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Asperity distribution of the 1964 Great Alaska earthquake and its relation to subsequent seismicity in the region
Tectonophysics 367 (2003) 219 – 233 www.elsevier.com/locate/tecto
Asperity distribution of the 1964 Great Alaska earthquake and its relation to subsequent seismicity in the region S. Santini a,*, M. Dragoni b, G. Spada a b
a Istituto di Fisica, Universita` di Urbino, Via S. Chiara 27, Urbino 61029, Italy Dipartimento di Fisica, Settore di Geofisica, Universita` di Bologna, Viale B. Pichat 8, Bologna, Italy
Received 9 July 2002; accepted 20 March 2003
Abstract The 1964 Alaska earthquake was the second largest seismic events in the 20th century. The aim of this work is the use of surface deformation data to determine asperity and slip distributions on the fault plane of the Alaska earthquake: these distributions are calculated by a Monte Carlo method. To this aim, we decompose the fault plane in a large number of small square asperity units with a side of 25 km; this allows us to obtain plane surfaces with an irregular shape. In the first stage, each asperity unit is allowed to slip a constant amount or not to slip at all, providing the geometry of the dislocation surface that best reproduces the observed displacements. To this purpose, a large number of slip distributions have been tried by the use of the Monte Carlo method. The slip amplitude is the same for all the asperities and is equal to the average fault slip inferred from the seismic moment. In the second stage, we evaluate the slip distribution in the dislocation area determined by the Monte Carlo inversion: in this case, we allow unit cells to undergo different values of slip in order to refine the initial dislocation model. The results confirm the previous finding that the slip distribution of the great Alaska earthquake was essentially made of two dislocation areas with a higher slip, the Prince William Sound and the Kodiak asperities. Analysis of the post-1964 seismicity in the rupture region shows a strong correlation between the larger earthquakes (Mw z 6) and the distribution of locked asperities following the 1964 event, which can be considered as an independent test of the validity of the model. We do not find slip values higher than 25 m for any of the patches, and we determine two separate high-slip zones: one correspondent to the Prince William Sound asperity, and one ( f 18 m slip) to the Kodiak asperity. The slip distribution connected with the 1964 shock appears to be consistent with the following seismicity in the region. D 2003 Elsevier Science B.V. All rights reserved. Keywords: Dislocation; Slip distribution; Displacement field; Monte Carlo method; Prince William Sound; Kodiak Island
1. Introduction On March 28, 1964, one of the largest earthquakes of the last century, with magnitude Mw = 9.2, occurred * Corresponding author. E-mail address: [email protected] (S. Santini).
in the south central Alaska, where the Pacific Plate is subducted under the North American Plate. The earthquake ruptured an 800-km-long segment of the subduction zone, with maximum surface displacements of more than 10 m (Fig. 1). The focal mechanism indicates that the fault movement was that of a thrust fault, with a dip angle of about 9j.
0040-1951/03/$ - see front matter D 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0040-1951(03)00130-6
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Fig. 1. Coseismic displacement field of the great Alaska earthquake as given by Plafker (1965), and the surface projection of our fault plane model (DEFG rectangle).
In the decades following the event, several papers have been devoted to the study of this large earthquake and have added much to our knowledge of it. Pioneering studies were done by Plafker (1965) and Wood (1966). The extent of the rupture zone was inferred by aftershock studies (Stauder and Bollinger, 1966; Algermissen et al., 1969) and by modelling of geologic and geodetic data (Plafker, 1969, 1972; Savage and Hastie, 1966; Hastie and Savage, 1970; Prescott and Lisowski, 1977; Miyashita and Matsu’ura, 1978). More recently, Holdahl and Sauber (1994) proposed an inversion of coseismic displacement data, obtaining
a slip distribution on the fault plane. Johnson et al. (1996) performed a joint inversion of geodetic data and tsunami waveforms, substantially confirming that the slip distribution on the fault plane was dominated by two areas of large slip, the Prince William Sound asperity and the Kodiak asperity. They assumed a dip angle equal to 3j in the Prince William Sound area but a different angle in the Kodiak region. The present paper employs the coseismic surface displacement data in order to constrain the geometry of the dislocation surface and the slip distribution on the fault plane of the Alaska earthquake. In order to
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retrieve the slip distribution which best fits the geodetic data, we use a Monte Carlo method (Metropolis and Ulam, 1949) testing the performances of a large set of a priori random asperity distributions on the fault plane. The procedure is made of two stages. In the first stage, geodetic data are used in order to constrain the geometry of the dislocation surface. To this aim, an asperity model is employed, where the fault plane is divided in a large number of square asperity units which can slip by a constant amount or remain locked. In the second stage, the asperity units are allowed to slip by variable amounts, in order to reproduce a nonuniform slip distribution on the fault plane. In order to reach a good fit between the observed and the calculated surface displacements, many slip distributions are tried by the use of Monte Carlo simulations. In this work, the distribution of asperities (or slip) on the fault plane is found using only the fault geometry, the geodetic data and the seismic moment related to the 1964 Alaska earthquake. The model is developed without taking into account the seismicity preceding or following the 1964 main shock. However, the subsequent seismicity will be considered as a test for the slip distribution obtained in the model.
