val-idity of a characteristic earthquake model [48], theannual secular stress increase may be estimated bythe (approximately constant) coseismic stressdrop, vcW10 MPa, divided by the average recur-rence interval, trW300 years, of large earth-quakes. Estimated annual pore-£uid pressure £uc-tuations of 0.01 MPa/year at Mt. Hood at a meanearthquake depth of z= 4.5 km are comparable tovc/trW0.03 MPa/year. Therefore, the pore-£uidpressure £uctuations below Mt. Hood at depthsof about 4.5 km caused by groundwater rechargemay be large enough to induce seasonal hydro-seismicity.

The concentration of (hydro-)seismicity southof Mt. Hood may be due to preferential occur-rences of active faults in this region [28,49,50].Jones and Malone [50] performed earthquake re-locations and determined focal mechanisms ofevents from the June^July 2002 swarm which re-veal distinct clusters along normal faults (e.g.,White River fault) located south of Mt. Hoodas well as events located beneath the summitthat appear to be magma-related. This relationbetween snow melt, groundwater recharge, andseismicity on faults that are kept relatively perme-able may also be re£ected by the occurrence of theonly hydrothermal springs (Swim Warm Springs,Meadows Spring) at Mt. Hood [27,28] in the re-gion south of the volcano (Fig. 1a).

3.5. Hydraulic conductivity and permeability

Once the hydraulic di¡usivity, U, is known, thehydraulic conductivity, Kh, permeability, k, orspeci¢c storage, Ss, can be determined by Eq.10. The speci¢c storage is given by:

Ss ¼ bgðK þ nL Þ ð16Þ

where K is the bulk aquifer compressibility (atconstant vertical stress and zero lateral strain), nis the pore fraction, and L= 4.8U10310 m2/N isthe compressibility of water. If we assume a meannW0.05 for the study region [33] and K= 10310

m2/N for fractured rock [6,51], then, for the hy-

draulic di¡usivity range given in Eq. 14, the hy-draulic conductivity is:

8U10389Kh ¼ USs95U1037 m=s ð17Þ

which, from Eq. 10 and for a kinematic waterviscosity of XW1037 m2/s at 80‡C, correspondsto a permeability range of:

8U103169k95U10315 m2 ð18Þ

for the upper V6 km of the crust at Mt. Hood.The suggested permeabilities are relatively high

compared with a maximum of kW10316 m2 re-quired for mostly conductive heat transfer [52]as suggested for the Oregon Cascades at depthsbelow about 2 km. However, we suggest two pos-sible arguments that potentially explain why k ishigher than may be expected.

First, a reasonable assumption is that perme-ability is much higher at shallower depths anddecreases with depth due to compaction. There-fore, pore-£uid di¡usion is much faster in theshallower section and most of the observed timedelay probably occurs at deeper portions of thepro¢le. Reducing z for example by a factor of twoin Eq. 13 would decrease U, Kh, and k by a factorof four.

Second, we suggest that the region south of Mt.Hood is anomalous with respect to conductiveheat transfer because it hosts the only two hotsprings observed on the £anks of Mt. Hood todate [28]. The presence of hot springs suggeststhat geothermal £uids rise relatively quickly alonghigher-k paths (e.g., faults) so that time scales forcomplete conductive thermal equilibration be-tween hot £uids and colder surrounding rockare larger than the travel times of £uids. Indeed,Forster and Smith [21] suggest that hot springscan only be expected for a permeability windowof 10317 9 k9 10315 m2. Our permeability valuesfrom Eq. 18 fall in the upper range suggested forhot springs by Forster and Smith [21]. Here, highpermeabilities lead to increased water £uxes thatresult in lower geothermal spring temperaturesthat are consistent with those (5‡C to about25‡C [28]) observed at Meadows Spring andSwim Warm Springs.

The magnitudes for (mostly vertical) permeabil-ity, k, calculated here, re£ect values for a large



spatial scale that includes Mt. Hood and its near-by active (normal) faults that are kept permeableby rupture and appear to provide £uid pathways.That the magnitudes of hydraulic di¡usivity, U,and permeability, k, are plausible further supportsthe hypothesis of seasonal elevated seismicity lev-els due to groundwater recharge in this region.

