Crustal uplift in the south central Alaska subduction zone: New analysis and interpretation of tide gauge observations

JOURNAL OF GEOPHYSCAL RESEARCH, VOL. 106, NO. 6, PAGES 11,259-11,270, JUNE 10, 2001 Crustal uplift in the south central Alaska subduction zone: New analysis and interpretation of tide gauge observations Steven C. Cohen Geodynamics Branch, Goddard Space Flight Center, Greenbelt, Maryland Jeffrey T. Freymu½ller Geophysical nstitute, University of Alaska, Fairbanks, Alaska Abstract. We have examined tide gauge measurements of apparent sea level height in south central Alaska to determine the history of crustal uplift subsequent to the 1964 Prince William Sound earthquake. There are spatial and temporal variations in the uplift rate since the 1994 earthquake that depend on the location of the tide gauge relative to the coseismic rupture features. At Seward, on the eastern side of the Kenai Peninsula, we find slow uplift that is consistent with elastic strain accumulation at the locked North American-Pacific Plate boundary. Conversely, at Seldovia and Nikiski, on the western side of the Kenai Peninsula, we find persistent rapid uplift of -10 mm yr - that may be longterm transient response to the earthquake but that cannot be sustained over the entire several hundred year recurrence interval for a great earthquake. Farther to the southwest, at Kodiak, the rate of uplift is several millimeters per year but has slowed significantly over the past three and a half decades. To the east of the Kenai Peninsula we find subsidence at Cordova and an uncertain behavior at Valdez. At Cordova, and to a lesser extent Valdez, there is a mathematically significantime dependence, although the evidence for the time dependence is less compelling than at Kodiak. At Anchorage, there is little evidence of vertical motion since the earthquake. The along-strike spatial variability in the relaxation time of the rates of vertical motion since the 1964 earthquake may be related to variations in the updip coseismic slip during the megathrust event. 1. ntroduction The spatiotemporal pattern of the crustal movement that has occurred in south central Alaska since the 1964 Prince been previously available. Our analysis is, in part, an update and extension of two previous studies of the tide gauge data in south central Alaska. While we defer a detailed discussion of previous results until section 5.1, we note here that Brown et at. [1977] examined tide gauge records of up to 10 years length William Sound earthquake (M w = 9.2) is far more complex than that predicted by constant loading rate, two-dimensional collected at five south central Alaska sites. They found postmodels of postseismic and interseismic strain accumulation. seismic uplift at sites that subsided coseismically and vica versa, For example, analysis of repeated leveling surveys conducted but as noted by SP91, the correlation between the coseismic along Turnagain Arm (Figure 1) revealed that although the motion and the postseismic uplift rate was weak. SP91 reexcrust rose rapidly after the earthquake, with a maximum uplift amined the tide gauge observations at the same locations and rate of 150 mm yr-, the rate of uplift decreased substantially two others with a data set that was up to 24 years long. n on the timescale of a few years [Brown et at., 1977; Cohen, general, they found slower, sometimes considerably slower, 1998]. n contrast, only modest time variations, at most, were rates of vertical motion than did Brown et al. [1977], although seen in uplift rates deduced from tide gauge data collected at they did not report any temporal variation in the uplift rates coastal locations [Savage and Plafker, 1991, hereinafter re- except to distinguish between rates derived from the entire ferred to as SP91]. Moreover, recent GPS observations on the data set and from data subsequent to 1973 (i.e., approximately Kenai Peninsula and adjacent regions have revealed considera decade after the earthquake). able spatial variability in the horizontal motion with NNW t is an appropriate time to reexamine what can be learned motion relative to the stable North American Plate occurring on the eastern Kenai Peninsula and SE, i.e., trenchward, mofrom the tide gauge data. A decade has passed since the last tion occurring on the western Kenai Peninsula [Cohen and analysis; hence the length of the postseismic data records has increased to -35 years. As the mean sea level data are subject Freymuetter, 1997; Savage et at., 1998; Freymuetter et at., 2000]. These complex and seemingly contradictory aspects of southto both interannual and several-years-long noise components, ern Alaska crustal deformation are addressed in this paper. We the improvement in the rate reliability obtained using the will provide new determinations of crustal uplift rates and longer record is more than that expected from the averaging of examine their temporal and spatial variability using a longer, random noise. n addition, it is now possible to detect rate and therefore more robust, tide gauge data series than has changes that have occurred over the past three and half decades. Furthermore, the information from the tide gauges can Copyright 2001 by the American Geophysical Union. be analyzed with new insights derived from recent Global Po- Paper number 2000JB900419. sitioning System (GPS) measurements and other recent obser- 0148-0227/01/2000JB900419509.00 vations into a comprehensive picture of the spatial and tem- 11,259