2. The data The data that we use are the coseismic displacement field at the Earth’s surface (Plafker, 1965), the geometry of the fault and the average slip determined by previous studies (Savage and Hastie, 1966; Stauder and Bollinger, 1966). We assume that the fault is a rectangle with a length L = 600 km and a width W = 250 km. The fault is embedded in an elastic half-space with Lame` constants k = l (Poisson’s solid). The shear modulus l is assumed to have a value equal to 5.5 1010 Pa, calculated as an average on the relevant crustal thickness (Dziewonski and Anderson, 1981). The average fault slip U is assumed to be equal to 14 m, a value given by Johnson et al. (1996). The seismic moment is then (e. g. Kasahara, 1981) M0 ¼ lUA
ð1Þ
where A is the dislocation area. We shall estimate A on the basis of the moment magnitude Mw. The seismic
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moment M0 is related to the moment magnitude Mw by the following equation (Kanamori, 1977): logM0 ¼ 9:1 þ 1:5Mw
ð2Þ
where M 0 is expressed in N m. If we consider Mw = 9.2, then M0 = 0.79 1023 N m. From Eq. (1), we obtain A = 105 km2. Following Savage and Hastie (1966), who assume a length L = 600 km and a width W = 125 km, giving a dislocation area AV= 7.5 104 km2, we retain this last value, corresponding to a seismic moment M0V equal to about 75% of the seismic moment M0 determined from long-period surface waves. This value does not include a possible seismic slip that occurred on the fault in the weeks or months following the main shock. The value M0V = 5.8 1022 N m is close to the seismic moment of 5.9 1022 N m obtained by Kikuchi and Fukao (1987). As to geodetic data, we refer the reader to the detailed description of the data acquisition and interpolation given in Plafker (1965). This article makes available a summary of the basic data acquired during the 1964 field season on the tectonic deformations that accompanied the earthquake. In Plafker (1969), the complete data set is reported. The vertical tectonic movements in coastal areas were determined mainly by making more than 800 measurements of displacement of intertidal sessile marine organisms along the coast. These measurements were supplemented at 16 tidal bench marks by coupled pre- and post-earthquake tide-gauge readings made by U.S. Coast and Geodetic Survey, and by numerous estimates of relative changes in tide levels by local residents. The major area of uplift is about 800 km long and trends north – east from southern Kodiak Island to Prince William Sound, and east –west to the east of Prince William Sound. The maximum measured uplift on land is 10 m at the south – west end of Montague Island and more than 15 m offshore from Montague Island. Holdahl and Sauber (1994) improved upon earlier geodetically derived coseismic slip models by inverting simultaneously vertical and horizontal geodetic, tide gauge, and geologic data for a more detailed distribution of coseismic slip by using the fault geometry inferred from other geophysical informa-
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tion. They examined the hypothesis that there were regions of high slip separated by regions of more moderate slip. Johnson et al. (1996) used all the data used by Holdahl and Sauber (1994). In Fig. 1, the observed vertical displacement field is shown. Excluding Prince William Sound area, we have a maximum value of about 3 m and a minimum value of about 2 m; but a maximum vertical coseismic displacement of 10 m is reached in the Montague Island zone. In the Kodiak area, a maximum displacement between 1 and 2 m is observed. Plafker (1965) considered the presence of two smaller faults in the Montague Island zone: they produced secondary dislocations, much more superficial in respect to the main dislocation. The additional coseismic deformation, observed in the Prince William Sound area, is due to the presence of the two secondary dislocations. There are no contour lines between Kodiak Island and the Aleutian Trench Axis due to the presence of the sea.
3. The model Let us consider an elastic, homogeneous and isotropic half-space, occupying the region x3 z 0 in a Cartesian coordinate system, and assume that the fault surface is a rectangle belonging to a half-plane intersecting the Earth’s surface with a dip angle d. The x3 axis is parallel to the fault strike and contains the projection of the bottom side of the fault surface on the Earth’s surface. The depth of the bottom side of the fault surface is D.
Due to inhomogeneity of friction on faults, dislocation surfaces have usually irregular shapes. In order to take this into account, we assume that the fault rupture is the consequence of the failure of a large number of small square asperity units (Fig. 2). In the case of a rectangular dislocation, the displacement field at the Earth’s surface can be obtained by available analytical solutions (Okada, 1985). From the solution for a square dislocation, it is easy to obtain the analytical solution for any dislocation with a polygonal contour. As a consequence, it is possible to model the effect of dislocations with any shape by employing suitably small asperity units (e.g. Dragoni, 1988; Santini et al., 2000). In order to retrieve the slip distribution associated with the 1964 Alaska earthquake, we implement the following procedure. The slip distribution (or dislocation surface) is the effect of the failure of a corresponding distribution of square asperity units and is obtained on the basis of the fault geometry, the focal mechanism and the seismic moment of the 1964 Alaska earthquake. The aftershock distribution is not taken into account at this stage. The procedure is made of the following steps: 1. Individuation of the fault plane, using geological constraints and the total seismic moment. According to the calculated focal mechanism (Savage and Hastie, 1966), the type of fault movement is that of a thrust fault, with a dip angle of 9j; the dislocation area is 75,000 km2 and the average slip is about 14 m.