4. Conclusions

Several arguments support the hypothesis thatsome seismicity at Mt. Hood, Oregon, is triggeredby pore-£uid pressure di¡usion as a result of rap-id groundwater recharge due to seasonal snowmelt. Statistically signi¢cant cross-correlation co-e⁄cients between groundwater recharge and seis-micity suggest a time lag of about 151 days. Thevalues of the correlation coe⁄cients are distinctfrom those for random temporal earthquake dis-tributions determined by Monte Carlo simula-tions. The time lag and mean earthquake depthprovide a reasonable (mostly) vertical hydraulicdi¡usivity (UW1031 m2/s), hydraulic conductivity(KhW1037 m/s), and permeability (kW10315 m2)that agree with other studies [1,21,36]. Finally, wedetermine the critical fraction (PP/P0 = 0.1) of theperiodic near-surface pore-£uid pressure £uctua-tions (P0W0.1 MPa) that reach the mean earth-quake depth, suggesting that PPW0.01 MPa cantrigger seismicity. This value of PPW0.01 MPa isat the lower end of the range of critical pore-£uidpressure changes of 0.019PP9 0.1 MPa sug-gested in previous studies [6,29,43,47]. Therefore,while seismicity is distributed throughout the yearat Mt. Hood, we conclude that some earthquakesare hydrologically induced by a reduction in ef-fective stress due to a seasonal increase in hydro-static pore-£uid pressure, Ph, by a small amountPP. In fact, elevated seismicity levels due to suchsmall e¡ective stress changes suggest that the stateof stress in the crust at Mt. Hood, Oregon, couldbe near critical for failure.

Acknowledgements

This work was supported by the Director, Of-

¢ce of Science, of the U.S. Department of Energyunder Contract No. DE-AC03-76SF00098 and bythe Sloan Foundation. We thank J. Rector forhelpful discussions related to signal processing,J. Kirchner for suggesting the approach to deter-mine con¢dence intervals on correlation coe⁄-cients, M. Singer for helpful insights into Box^Jenkins methods, and E. Brodsky for discussionsabout catalog completeness. We also thank C.Pa¡enbarger for e⁄cient computer system admin-istration. The reviewers, K. Heki, S. Ingebritsen,and L. Wolf, are thanked for their excellent com-ments and suggestions. Earthquake and streamdischarge data were obtained from the Paci¢cNorthwest Seismograph Network (PNSN) andfrom the USGS, respectively. The shaded reliefmap was made using the Generic Mapping Tools(GMT) and digital elevation models (DEM) fromthe USGS.[SK]

Appendix A. Seismometer information

The information in Table A1 about the short-period vertical-motion seismometers in the vicin-ity of Mt. Hood was provided by the Paci¢cNorthwest Seismograph Network. The date col-umn refers to the seismometer installation date.

Appendix B. Box^Jenkins method

The stream discharge of Salmon River is pre-dicted beyond its last measurement by employinga transfer function between Hood River and Sal-mon River. The transfer function is determinedusing a Box^Jenkins [23] method. In the case ofa single input channel, Xt, investigated here, theoutput (or lag) channel, Yt, can depend on bothcurrent (t= 0) and previous (t6 0) input, Xt, aswell as on previous output, Yt. Thus, input andoutput are related by:

Yt ¼g ðBÞN ðBÞXt3b þNt ðB1Þ

where:

g ðBÞN ðBÞ ¼

g 0 þ g 1Bþ g 2B2 þ Tþ g nBR

N 0 þ N 1Bþ N 2B2 þ Tþ N nBQðB2Þ



is the transfer function with coe⁄cients g and N.Because coe⁄cients in g act on current and pre-vious input and coe⁄cients in Q act on previousoutput, they may be denoted as moving average(MA) and auto-regressive (AR) processes and thetransfer function as a so-called ARMA model. Inthe previous equations, t is a time index, B is thebackshift operator such that BbXt =Xt3b, R and Q

are the number of delays for input and output,respectively, and Nt is noise assumed unrelated tothe input. Therefore, if the noise, Nt, is neglectedand (in our case) R= 4 and Q= 1 is selected thenthe output, Yt, at time t is given by:

N 0Yt ¼ N 1Yt31 þ g 0Xt þ g 1Xt31 þ g 2Xt32

þg 3Xt33 þ g 4Xt34 ðB3Þ

where N0 = 1 is commonly assumed (or else Eq. B3is divided by N0). Therefore, in this example, thecurrent output depends on one (b= 1) previousoutput (Salmon River discharge) as well as onthe current (b= 0) and previous four (19 b9 4)inputs (Hood River discharge).