... 11,260 COHEN AND FREYMUELLER: CRUSTAL UPLFT FROM ALASKA TDE GAUGES / l!i::' [ :. /.J,5 /,, ',/ / SUBMARNE :00NTOC $.N FEET J- L..,.,:-::' : : ': :: :.;L._;, --.,,.,:.4.:... -: Figure 1. Map of south central Alaska showing major cities, tide gauge locations (note that Nikiski is immediately northwest of Kenai), and coseismic uplift pattern for the 1964 Prince William Sound earthquake. From Plafker [1971]. poral patterns of crustal deformation in this portion of the Alaska subduction zone. gauge rates at the individual stations and the average residuals from detrended rates at the three southeast Alaska locales, a region well removed from 1964 rupture zone. The only significant difference between our procedure and that of SP91 is that we rejected any annual means that were derived from less than nine monthly means, whereas some of the annual means 2. Data Analysis We extracted monthly mean sea level height determinations for tide gauge stations from the National Oceanographic and Atmospheric Administration data archives accessible over the of SP91 were derived from yearly data containing less than six World-Wide Web. The seven south central Alaska sites used in monthly values. Since there is a strong annual oscillation in the our study are Anchorage, Seldovia, Cordova, Valdez, Seward, sea heights, we sought to minimize the possibility that the Nikiski, and Kodiak (St. Paul Harbor and Women's Bay). We analysis would be biased by seasonal effects even if it meant also extracted records for three southeast Alaska sites (Sitka, reducing the data set somewhat. Nevertheless, the apparent Ketchikan, and Juneau) for use in correcting the records for sea level rates that we obtained by analyzing the data through local oceanographic effects. Some of the Seward data were not 1988 closely agreed with the rates reported by SP91. We estiavailable over the Web, so they were obtained from paper mated uplift rates at each of the sites by taking the negative of records. From these monthly data we formed annual means the apparent rate of sea level change and adding 2 mm yr - to from which we derived rates of apparent sea level change account for eustatic sea level change and postglacial rebound. following the procedure outlined by SP91. The procedure cor- Although the value of 2 mm yr - is somewhat arbitrary at the rects for local oceanographic and atmospheric effects based on millimeter per year level, and may in reality have site-to-site the coherence between the residuals to the aletrended tide variability, we did not attribute any additional uncertainty in

COHEN AND FREYMUELLER: CRUSTAL UPLFT FROM ALASKA TDE GAUGES 11,261 Table 1. Tide Gauge Sites Site Cordova Valdez Seward Kodiak Seldovia Anchorage Nikiski Comment Record is among the most complete with significantemporal gaps only in the middle to late s. There are no data prior to 1975; otherwise, the record is fairly complete. Some data are missing, but the record extends over the entire postseismic interval. The operational tide gauge was located at St. Paul Harbor until 1984, then it was moved a few kilometers to Women's Bay. A leveling survey connects the two sites, and the leveling result was verified by the simultaneous operation of tide gauges at both sites for 2 months in 1984. The tide gauge and leveling data agree in the offset to within 15 mm. Separate analyses of the St. Paul Harbor (1967-1982) and Women's Bay (1985 to present) records reveal a substantially faster uplift rate when the gauge was located at St. Paul Harbor than at Women's Bay. Record is strong with only a few missing data points. There is a significant anomaly in the late 1970s which is not removed by the correction procedures employed herein; however, the subsequent record is well behaved. nterpretation of the tide gauge signal at Anchorage is handicapped by two factors. First, as Brown et al. [1977] and Savage and Plafier [1991] point out Anchorage (and to a much lesser extent Seward) may exhibit a sinusoidal oscillation with a period of several years in the first decade following the earthquake. This oscillation is less obvious at Anchorage in our data set than in Savage and Plafier's data set because we have deleted the annual means that are based on less than nine monthly means. There are very few data available from the early 1970s until the mid- 1980s. After that the record becomes more robust. An alternative sea level record has been derived from the more complete set of monthly mean tide data. The tide gauge operated through much of the 1970s, then was reactivated in 1997. our rate estimates due to this choice. The site-specific aspects 4. ndividual Site Results of the sea level data record at each of the seven tide gauges are We will discuss the results at the individual sites starting at summarized in Table 1. Cordova, the site located closest to the downdip end of the 1964 coseismic rupture, and progressing to other sites at in- 3. Constant and Time-Dependent Rate Analysis creasing distance from the rupture edge. At Cordova the rate of sea level change from the linear analysis is 6.7 _ 0.4 mm Figure 2 shows the apparent sea level through 1998 for all yr -. This compares to the SP91-determined rate of 9.7 +_ 0.5 seven sites with each plot showing both the uncorrected and mm yr -. Since, as we discuss in section 5.2, rates approaching corrected sea level heights and the line derived from a linear 10 mm yr - are unlikely to be sustained over the entire earthregression on the corrected observations. The slope of each quake cycle, it is not surprising that the rate at Cordova apregression line, i.e., the apparent rate of sea level change, is pears to be decreasing. The quadratic regression analysis gives given in Table 2 as are the rates derived from earlier studies, to a rate change c in the sea height equation, which we refer to in section 5.1.3. Since the errors in the tide gauge observations and monthly and annual means are not known, we estimated rate and rate change errors from the misfit of the regression curve to the data, as outlined by Press et al. [1986]. The variance reduction achieved by the southeast Alaska sea