Fig. 2. Model for the fault plane of the 1964 Alaska earthquake.
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2. The subdivision of the fault surface in n = 120 square asperity units, with a side d equal to 25 km: this number is chosen in order that, with a slip amplitude U in the order of 1 m, the failure of an asperity unit releases a seismic moment corresponding to the typical magnitude (Mw c 6.5) of the largest aftershocks of the Alaska earthquake (Kasahara, 1981). 3. The use of a Monte Carlo method in order to generate a large number of possible slip distributions; the calculation of the vertical surface displacement for each slip distribution and the comparison with the available displacement data, in order to minimize the misfit between the predicted and observed data. The slipping area (dislocation) of the fault is obtained assuming that each asperity unit has two possible states: locked or slipping. 4. The use of a chi-square test for each asperity (or slip) distribution, with the calculation of the chisquare value (as described below in this paragraph) which determines how long the Monte Carlo program has to run. 5. The assignment to each dislocation unit of the amount of slip which minimizes the chi-square value; the association of this value with the corresponding asperity (or slip) distribution.
amount of slip for each slipped asperity unit, with the total seismic moment maintained constant. Also in this case we use a chi-square test in order to determine the quality factor of the slip distributions calculated by Monte Carlo simulations; it determines the goodness of the fit with the observed geodetic data (Plafker, 1965). The nonuniform slip model gives of course a better chi-square value. The Monte Carlo method (Metropolis and Ulam, 1949) in employed with the aim of testing the performances of a large set of a priori possible distributions of asperity failures on the fault plane. The asperity distribution is selected from a large number of random distributions on the fault. The depths of the fault top and bottom are, respectively, equal to 12.2 and 51.3 km. We generated a set of 25,000 random slip distributions, yielding a seismic moment equal to M0V and calculated the surface vertical displacement u3 using analytical formulae given by Okada (1985). We p employ the symbol u3,k to indicate the vertical displacement predicted by the model at the generic k-th point at the Earth’s surface. It is given by a sum over the n square asperity units:
As a further, qualitative check on the obtained slip distribution, we shall consider the aftershock distribution of the 1964 Alaska earthquake and examine the aftershock location with respect to the dislocation surface. In more detail, we first work out a dislocation surface having the area of the rectangular model of Savage and Hastie (1966); the distribution of the corresponding slipped asperity units, obtained by the procedure described above, has an irregular shape. Assuming a uniform slip, we obtain a maximum value of surface vertical displacement equal to about 3 m and a minimum value of about 2 m: these values, comparable to those calculated by Savage and Hastie, give a qualitatively good fit with the geodetic data by Plafker (1965). Then the shape of the dislocation surface is retained as a constraint for the variable slip inversion, where for each slipped unit cell the slip value is allowed to vary. We consider a variable slip within the determined dislocation surface, determining the
In order to compare the displacement values predicted by the model with the values observed by Plafker (1965), we consider a square grid covering the Earth’s surface in the fault region. The grid side is equal to 600 km and the distance from each point of the grid to one of the surrounding points is equal to 30 km, implying that the total number of points is N = 21 21 = 441. We indicate the observed values of vertical displacement at the k-th point of the Earth’s o surface by the symbol u3,k . The v2 value is calculated for each slip distribution according to the formula
up3;k ¼
n X
up3;j
ð3Þ
j¼1
2
v ¼N
1
N ðuo up Þ2 X 3;k 3;k k¼1
rok
ð4Þ
in units of meters, where rok is the standard deviation of the observations. In order to find the best shape of the dislocation surface, we choose the slip distribution having the smallest v2 value. When we consider a variable slip on this surface, in the set of 25,000 distributions gener-
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ated by Monte Carlo method we retain as acceptable the subset of slip distributions, corresponding to 1% of the total number, having the smaller v2 values. For them there is at least a 99% probability of finding a worse solution. We define v992 the minimum of v2 values associated with the 1% of better distributions: in our case, v992 = 0.50. In the subset, we retain as the best solution the one for which the slip is a function as smooth as possible of the position on the fault. In a previous paper (Santini et al., 2000), we studied the displacement fields produced by dislocations with irregular shapes. We now apply this methodology to the inversion of displacement data surveyed by Plafker (1965), including the offshore extrapolation inferred
by him (Fig. 1). Holdahl and Sauber (1994) used earlier Johnson and Satake’s (1993) results to introduce a priori information for the offshore region. In particular, we try to reproduce the fault asperities and the slip distribution of the Alaska 1964 dislocations, showing that geodetic data can be interpreted in terms of complicated asperity distributions on a fault plane.