Appendix C. Moving polynomial interpolation

The daily binned seismic data have to be inter-polated so that continuous time series are ob-tained on which standard spectral analyses can

be performed. We apply a moving polynomialinterpolation, rather than convolution of thedata with a Gaussian normal curve, so that noarti¢cial frequency is introduced by a convolutionkernel. In addition, the moving polynomial ap-proach allows interpolation with low-order (9 5)polynomials while ensuring that the data are op-timally matched in a least-squares sense. For allthree series, Q, N, and Mo, the width of the mov-ing window is 1/12th of the total series length andthe step width is 1/10th of the window width. Thepolynomial coe⁄cients, mLS, are found using thestandard least-squares solution from inversetheory given as mLS = [GTG]31GTd, where G isthe (up to) ¢fth-order polynomial model matrixand d is the data vector. Multiple interpolationvalues for a given time step result from the over-lap of the moving window and are averaged.

Appendix D. Correlation coe⁄cients

We determine auto- (f= g) and cross- (fgg) cor-relation coe⁄cients for time series f and g as de-scribed in principle by Eqs. 3 and 4. In practice,correlation coe⁄cients, Pfg, for positive time lags,l, are calculated by:

P fgðlÞ ¼1M3l

XM3l31

m¼0

f mþlgm ðD1Þ

Table A1Seismometer locations and installation dates

Key Latitude Longitude Elevation Date(km) (mm/yy)

KMO 45‡38P07.80Q 3123‡29P22.20Q 0.975 09/82SSO 44‡51P21.60Q 3122‡27P37.80Q 1.242 09/91TDH 44‡17P23.40Q 3121‡47P25.20Q 1.541 09/82VBE 45‡03P37.20Q 3121‡35P12.60Q 1.544 10/79VCR 44‡58P58.18Q 3120‡59P17.35Q 1.015 08/83VFP 45‡19P05.00Q 3121‡27P54.30Q 1.716 10/80VG2 45‡09P20.00Q 3122‡16P15.00Q 0.823 09/85VGB 45‡30P56.40Q 3120‡46P39.00Q 0.729 04/80VLL 45‡27P48.00Q 3121‡40P45.00Q 1.195 10/80VLM 45‡32P18.60Q 3122‡02P21.00Q 1.150 06/80PGO 45‡27P42.60Q 3122‡27P11.50Q 0.253 06/82AUG 45‡44P10.00Q 3121‡40P50.00Q 0.865 10/81GUL 45‡55P27.00Q 3121‡35P44.00Q 1.189 07/86MTM 46‡01P31.80Q 3122‡12P42.00Q 1.121 03/80



where m and M are the index and the length ofthe (zero-padded) time series, respectively. Divid-ing by (M3l) provides so-called unbiased cross-correlations where the reduced overlap length ofthe series for large time lags is accounted for.Correlation coe⁄cients are then normalized as de-scribed by Eq. 3.

We determine con¢dence intervals for the casewhere one of the two time series is assigned ran-dom phases for each frequency so that its auto-correlation is una¡ected. Typically 500 iterations(each assigning new random phases for each fre-quency) of cross-correlations, Pfg(t), at lag t, areperformed by spectral multiplication directly inthe frequency domain as:

P fgðtÞ ¼ F31fFff gF �fggg ðD2Þ

where F, F31, and F* denote the Fourier trans-form, its inverse, and its complex conjugate, re-spectively. The range of values that contain 90%of the data for a given time lag is the 90% con-¢dence interval for that time lag.

To reduce the e¡ect of years with unusuallyhigh seismicity, moving cross-correlation coe⁄-cients within overlapping subsections (windows)of the time series are also determined. Here, basedon all windows that provide output for a giventime lag, the mean coe⁄cient per time lag is de-termined. Each window has to be short enough sothat the years with dominant seismicity do not fallin all windows but large enough so that cross-correlations are performed over several periods(we chose 3 years). Furthermore, the time lagsof coe⁄cients that are distinct from the con¢-dence interval for random phase distributionsare used to calculate a mean and a standard de-viation for the (positive) time lag around the ¢rstlocal maximum coe⁄cient.

Appendix E. Normal and shear stresses

The e¡ective normal stress, cPn, is given by:

c0n ¼

c01 þ c

03

2þ c

013c

03

2cosð2a Þ ðE1Þ

where cP1 and cP3 are the e¡ective principal max-imum and minimum compressive stresses, respec-

tively, and a is the angle between cP1 and thenormal to the failure plane (Fig. 10a). The shearstress, d, is given by:

d ¼ c013c

03

2sinð2a Þ

�� ðE2Þ

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