level correction is 85, 80, 42, 47, and 82% at Cordova, Valdez, Seward, Seldovia, and Anchorage, respectively, and nearly zero at Kodiak and Nikiski. Figure 3a shows the residuals to the linear fit at each of the seven locales. t is noteworthy that there are several correlated residuals (e.g., between 1996 and 1998), suggesting that while the southeast sea level correction is successful in reducing the variance at most locales, it does not fully remove all correlated sea level fluctuations. Of even greater importance are the systematic residuals apparent at Kodiak, Cordova, and possibly Valdez. The shape of these residual suggests a time dependence to the apparent sea level rate. We performed an additional least squares regression on the data using a quadratic polynomial in time for each site except Nikiski and Anchorage (for which the data set is too sparse) and found that the rate change was formally above the corresponding uncertainty at Kodiak, Cordova, and Valdez but was indistinguishable from zero at Seward and Seldovia. The apparent sea level rates derived from the quadratic regressions are also summarized on Table 2 and the residual after removal of the quadratic term at the aforementioned three sites is shown in Figure 3b. n Figure 4 we show the linear and quadratic fits to the data at Kodiak, Valdez, and Cordova. We will say more about the credibility of the quadratic terms, i.e., the rate variations, in section 4. ½ h =a +bat+ (At) 2, (where At = t - to and t o is a reference time) of c - -0.39 +_ 0.06 mm yr -2. While prudence dictatesome skepticism as to whether the mathematically significantemporal variation in the uplift rate is physically real, even a visual inspection of the corrected uplift rates as shown in Figure 2 reveals that there has been a slowdown or halt in sea level change since the late 1980s. Formally, the quadratic least squares analysis indicates that the postseismic uplift rate decays to one half its initial (i.e., year 1965) value in -17 years. We applied the F test to determine whether the improvement in the residuals with the quadratic curve over the linear case is statistically significant. The improvement passes the F test [Mikhail, 1976] at the 1% level, indicating a 99% probability that the improvement is formally meaningful. The F statistic is [Zhao et al., 1995] (SSR1- SSR2)/(DF1- DF2) F = (SSR2)/(DF2) ' (1) where SSR is the sum of the squared residuals and DF is the number of data points minus the number of parameters and the subscripts refer to the two different models. At Valdez the data record dates back to 1975, 11 years after the Prince William Sound earthquake. The rate of apparent sea level change since that time, -0.2 _+ 0.7 mm yr -, is not

._ 11,262 COHEN AND FREYMUELLER: CRUSTAL UPLFT FROM ALASKA TDE GAUGES Cordova Valdez 4.1 4.3 44.1-4.0-3.7-3.9-3.6 1970 1980 1990 2000 3.8...,...,...,... 1970 1980 1990 2000 Seward Kodiak 3.8 2.6.2.5 J - 3.6 -. 2.4 *':t.5 -- 2.3 3.4-2.2 3.3 2.1 1970 1980 1990 20 1970 1980 1990 2000 5.5 o Seldovia 7.2 E _-7.1 - Anchorage - 5.3 - *'5.2 - -9.3 + 0.8 mm/yr ß 7.0-6.9-6.8-0.8 +_ 1.3 mm/yr 5.0 i i i 1970 1980 1990 Nikiski 2000 6.7 1970 1980 1990 2000 5.9 E ' 5.7 - *'5.6 -- [s.s - 5.4 i i 1970 1980 1990 2000 Figure 2. Uncorrected (circles) and corrected (squares) annual sea level heights and linear least squares line with slope as given on Table 2. significantly different from zero but is less than the SP91 rate assessment of the residuals in Figure 3a make us particularly of 5.5 + 0.9 mm yr -. There is a mathematically significant skeptical about ascribing a great deal of physical significance to change in the sea level rate of -0.76 _+ 0.14 mm yr -2 that the mathematical result. produces a rapid transition from crustal subsidence to crustal uplift. Although the quadratic sea height solution passes the F At Seward the apparent sea level change is -1.2 _+ 0.7 mm yr-, and the rate change is insignificantly different from zero. test, the lack of data prior to the 1970s and our qualitative Our previous analysis of GPS horizontal velocity vectors shows

COHEN AND FREYMUELLER: CRUSTAL UPLFT FROM ALASKA TDE GAUGES 11,263 Table 2. Rate r of Apparent Sea Level Change, Most Recent to Oldest Determinations r, Quadratic Sea Level Analysis, r = h = b + cat r = h, Linear Sea Level Tide Gauge Time Period Analysis, mm yr - b, mm yr - c, mm yr -2 Ref. a Comment Cordova 1965-1998 6.7 +_ 0.4 6.9 +_ 0.3-0.39 _+ 0.06 1 1974-1988 9.4 2 1964-1988 9.7 _+ 0.5 2 1964-1974 12.7 + 2.4 3 Valdez 1975-1998 -0.2 _+ 0.7-0.3 +_ 0.4-0.76 +_ 0.14 1 1974-1988 5.5 _+ 0.9 2 Seward 1965-1998 -1.2 +_ 0.7-1.2 _+ 0.7-0.09 _+ 0.15 1 1974-1988 2.9 2 1964-1988 0.1 _+ 1.0 2 1964-1973 - 11.3 _+ 3.7 3 Kodiak 1985-1998 -8.1 _+ 1.1 1 1967-1998 -14.5 +_ 0.7-14.7 +_ 0.4 0.67 +_ 0.11 1 1974-1988 - 14.8 2 1967-1988 - 17.5 _+ 0.8 2 1967-1981 -21.1 +_ 1.4 1 1965-1974 -86.8 _+ 38.4 3 Seldovia 1966-1998 -9.3 +_ 0.8-9.2 _+ 0.8-0.16 +_ 0.18 1 1974-1988 -7.0 2 1964-1988 -7.2 +_ 1.4 2 1964-1974 -28.1 _+ 8.1 3 Anchorage 1984-1998 0.8 _+ 1.3 1 1965-1998 -0.7 _+ 0.9 1964-1988 1.9 +_ 1.9 2 1964-1974 -14.3 _+ 7.6 3 Nikiski 1972-1998 -9.9 _+ 0.8 1 1971-1979 -18.7 _+ 1.7 2 to = 1982.5 t o = 1987.5 t o = 1982.5 Women's Bay (WB) WB and SP; to - 1982.5 St. Paul's Harbor (SP) SP t o = 1982.5 mean sea level mean tide level no data from 1981 through 1996 no data after 1984 areferences: 1, this study; 2, Savage and Plafker [1991]; 3, Brown et al. [1977]. that Seward is within a zone where elastic strain is accumulat- was associated with the site relocation. However, as the coming; that is, it lies slightly trenchward of the downdip end of the ments in Table 1 indicate, there was a consistency check belocked tectonic plate interface [Freymueller et al., 2000]. An tween the observations at the two sites, so we have no substanelastic