4. Uniform slip model Among the first papers dealing with dislocation modelling of the 1964 Alaska earthquake, the most complete work is that of Savage and Hastie (1966). The authors use geological data by Plafker (1965) and
Fig. 3. Comparison between the models ‘‘MOD2’’ and ‘‘MOD3’’ by Savage and Hastie (1966) and the contour of our model. In order to compare the sizes of rectangles, our fault model has been rotated; the geographic coordinates are given in Fig. 1. An asperity unit, 25 25 km2, is shown in the lower left corner.
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Fig. 4. (a) Uniform slip distribution of asperities on the fault plane. (b) Surface vertical displacement produced by a dislocation with the slip distribution as seen in Fig. 6a. (c) The misfit: v2 = 0.54.
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Fig. 5. (a) Variable slip distribution of asperities on the epicentral zone of the fault plane. (b) Surface vertical displacement produced by a dislocation with the slip distribution as seen in Fig. 7a. (c) The misfit: v2 = 0.52.
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Fig. 6. (a) Variable slip distribution of asperities on the total fault plane. (b) Surface vertical displacement produced by a dislocation with the slip distribution as seen in Fig. 8a. (c) The misfit: v2 = 0.47.
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Fig. 7. (a) Main dislocation (long green line in the section) and secondary dislocations (shallower dark green lines and deeper dark green line in the Montague Island zone). (b) Surface vertical displacement produced by the main dislocation, with the slip distribution as seen in Fig. 8a, and the secondary dislocations, with uniform slip = 5 m. (c) The misfit: v2 = 0.43.
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a uniform slip modelling approach, in order to constrain three fault models. Here we consider two of them, that we call MOD2 and MOD3 (Fig. 3). They are grossly consistent with the observed vertical displacement and the calculated seismic moment. However, MOD2 (L = 600 km, W = 125 km) gives a reasonable seismic moment, but it does not determine a good fit to the vertical displacement; MOD3 (L = 600 km, W = 200 km) gives a reasonable fit of the vertical displacement, but it does not produces a suitable seismic moment. As a starting point, we assume a uniform slip of the fault (U = 14 m) and approximate the fault with a single fault surface whose parameters were defined on the basis of earthquake focal parameters (Stauder and Bollinger, 1966), geologic and geodetic studies (Plafker, 1969, 1972; Savage and Hastie, 1966; Hastie and Savage, 1970), and seismicity studies (Algermissen et al., 1969). The model yields the slip distribution shown in Fig. 4a. This distribution corresponds to v2 = 0.54, and so we consider it fairly good. The rupture does have an irregular shape, with a larger eastern lobe. The top of the ruptured area is at about 12 km depth, with a maximum length of 600 km. The average dislocation width is about 125 km. In Fig. 4b, we show calculated vertical displacement. Plafker (1965) predicted a possible uplift in the Aleutian and Alaskan ranges: this appears to be confirmed by our model. We define as misfit the difference between the observed and calculated displacements. It is shown in Fig. 4c where it is possible to note that the largest difference is located in the Montague Island zone. Since the misfit is about 10%, we conclude that the displacement field calculated by the uniform slip model provides a reasonable fit to the Plafker data. In particular we confirm, as in the Holdahl and Sauber (1994) model, that the top of the fault plane cannot be deeper than 20 km in order to maintain a reasonable fit.
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The following constraints are assumed: (1) the total geodetic moment is equal to the seismic moment M0V obtained for the uniform slip case, and (2) the shape of the dislocation is maintained equal to that shown in Fig. 4a. We perform a large number of Monte Carlo simulations allowing asperity units to undergo variable amounts of slip. As a first trial, we condition the Monte Carlo program to maintain uniform the slip in the western part of the fault; this determines a larger slip in the epicentral zone of the fault plane (Prince William Sound asperity). However this yields a minimum v2 value equal to 0.52>v992, as shown in Fig. 5a. In Fig. 5b, we show the calculated vertical displacement. The misfit is shown in Fig. 5c where it is possible to note that the largest differences are located in the Montague Island and Kodiak Island zones. The latter discrepancy is presumably due to the presence of a second slip area near the western end of the fault. If we run the Monte Carlo program without any condition we obtain a minimum v2 value equal to 0.47 < v992, corresponding to the distribution shown in Fig. 6a. In Fig. 6b, we show the calculated vertical displacement for this case. The misfit is shown in Fig. 6c where it is possible to note that after the presence of another slip area near the western end of the fault
5. Variable slip model We now redistribute the slip on the fault in order to infer the variable slip distribution over the dislocation area as determined in the previous section for the uniform slip.
Fig. 8. Histogram showing the distribution of shocks as a function of time after the great 1964 Alaska earthquake. The green bars indicate the aftershocks occurred inside the dislocation area and the red bars indicate events occurred inside the unbroken asperities. Note that all events occurred inside the asperities after year 1970.