dislocation model predicts that the vertical motion tive reason to believe that the rate change is an artifact of the should be small, i.e., only a few millimeters per year, and the relocation. From the time-dependent crustal uplift rate at Koobserved uplift rate of 3.2 _+ 0.7 mm yr-, as inferred from the diak of h = 6.1 + 0.66 (1998.5 - t) mm yr -, we estimate tide gauge observations, confirms this prediction. that the uplift rate there decreased to half its immediate post- At Kodiak the rate of apparent sea level change from the seismic rate in ---12 years. This is somewhat faster than the 3-6 linear analysis -14.5 _ 0.7 mm yr- ; however, there appears year decay estimated by Cohen [1998] for an amalgamation of to be a significant change in the rate of 0.67 _+ 0.11 mm yr -2. sites along Turnagain Arm, the eastern Kenai, and elsewhere Several other lines of argument suggesthat the time depen- and, as we discuss below, may reflect the somewhat different dence is real. First, an examination of the height residuals tectonic settings of the sites. The various crustal uplift rate shows that the temporal variation is more extensive than in the determinations that have been derived from the sea height previous cases; that is it appears to span almost the entire data can be summarized in a rate plot, as we will do in section domain of the data set. The quadratic solution passes the F test 5. with a 99% probability that the improvement over the linear fit The rate of sea level change at Seldovia is -9.3 _+ 0.8 mm is statistical significant. Furthermore, the rate that we derived yr -, in good agreement with SP91's rate of -7.2 _+ 1.4 mm from the data through 1998 is slightly lower than that derived yr - and implying a crustal uplift rate around 10 mm yr -. The by SP91 from the data through from 1965 to 1988, i.e., -17.5 _+ rate change, 0.16 + 0.18 mm yr -2, is not significant. 0.8 mm yr -. The crustal uplift rate that we predict from the At Anchorage we obtained an apparent sea level uplift rate time-dependent change in apparent sea level for 1990 is ---12 of 0.8 +_ 1.3 mm yr-, a resulthat is quite consistent with the mm yr -, which is in good agreement with the 14.8 _+ 7.2 mm SP91 result of 1.9 _+ 1.9 mm yr - and suggests that very little, yr- uplift rate derived from very long baseline interferometry if any, vertical crustal movement is occurring at Anchorage. (VLB) measurement made in the late 1980s and 1990 [Ryan et Our analysis was based on data beginning in 1984 since the al., 1993], although the mean rate is also consistent with the earlier records are quite incomplete. However, there is a some- VLB data. The sea level rate for the period (1985-1998) that what more robust set of monthly mean tidal heights (as distinct the tide gauge was located at Women's Bay is -8.1 _+ 1.1 mm from mean sea level). This data set goes back to 1965 but still yr -, slower than the rate of -21.1 _+ 1.4 mm yr - derived for is missing yearly heights for most of the 1970s and early 1980s. the period from 1967 to 1981 when the gauge was at St. Paul Analysis of the tidal heights yields a rate of -0.7 +_ 0.9 mm Harbor. This adds further credence to the suggestion that the yr -, again suggesting little vertical movement. rate has changed but raises the possibility that the rate change The apparent sea level rate at Nikiski was derived from

11,264 COHEN AND FREYMUELLER: CRUSTAL UPLFT FROM ALASKA TDE GAUGES a. Residuals, linear least squares 0.4 4.2-- Cordova 0.2 0.1 ] \ t Cordova -o- Valdez Seward 0.0 --<>- Kodiak v Sel dovia - - Anch age 3.9-3,7- c = -0.39_+ 0.06 mm/yr 2 i 1970 1980 1990 2000,.,. [] Kodiak -0.3- o- b' -0. 960,,, 1 65.,, ' ''.' '',,, i1,,.,, 1995., 2OOO b. Residuals, quadratic least squares 2.3-2.2-2.1-4,3-- c 0.67_+ 0.11 mm/yr 2 1970 1980 1990 2000 Valdez o.o _o. --0.2......... ;............... 1965 1970 1975 1980 1985 1990 1995 2000 Tim e, yr --rn-- Cordova -o--valdez Kodiak Figure 3. Sea level height residuals (corrected sea level heights minus least squares line). (a) Linear least squares analysis of corrected yearly mean sea level data. (b) Quadratic least squares analysis of corrected yearly mean sea level data. E._-4.2 - il) '4.1 - E4.0-3.9-3.8- c = - 0.76 + 0.14 mm/yr 2 1970 1980 1990 2000 Figure 4. Corrected sea level heights and linear and quadratic least squares line for Cordova, Kodiak, and Valdez. The rate changes are 0.39 _+ 0.04, 0.67 _+ 0.11, and -0.76 _ 0.14 mm yr -2 for the three sites, respectively. mean tide heights as well and is -9.9 _ 0.8 mm yr -. Given the fact that no data were collected at Nikiski from 1979 to 1997, the fact that SP91 obtained a higher rate of -18.7 _+ 1.7 mm yr - is probably not significant. As we mentioned in section 1, a portion of the eastern Kenai Peninsula and the Turnagain Arm region may have experienced postseismic uplift with a rate relaxation time of a few years. To determine whether any similar short-term relaxation influenced our estimates of changes in uplift rate, we recomputed the quadratic regression curves excluding data through 1973. None of the quadratic solutions were strongly affected by this perturbation. At Kodiak the rate change with the reduced data set was -0.59 _ 0.16 mm yr -2, which agrees very well with the rate change of -0.66 _+ 0.11 mm yr -2 derived from the entire data set. Similarly, at Cordova the post-1973 rate change is 0.33 _+ 0.09 mm yr -2 compared to the 1965-1998 rate change of 0.39 _ 0.11 mm yr -2. At Valdez the data set begins in 1975, so it does not contain any observations from the first decade after the earthquake. 5. Discussion and nterpretation n this section we will discuss and interpret the results we have obtained. Before doing so, it is useful to summarize the results of previous studies that have a direct bearing on the interpretations advanced in this paper.

COHEN AND FREYMUELLER: CRUSTAL UPLFT FROM ALASKA TDE GAUGES 11,265 5.1. Discussion of Summary of Previously Published Observations 5.1.1. Leveling surveys. As briefly alluded to in section 1, Brown et al. [1977] analyzed data from four leveling surveys undertaken between 1964 and 1975 along the highway between Anchorage and Portage (Figure 1) on the northeast side of Turnagain Arm of Cook nlet. The analysis revealed that rapid uplift occurred in the immediate aftermath of the earthquake. The maximum cumulative postseismic uplift after a decade was estimated to be -- 0.5 m, although the absolute uplift above sea level may have been overestimated since Brown et al. [1977] used a rate of 16.7 mm yr - for the uplift rate at the Anchorage GPS sites located on the Kenai Peninsula. The horizontal velocities on the eastern side of the Kenai Peninsula were oriented in the direction of Pacific Plate motion relative to North America, and the magnitudes were roughly consistent with elastic strain accumulation along the plate tectonic plate interface. Similarly, Savage et al. [1998] showed that the motion along a profile oriented nearly normal to the plate boundary in the Prince William Sound region was in the direction of Pacific Plate motion relative to North America, although they suggested that the elastic strain accumulation model fit the data better if a plate convergence velocity of 65 mm yr - was used rather than the 55 mm yr- given in NUVEL-1A [DeMets et al., 1994]. Freymueller et al. [2000] observed the velocities on the western side of the Kenai Peninsula, by contrast, were directed toward, rather than away from, the plate boundary, and speeds were of the order of a few tens of millimeters per year. Freymueller et al. [2000] and C. Zweck et al. (Elastic dislocation tide gauge, a rate that is too fast according to both our analysis modeling of postseismic response to the 1964 Alaska earthand that of SP91. The uplift peaked near the middle of the quake, submitted to Journal of Geophysical Research, 2000) attribute the deformation on the western side of the Kenai to Turnagain Arm profile and fell to nearly zero at both ends of ongoing or delayed creep at depth. They also suggest that the estuary. Brown et al. [1977] also estimated decay rates for elastic strain accumulation is not seen on the western side of the uplift rates and found them to be typically a few years but the Kenai Peninsula because the shallow plate boundary is possibly varying from locale to locale. Cohen [1998] discussed unlocked there, a view consistent with the observation of small a partial resurvey of the Turnagain Arm route that was undercoseismic moment release in that region. taken only 6 months after the original postearthquake survey in 5.1.3. Tide gauge studies. Brown et al. [1977] examined the 1964. The uplift rates obtained from height differences using tide gauge records at Cordova, Seward, Kodiak, Seldovia, and these first two surveys agree with the uplift rates deduced from Anchorage, while SP91 examined the records at these sites and surveys a year apart, indicating that the rapid uplift was main- Valdez and Nikiski. n the Brown et al. [1977] analysis the tained at a nearly constant rate for ---1 year. There was no absolute value of the uplift rate exceeded 10 mm yr - at all evidence for any relaxation occurring on a timescale faster sites with a maximum uplift rate of 88 _+ 38 mm yr- at Kodiak than a few years. As mentioned earlier, the maximum uplift and a minimum of -12 _+ 2 mm yr- at Cordova. Some of the rate was ---150 mm yr -. apparent sea level rates are probably unreliable because of the 5.1.2. GPS surveys. Cohen et al. [1995] and Cohen and short extent of the data record used. For this reason, we tend Freymueller [1997] determined the cumulative postseismic upto mistrust, for example, this earliest rate determination at lift on the Kenai Peninsula through the early to mid-1990s by Kodiak. SP91 derived uplift rates over two time spans, one comparing contemporary GPS observations to leveling obserbeing the entire postseismic period through 1988 and the other vations made shortly after the earthquake. The cumulative being from 1974 to 1988, the latter being considered in order uplift had a maximum of nearly 1 m located in the center of the to eliminate short-term postseismic transients. The rates de- Kenai Peninsula. The uplift contours were oriented SW to NE rived using only the post-1973 data were slower than those in rough agreement with the trend of the trench, surface faults, derived from the entire time series, but the differences were and other geological and geophysical features in the region. insignificant, i.e., only fractions of a millimeter per year, except The uplift contours were not symmetric; somewhat more uplift at Kodiak and Seward where the rates derived from the postoccurred in the northeast section of the surveyed region than in 1973 data were almost 3 mm yr- less than those derived from the southwest. the full data set. Even with the slower uplift rates found by Both the leveling sites and newly installed GPS sites have SP91 rather than the faster rates from Brown et al [1977], the been occupied on several occasions. At Seward, GPS observa- predicted cumulative vertical motions over the earthquake retions began in 1993, and since 1995, observations have been currence interval are large. For example, an interseismic submade at least once a year at the original mark, at a new one a sidence rate of 10 mm yr - at Cordova would result in a total few kilometers away, or, in most cases, at both. The Seward subsidence of 7.5-10 rn if the recurrence period is 750-1000 GPS site show uplift rates of ---10_+ 3 mm yr - relative to the years (as cited by, for example, SP91). Since the long-term interior of North America. Similarly the GPS-derived uplift topographic change at Cordova is small and the coseismic rate for two sites near Nikiski is 11 + 2 mm yr -. Since we uplift is only a few meters, either the rate cannot be