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Fig. 9. (a) Aftershocks epicentres (green dots are the events with Mw z 6) and the distribution of asperities (red area). (b) Post-1965 events (red dots with Mw z 6 and bleu dots with Mw z 6.5) and the dislocation surface (green area).
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(Kodiak asperity), only one is left in the Montague Island zone. Finally, we take into account the two small secondary dislocations surveyed by Plafker (1965) in the Montague Island zone (Fig. 7a): it has been hypothesized that they became active as a consequence of the main dislocation. The fault along the south –east side of the island was informally named the Patton Bay Fault; the one on the north – west side of the island, the Hanning Bay Fault. In order to calculate vertical and horizontal displacements connected to the 1964 main shock, we superimpose the secondary dislocations of Montague Island to the effects of the main dislocation. In doing so, we obtain a minimum v2 value equal to 0.43 corresponding to the slip distribution on the main dislocation shown in Fig. 6a plus the two secondary dislocations with uniform slip equal to 5 m. Fig. 7b shows a maximum of displacement in correspondence of Montague Island. Fig. 7c shows that the superimposition of the effects of the main dislocation, with two principal asperities, and of the secondary dislocations on the two minor faults gives a better fit between observed and calculated vertical displacements, as noted by previous papers (Holdahl and Sauber, 1994; Johnson et al., 1996). The low v2 value indicates a good approximation. We calculate also the horizontal displacement produced by the main dislocation, with the nonuniform slip distribution shown in Fig. 6a, and by the secondary dislocations. The maximum displacements are
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again observed in correspondence of Montague Island. We cannot show the horizontal displacement field because we did not have the possibility to compare our predicted data with a well-constrained set of observed data.
6. Post-1964 seismicity In Fig. 8, we point our attention to the Alaska seismicity after the 1964 main shock up to year 1999. The green bars indicate the aftershocks that occurred inside the main shock dislocation area, and the red bars indicate seismic events that occurred inside the surrounding asperities. We have plotted post-1964 events with a magnitude greater than 6.0: it can be seen that after 1970, all seismic events occurred inside the asperities. As a further test of the slip distribution obtained by the Monte Carlo simulation, we consider the seismicity that occurred in the area after the great Alaska earthquake. In Fig. 9a, we can see the 1964 aftershocks (from NEIS data). We consider only the shocks having magnitude Mw z 6. For earthquakes with magnitudes between 6.0 and about 6.6 (the maximum value in this period), the depth values range between 10 and 50 km (Table 1). It is possible to note that most of the early aftershocks are concentrated within the dislocation area obtained in our model.
Table 1 NEIS seismological parameters of aftershocks (until December 31, 1964) Category
Year
Month
Day
Time
Lat – long
Depth (km)
Mw
USHIS USHIS USHIS USHIS USHIS USHIS USHIS USHIS USHIS USHIS USHIS USHIS USHIS USHIS USHIS USHIS
1964 1964 1964 1964 1964 1964 1964 1964 1964 1964 1964 1964 1964 1964 1964 1964
3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4
28 28 28 28 28 28 28 28 30 30 4 4 4 5 12 16
45,407.9 71,022 90,100.9 95,256 103,538 122,050 144,737.3 144,914.2 21,806.8 70,933.8 84,030.8 174,609 175,944 12,214 12,431.2 192,656.7
59.80 – 149.40 58.83 – 149.29 56.42 – 152.01 59.72 – 146.47 57.17 – 152.45 56.45 – 153.94 60.36 – 146.61 60.51 – 146.70 56.65 – 152.82 59.89 – 145.66 56.52 – 152.56 56.30 – 154.40 56.51 – 154.33 56.28 – 153.34 56.60 – 152.20 56.41 – 152.90
25 17 23 30 26 25 12 10 22 13 19 24 22 24 22 25
6.1 6.2 6.2 6.2 6.3 6.5 6.3 6.5 6.6 6.2 6 6.5 6.13 6 6.25 6.63
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Table 2 NEIS seismological parameters of post-1964 events (from year 1965 to 1999) Category
Year
Month
Day
Time
Lat – long
Depth (km)
Mw
USHIS USHIS USHIS USHIS USHIS USHIS PDE PDE PDE PDE PDE PDE PDE PDE PDE PDE PDE
1965 1965 1966 1968 1969 1970 1974 1974 1974 1978 1982 1983 1983 1986 1986 1999 1999
9 12 4 4 11 3 8 8 8 4 9 7 9 6 9 5 12
4 22 16 23 24 11 1 1 1 12 6 12 7 19 12 7 7
143,250.2 194,121.6 12,714.1 202,914.6 225,149.6 223,832.4 50,759 55,538.2 75,956.9 34,203.5 74,854.99 151,003.4 192,205.15 90,909.21 235,715.61 141,352.36 1949.61
58.29 – 152.50 58.35 – 153.13 56.93 – 153.61 58.69 – 149.93 56.14 – 153.66 57.39 – 153.97 56.52 – 152.32 56.67 – 152.10 56.63 – 152.26 56.42 – 152.69 56.84 – 151.59 61.03 – 147.29 60.98 – 147.50 56.33 – 152.91 56.20 – 153.40 56.42 – 152.94 57.36 – 154.51