sustained cannot ignore the possibility that there is a bias in the vertical over the entire recurrence interval or that interval is substan- GPS rates, we will defer an extensive discussion of present-day tially shorter than geological information indicates. n Figure 5 GPS uplift rate determinations until more GPS observations we plot the uplift rates reported in this and other studies as a have been taken and the issues of GPS height reliability can be addressed in detail. GPS horizontal velocity determinations are subject to much less uncertainty than the vertical ones, so they can be used with greater confidence in the interpreting crustal deformation function of time for Kodiak and Cordova (excluding the Kodiak rate derived by Brown et al. [1977] because of its high uncertainty, _+38 mm yr- ). Figure 5 lends credence to the suggestion that the vertical rates at these two locales, at least, have slowed substantially over the past 30 years so that the characteristics. Cohen and Freymueller [1997] and Freymueller cumulative uplifts estimated from an extrapolation of the earet al. [2000] reported the contemporary horizontal velocities of lier rate determinations will not realized. n most previous studies the rapid uplift in the Turnagain Arm region and the large cumulative uplift observed on the Kenai Peninsula have been attributed to postseismic slip along the plate interface at depths greater those than slipped during the earthquake, although the possibility of viscoelastic relax-

11,266 COHEN AND FREYMUELLER: CRUSTAL UPLFT FROM ALASKA TDE GAUGES 25- Uplift Rate Determinations for Kodiak St. Paul Harbor data!5-20- r- Savage and Ptafker, 1967-1988 date '( ß +-... -Savage and Plafker, All 1974-1988 data data - - + - - VLB 10- + Womens Bay data ½ - - Topex+tide gauge 5 1965 1970 1975 1980 1985 1990 Year i i 1995 2000 2005 2010 5 - Uplift Rate Determinations for Cordova All data '=- -10 Brown et al., 1964-1974 data Savage and Plafker, 1974-1988 data Savage and Plafker, 1964-1988 data -15-20 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 Year Figure 5. Uplift rates from this and other studies showing the apparent time dependence in the rates at Kodiak and Cordova. The references for the VLB data are Ma et al. [1990] and Ryan et al. [1993], while the results labeled "Topex + tide gauge" are from an analysis of radar altimetry data along with daily tide gauge observations (S. Nerem and G. Mitchum, personal communication, 2000). ation of the lower crust or asthenosphere has also been considered [Brown et al., 1977; Cohen et al., 1995; Cohen, 1996]. Wahr and Wyss [1980] also experimented with a model that employed a viscoelas.tic inclusion at the downdip end of the coseismic rupture plane, although the parameters of that model do not agree well with today's knowledge of the subduction zone geometry. 5.2. nterpretation We now turn to a discussion of the physical significance of the tide gauge results. Table 3 gives the uplift rates deduced from the tide gauge observations. Also given are GPS uplift rates at Seward and Nikiski and a VLB uplift rate at Kodiak. As suggested by Figure 1, all of the sites, with the exception of Cordova, lie landward of the 1964 megathrust, and all, except Cordova, are subsiding or showing little motion. Cordova lies over the coseismic slip plane and has subsided since experiencing uplift in the earthquake. The strike of the offshore trench varies with locale but is about N44W in the center of Figure 1. The dip angle of the interseismically locked plate boundary increases from a few degrees in the NE portion of Figure 1 to ---10 ø at Kodiak [Brocher et al., 1994; Johnson et al., 1996]. The velocity of the Pacific Plate relative to North America [DeMets et al., 1994] is ---55 mm yr - in a direction N17W at Seward, with an obliquity of 25 ø there and 59 mm yr - at N28W at Kodiak, where there is <5 ø obliquity. The eastern

COHEN AND FREYMUELLER: CRUSTAL UPLFT FROM ALASKA TDE GAUGES 11,267 Table 3. Tide Gauge Crustal Uplift Rates a Mean Uplift Rate, mm yr- 1996.5 Uplift Rate b Uplift Rate, GPS or Other Technique, mm yr- GPS Site or other Technique mm yr - Cordova Valdez Seward -4.7 _+ 0.4 2.2 _+ 0.2 3.2 +_ 0.7 1.8 + 1.0 Kodiak c 16.5 _+ 0.7 7.4 +_ 2.1 Seldovia 11.3 _+ 0.8 Anchorage f 2.7 _+ 0.9 Nikiski f 11.9 _+ 0.8 T19 10.0 _+ 3.4 UAMF 11.0 +_ 2.3 VLB d radar altimetry e 14.8 +_ 7.2 d 9.7 + 1.4 e NK/NK2 11.2 + 2.3 aassuming combined effects of eustatic sea level rise and postglacial rebound of 2 mm yr - for the tide gauge-derived rates. busing results of quadratic analysis for Cordovand Kodiak. CCombined Women's Bay and St. Paul Harbor. dvlb rate from data collected in late 1980s and 1990 [Ma et al., 1990; Ryan et al., 1993]. etopex radar altimetry and daily tide gauge observations, 1993-1999 (S. Nerem and G. Mitchum, personal communication, 000). fmean tide level analysis. region tends to rupture in infrequent great earthquakes with Nikiski lie in a tectonically different environmenthan the sites recurrence intervals of several hundred years, while the Kodiak on the eastern side of the Kenai Peninsula, an inference that is sland region ruptures both in infrequent great earthquakes buttressed by the observation of only a small coseismic moand more frequent (50-60 years) large earthquakes [Nishenko ment release in this region during the 1964 earthquake. t is a and Jacob, 1990; Perez and Scholz, 1997]. simple matter to find a deep-creep model that fits the obser- The simplest model that we consider is an elastic dislocation vations. For example, Figure 7 shows the dislocation theory model that attributes the deformation to strain accumulation results for slip on a plane dipping at 25 ø between depths of 40 at the locked plate boundary. Given the considerable variation km [Oleskevich et al., 1999] and 80 km. The geometry is a in trench orientation and slab dip in the region under study and reasonable fit to the plate interface geometry found by Doser et the lack of data from locations close to