30 38 23 22 28 16 10 33 33 14 33 37 45 16 31 20 40
6.8 6.88 6.25 6.3 6 6.4 6.1 6.3 6 6.6 6 6.4 6.2 6.4 6.3 6.2 6.5
In Fig. 9b, we can see the post-1965 events (always NEIS data). The magnitudes range between 6.0 and about 6.9 and the depths range between 10 and 50 km (Table 2). It appears that most of the seismic events that occurred after 1965 are located within the areas that remained asperities in our model. Fig. 9 and Tables 1 and 2 show the locations and attributes of significant, post-1964 earthquakes; the location accuracy is different if the horizontal or vertical position is considered. In the case of horizontal position, 100 m is the nominal precision of the reported coordinate values. In the case of vertical position, the nominal precision is 1 km. However, the actual accuracy is considerably less: it depends upon numerous factors including imprecision of the velocity model of the Earth, uneven distribution of seismic stations, and imprecisions in the computational algorithm. Even if the actual uncertainty of hypocentre location is greater than the nominal values, it is however much smaller than the size of the asperity units considered in the model (25 25 km2).
7. Conclusions The interpretation of geodetic measurements in terms of nonuniform slip is nowadays commonly employed in modelling seismic sources. The displacement at the Earth’s surface connected with fault slip is
remarkably affected by inhomogeneity of slip on the fault. Moreover, the asperities which remain unbroken in the main shock are the probable candidates for aftershocks and subsequent seismicity in the source region. In the present paper, we considered the slip distribution on the fault plane of the 1964 great Alaska earthquake. Assuming first a uniform slip, we obtained a best fit of surface coseismic deformation for a dislocation surface with an irregular shape. The agreement with observations is improved by redistributing fault slip on the dislocation surface at constant seismic moment. The results show the previous finding that the slip distribution of the great Alaska earthquake was essentially made of two dislocation areas with a higher slip, the Prince William Sound and the Kodiak asperities. The presence of a large area with high slip (average slip f 24 m) below Prince William Sound zone and a smaller area with a medium slip (average f 18 m) below the town of Kodiak is confirmed, as found by Christensen and Beck (1994), Holdahl and Sauber (1994), and Johnson et al. (1996). Analysis of the post-1964 seismicity in the rupture region shows a strong correlation between the larger earthquakes (Mw z 6) and the distribution of locked asperities following the 1964 event, which can be considered as an independent test of the validity of the model. In particular, we do not find slip values higher than 25 m for any of the patches, and we determine
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two separate high-slip zones: one correspondent to the Prince William Sound asperity, and one ( f 18 m slip) to the Kodiak asperity. The slip distribution connected with the 1964 shock appears to be consistent with the following seismicity in the region. The early aftershocks (during year 1964) are mostly located within the coseismic area, while the following earthquakes (1965 –1999) are located close to the fault plane but outside of regions of highest slip, often in the vicinity of the border. The present distribution of asperities on the fault can be seen as an indicator of the location where future medium-size earthquakes are likely to occur (Dmowska and Lovison, 1992).
Acknowledgements We are grateful to Renata Dmowska for useful comments and suggestions on the subject of the paper. Many thanks are due to Jeanne Sauber and James C. Savage for interesting comments and suggestions on the preliminary version of this paper. References Algermissen, S.T., Rinehart, W.A., Sherburne, R.W., Dillinger Jr., W., 1969. Preshocks and aftershocks of the Prince William sound earthquake of March 28, 1964. Coast Geod. Surv. 211, 23 – 43. Christensen, D., Beck, S., 1994. The 1964 Prince William Sound earthquake: rupture process and plate segmentation. Pure Appl. Geophys. 142, 29 – 53. Dmowska, R., Lovison, L.C., 1992. Influence of asperities along subduction interfaces on the stressing and seismicity of adjacent areas. Tectonophysics 211, 23 – 43. Dragoni, M., 1988. Role of geodetic measurements in the detection of fault asperities. In: Baldi, P., Zerbini, S. (Eds.), Proc. Third Int. Conf. on the WEGENER/MEDLAS Project, 129 – 146. Bologna. Dziewonski, A.M., Anderson, D.L., 1981. PREM. Phys. Earth Planet Inter. 25, 297 – 356.