the trench, we have al. [1999], but none of the parameters are uniquely confound it more instructive to plot the uplift data as a function of strained. We claim that the observations on the western side of distance from the axis of maximum coseismic subsidence [Plafker, 1971] than as a function of distance from the trench. This origin is of considerable interest in the interpretation of Elastic Dislocation Model: vel---55 mm/yr, dip---5 deg; depth---5-25 km geodetic data for it lies directly over the downdip end of the 20- rupture in a uniform slip, elastic dislocation model of the earthquake. Assuming that the coseismically ruptured and interseismically locked portions of the megathrust are the same, this axis also lies over the downdip end of the locked region. The data plotted in Figure 6 show the interseismic vertical motions as a function of distance. Also shown is a prediction of the rate of interseismic uplift derived from an elastic disloca- Nikiski tion calculation [Okada, 1985, 1992], assuming representative 10- parameters, i.e., a plate convergence rate of 55 mm yr -1, dip angle of 5 ø, and the plates locked at depths of 5-25 km. We ignore the effects of the obliquity of the plate velocity vector relative to the trench normal. Both mean and recent (1996.5) values of the uplift rates are shown for Cordova and Kodiak. n considering the agreement or disagreement between the elastic dislocation model and the observations, we first focus on the four sites on or near the Kenai Peninsula (i.e., Seward, 0 Anchorage, Nikiski, and Seldovia). The elastic dislocation model predicts small uplift rates at Seward and Anchorage in agreement with the observations there. This is in accord with the interpretation of contemporary horizontal velocity vectors in the eastern Kenai region by Cohen and Freymueller [1997] and Freymueller et al. [2000] as being due to strain accumulation at the locked North American-Pacific Plate boundary. By contrast, the crustal uplifts at Nikiski and Seldovia are much -10 - faster than predicted by the elastic strain accumulation model. -100-50 0 5O 100 150 The uplifts of these western Kenai Peninsula sites and the Distance from Axis of Maximum Coseismic Subsidence, km previously mentioned trenchward horizontal motion of sites Figure 6. Uplift rate versus distance from axis of maximum throughouthe western side of the Kenai Peninsula suggesthe coseismic subsidence (data points) and dislocation model for occurrence of ongoing slip at depth. We infer that Seldovia and elastic deformation due to a locked megathrust (dashed line).

11,268 COHEN AND FREYMUELLER: CRUSTAL UPLFT FROM ALASKA TDE GAUGES 20-10- 0- Deep Slip Model: vel=50 mm/yr, dip=25 deg; depth=40-80 km Updip Tip of Fault Midway between Seldovia and Nikiski, eldovia o? ikiski -10 - i i i i -150-100 -50 0 50 100 Dislance from Axis of Maximum Coseismic Subsidence, km Figure 7. Uplift rate of western Kenai Peninsula sites (data points) and predicted uplift rate due to creep at depth in an elastic half-space (solid line). the Kenai Peninsula are consistent with deep transient slip but do not assert that this interpretation is the only possibility. Continuing to focus on the four sites on or near the Kenai Peninsula, we note that they are located downdip of the middle portion of the 1964 earthquake rupture zone. However, as shown in Figure 8 (from Holdahl and Sauber [1994] with results similar to those of Johnson et al. [1996]), the coseismic slip was far from uniform even in the central portion of the rupture. We have divided Figure 8 into four segments labeled r, '2, r, and r 3, with regions - and r 3 being those we have considered so far. n region - the coseismic slip was quite large, and the relaxation of the postseismic uplift was quite rapid as indicated by the leveling data collected along Turnagain Arm. The Anchorage and Seward tide gauges are located in this region. Although they do not show a time-dependent signal, the uplift rates are small, so any time-dependent signal would be difficult to detect. The fact that the aforementioned contemporary horizontal motion over almost the entire r regions is consistent with elastic strain accumulation does suggest, however, that any postseismic signal has decayed away. The region labeled r 3 lies immediately to the west of the 't region. Updip of this region the coseismic slip was quite small. t was, perhaps, even less than indicated in Figure 8 for there may be some data spillover into this region from the high slip region to the east. The tide gauges at Nikiski and Seldovia show large uplift rates and, at least in the case of Seldovia, no decrease in the uplift rate since the earthquake (at Nikiski the long period over which the tide gauge was not operational precludes looking for a time-dependent signal). As argued above and by SP91 the uplift rates at the two tide gauges in this region are too large to be sustained over the entire earthquake cycle. A decay in the uplift rate is expected, but it must occur on a timescale longer than three decades. The main point is that in contrast to region?, the postseismic signal in region r3 is ongoing and appears to have persisted over the past three and half decades. We now turn to the regions more on the periphery of the coseismic rupture zone. The r2 region includes Kodiak and is near the western edge of the coseismic rupture. ts shallower segments include the Kodiak asperity, a region of significant coseismic moment release. As previously mentioned, the tectonic environment of region r2 is somewhat different from the more easterly regions in that the Kodiak asperity ruptures in large earthquakes fairly frequently, possibly every few hundred years, whereas the Prince William Sound asperity ruptures in rarer great earthquakes. [Pulpan and Frohlich, 1985; Lu and Wyss, 1996]. Furthermore, the subduction angle of the Pacific Plate under the North American Plate increases more rapidly with depth than at the easterly sites, and the bottom edge of the coseismic