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Hastie, L.M., Savage, J.C., 1970. A dislocation model for the 1964 Alaska earthquake. Bull. Seismol. Soc. Am. 60, 1389 – 1392. Holdahl, R., Sauber, J., 1994. Coseismic slip in the 1964 Prince William Sound earthquake: a new geodetic inversion. Pure Appl. Geophys. 142, 55 – 82. Johnson, M., Satake, K., 1993. Slip distribution of the 1964 Alaska earthquake from inversion of tsunami waveforms (abstract). EOS, Trans. Am. Geophys. Union Suppl. 74, 95. Johnson, M., Satake, K., Holdahl, R., Sauber, J., 1996. The 1964 Prince William Sound earthquake: joint inversion of tsunami and geodetic data. J. Geophys. Res. 101, 523 – 532. Kanamori, H., 1977. The energy release in great earthquakes. J. Geophys. Res. 82, 2982 – 2983. Kasahara, K., 1981. Earthquake mechanics. Cambridge Earth Science Series. Cambridge Univ. Press, Cambridge. 248 pp. Kikuchi, M., Fukao, Y., 1987. Inversion of long-period P waves from great earthquakes along subduction zones. Tectonophysics 144, 231 – 247. Metropolis, N., Ulam, S.M., 1949. The Monte Carlo method. J. Am. Stat. Assoc. 44, 335 – 341. Miyashita, K., Matsu’ura, M., 1978. Inversion analysis of static displacement data associated with the Alaska earthquake of 1964. J. Phys. Earth 26, 333 – 349. Okada, Y., 1985. Surface deformation due to shear and tensile faults in a half-space. Bull. Seismol. Soc. Am. 75, 1135 – 1154. Plafker, G., 1965. Tectonic deformation associated with the Alaska earthquake. Science 148, 1675 – 1687. Plafker, G., 1969. Tectonics of March 27, 1964 Alaska earthquake. U.S. Geol. Surv. Prof. Pap. 543-I, 1 – 74. Plafker, G., 1972. Alaskan earthquake of 1964 and Chilean earthquake of 1960: implications for Arc Tectonics. J. Geophys. Res. 77, 901 – 925. Prescott, W., Lisowski, M., 1977. Deformation at Middleton Island, Alaska, during the decade after the Alaska Earthquake of 1964. Bull. Seismol. Soc. Am. 67, 579 – 586. Santini, S., Piombo, A., Dragoni, M., 2000. Ground displacement in a fault zone in the presence of asperities. Boll. Geofis. Teor. Appl. 41, 95 – 110. Savage, J.C., Hastie, L.M., 1966. Surface deformation associated with dip-slip faulting. J. Geophys. Res. 71, 4897 – 4904. Stauder, W., Bollinger, G.A., 1966. The focal mechanism of the Alaska earthquake of March 28, 1964, and its aftershock sequence. J. Geophys. Res. 71, 5283 – 5296. Wood, F.J. (Ed.), 1966. The Prince William Sound, Alaska, Earthquake of 1964 and Aftershocks. Coast and Geodetic Survey, 3 vols. U.S. Department of Commerce, Washington, DC.
Asperity distribution of the 1964 Great Alaska earthquake and its relation to subsequent seismicity in the region S. Santini a,*, M. Dragoni b, G. Spada a b
a Istituto di Fisica, Universita` di Urbino, Via S. Chiara 27, Urbino 61029, Italy Dipartimento di Fisica, Settore di Geofisica, Universita` di Bologna, Viale B. Pichat 8, Bologna, Italy
Received 9 July 2002; accepted 20 March 2003
Abstract The 1964 Alaska earthquake was the second largest seismic events in the 20th century. The aim of this work is the use of surface deformation data to determine asperity and slip distributions on the fault plane of the Alaska earthquake: these distributions are calculated by a Monte Carlo method. To this aim, we decompose the fault plane in a large number of small square asperity units with a side of 25 km; this allows us to obtain plane surfaces with an irregular shape. In the first stage, each asperity unit is allowed to slip a constant amount or not to slip at all, providing the geometry of the dislocation surface that best reproduces the observed displacements. To this purpose, a large number of slip distributions have been tried by the use of the Monte Carlo method. The slip amplitude is the same for all the asperities and is equal to the average fault slip inferred from the seismic moment. In the second stage, we evaluate the slip distribution in the dislocation area determined by the Monte Carlo inversion: in this case, we allow unit cells to undergo different values of slip in order to refine the initial dislocation model. The results confirm the previous finding that the slip distribution of the great Alaska earthquake was essentially made of two dislocation areas with a higher slip, the Prince William Sound and the Kodiak asperities. Analysis of the post-1964 seismicity in the rupture region shows a strong correlation between the larger earthquakes (Mw z 6) and the distribution of locked asperities following the 1964 event, which can be considered as an independent test of the validity of the model. We do not find slip values higher than 25 m for any of the patches, and we determine two separate high-slip zones: one correspondent to the Prince William Sound asperity, and one ( f 18 m slip) to the Kodiak asperity. The slip distribution connected with the 1964 shock appears to be consistent with the following seismicity in the region. D 2003 Elsevier Science B.V. All rights reserved. Keywords: Dislocation; Slip distribution; Displacement field; Monte Carlo method; Prince William Sound; Kodiak Island
1. Introduction On March 28, 1964, one of the largest earthquakes of the last century, with magnitude Mw = 9.2, occurred * Corresponding author. E-mail address: [email protected] (S. Santini).
in the south central Alaska, where the Pacific Plate is subducted under the North American Plate. The earthquake ruptured an 800-km-long segment of the subduction zone, with maximum surface displacements of more than 10 m (Fig. 1). The focal mechanism indicates that the fault movement was that of a thrust fault, with a dip angle of about 9j.