rupture may be somewhat closer to the trench here than elsewhere. Region r2 had intermediate slip in the 1964 earthquake, and we now find evidence that the rapid uplift at Kodiak is decreasing on a timescale that is slower than that along the Turnagain Arm but faster than that at Seldovia; that is the timescale is approximately decadal or intermediate between that of regions r and %. At the other end of the coseismic rupture zone, i.e., region r2, lie Valdez and Cordova. As at Kodiak, there was moderate slip updip of these sites during the earthquake, and we find that the subsidence-rate decay time at Cordova is again decadal, i.e., similar to that at Kodiak. (Recall that the decay time at Valdez, if any, is uncertain because there are no tide gauge records prior to the mid-1970s.) Thus regions r2 and r are similar in that the updip slip was moderate and the relaxation time for the postseismic signal appears to be approximately decadal. The general picture that emerges from these considerations is that we can account for the geographic variability of the postseismic response time by considering how a region is affected by the updip coseismic slip distribution. There is rapid decay in the postseismic uplift rate in areas that lie downdip of a megathrust segment that exhibited high slip, and slower decay in areas that lie downdip of segments with smaller slip. An inference is that the relaxation time for the postseismic process depends inversely on the coseismic stress transfer, although not necessarily in a linear fashion. Although our argument is somewhat speculative, this inference is both intuitively satisfying and in accord with mechanical theories if, for example, the postseismic deformation is due to downdip creep that is in turn a nonlinear viscoelastic process on a microscopic level. Thus it appears that the entire region affected by the 1964 ruptures undergoes a postseismic response with the timescale varying from locate to locale. 6. Conclusions The apparent sea level height records of the seven permanent tide gauges located in south central Alaska are a useful data set for studying the spatial and temporal distribution of vertical crustal motion subsequent to the great 1964 Prince William Sound earthquake. By incorporating an additional 10 years of observation since the last study we are able to determine more reliable mean uplift rates than have been previously determined and to search the record for time-dependent behavior. Uplift rates of 10 mm yr - or more observed at Sel- dovia and Nikiski on the western side of the Kenai Peninsula have persisted for at least three and a half decades and may be due to a long-lived postseismic transient. The slow uplift of a few millimeters per year observed at Seward on the eastern

COHEN AND FREYMUELLER: CRUSTAL UPLFT FROM ALASKA TDE GAUGES 11,269 Postseismic Relaxation Rates: ' 1 < ' 2 ~ ' ; < ' 3 Maximum postseismic uplift rate l> 10 mm/yr Maximum postseismic uplift rate < 10 mm/yr Seldovia Coseismic Dip Slip (meters) -- -5.7 to -0.9 ' -10.5 to -5.7 :; -15.3 to -10.5-20.0 to -15.3-29.6 to -20.0 Figure 8. Segmentation of south central Alaska plate boundary according to the magnitude of coseismic slip and the relaxation time of the postseismic vertical motion. The base figure and coseismic slip estimates are from Holdahl and Sauber [1994]. As discussed in the text, regions z, z2 (and ), and 3 have uplift rate relaxation times of a few years, decades, and longer than decades, respectively. The dots indicate locations of tide gauge stations, the square designated TA is in the middle of the Turnagain Arm leveling route, and the square designated KP is in the middle of the Kenai Peninsula, a region surveyed by leveling and GPS techniques. side of the Kenai Peninsula is consistent with elastic strain accumulation at the locked North American-Pacific Plate boundary as is the nearly zero vertical uplift rate at Anchorage, farther to the north. The rate of uplift at Kodiak on the west side of the coseismic rupture and, possibly, the rate of subsi- dence at Cordova on the east side have decreased with time. contributed to the preparation of the final version of this paper. The research was funded, in part, by NASA's Solid Earth and Natural Hazards Program. GPS work in the Anchorage area by J.F. was un- dertaken in cooperation with Peter Haussler and with support from the U.S. Geological Survey. GPS data collection since 1998 on the Kenai Peninsula was funded by the National Science Foundation. Overall, there appears to be a spatial inverse correlation between the decay time for the postseismic uplift rate and the amount of coseismic slip. The area downdip of the regions of References Brocher, T. M., G. S. Fuis, M. A. Fisher, G. Plafker, J. J. Tabor, and large coseismic slip exhibited an intense, but short (approxi- N.J. Christensen, Mapping the megathrust beneath the northern Gulf of Alaska using wide-angle seismic data, J. Geophys. Res., 99, mately years), episode of postseismic uplift, while areas that 11,663-11,685, 1994. are downdip of regions of lesser slip exhibit longer postseismic Brown, L. D., R. E. Reilinger, S. R. Holdahl, and E.. Balazs, Postrelaxation times. seismic crustal uplift near Anchorage, Alaska, J. Geophys. Res., 82, 3369-3378, 1977. Cohen, S.C., Time-dependent uplift of the Kenai Peninsula and ad- Acknowledgments. We thank Jeanne Sauber for her insights through an ongoing dialogue on Alaska tectonics. We also express appreciation to Scott Duncan for providing tide gauge records and leveling records that were not available through the internet. Helpful reviews from Tim Dixon, Jim Savage, and an anonymous reviewer jacent areas of south central Alaska since the 1964 Prince William Sound earthquake, J. Geophys. Res., 101, 8595-8604, 1996. Cohen, S.C., On the rapid postseismic uplift along Turnagain Arm, Alaska following the 1964 Prince William Sound earthquake, Geophys. Res. Lett., 25, 1213-1215, 1998.

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