0040-1951/03/$ - see front matter D 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0040-1951(03)00130-6
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Fig. 1. Coseismic displacement field of the great Alaska earthquake as given by Plafker (1965), and the surface projection of our fault plane model (DEFG rectangle).
In the decades following the event, several papers have been devoted to the study of this large earthquake and have added much to our knowledge of it. Pioneering studies were done by Plafker (1965) and Wood (1966). The extent of the rupture zone was inferred by aftershock studies (Stauder and Bollinger, 1966; Algermissen et al., 1969) and by modelling of geologic and geodetic data (Plafker, 1969, 1972; Savage and Hastie, 1966; Hastie and Savage, 1970; Prescott and Lisowski, 1977; Miyashita and Matsu’ura, 1978). More recently, Holdahl and Sauber (1994) proposed an inversion of coseismic displacement data, obtaining
a slip distribution on the fault plane. Johnson et al. (1996) performed a joint inversion of geodetic data and tsunami waveforms, substantially confirming that the slip distribution on the fault plane was dominated by two areas of large slip, the Prince William Sound asperity and the Kodiak asperity. They assumed a dip angle equal to 3j in the Prince William Sound area but a different angle in the Kodiak region. The present paper employs the coseismic surface displacement data in order to constrain the geometry of the dislocation surface and the slip distribution on the fault plane of the Alaska earthquake. In order to
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retrieve the slip distribution which best fits the geodetic data, we use a Monte Carlo method (Metropolis and Ulam, 1949) testing the performances of a large set of a priori random asperity distributions on the fault plane. The procedure is made of two stages. In the first stage, geodetic data are used in order to constrain the geometry of the dislocation surface. To this aim, an asperity model is employed, where the fault plane is divided in a large number of square asperity units which can slip by a constant amount or remain locked. In the second stage, the asperity units are allowed to slip by variable amounts, in order to reproduce a nonuniform slip distribution on the fault plane. In order to reach a good fit between the observed and the calculated surface displacements, many slip distributions are tried by the use of Monte Carlo simulations. In this work, the distribution of asperities (or slip) on the fault plane is found using only the fault geometry, the geodetic data and the seismic moment related to the 1964 Alaska earthquake. The model is developed without taking into account the seismicity preceding or following the 1964 main shock. However, the subsequent seismicity will be considered as a test for the slip distribution obtained in the model.
2. The data The data that we use are the coseismic displacement field at the Earth’s surface (Plafker, 1965), the geometry of the fault and the average slip determined by previous studies (Savage and Hastie, 1966; Stauder and Bollinger, 1966). We assume that the fault is a rectangle with a length L = 600 km and a width W = 250 km. The fault is embedded in an elastic half-space with Lame` constants k = l (Poisson’s solid). The shear modulus l is assumed to have a value equal to 5.5 1010 Pa, calculated as an average on the relevant crustal thickness (Dziewonski and Anderson, 1981). The average fault slip U is assumed to be equal to 14 m, a value given by Johnson et al. (1996). The seismic moment is then (e. g. Kasahara, 1981) M0 ¼ lUA
ð1Þ
where A is the dislocation area. We shall estimate A on the basis of the moment magnitude Mw. The seismic
221
moment M0 is related to the moment magnitude Mw by the following equation (Kanamori, 1977): logM0 ¼ 9:1 þ 1:5Mw
ð2Þ
where M 0 is expressed in N m. If we consider Mw = 9.2, then M0 = 0.79 1023 N m. From Eq. (1), we obtain A = 105 km2. Following Savage and Hastie (1966), who assume a length L = 600 km and a width W = 125 km, giving a dislocation area AV= 7.5 104 km2, we retain this last value, corresponding to a seismic moment M0V equal to about 75% of the seismic moment M0 determined from long-period surface waves. This value does not include a possible seismic slip that occurred on the fault in the weeks or months following the main shock. The value M0V = 5.8 1022 N m is close to the seismic moment of 5.9 1022 N m obtained by Kikuchi and Fukao (1987). As to geodetic data, we refer the reader to the detailed description of the data acquisition and interpolation given in Plafker (1965). This article makes available a summary of the basic data acquired during the 1964 field season on the tectonic deformations that accompanied the earthquake. In Plafker (1969), the complete data set is reported. The vertical tectonic movements in coastal areas were determined mainly by making more than 800 measurements of displacement of intertidal sessile marine organisms along the coast. These measurements were supplemented at 16 tidal bench marks by coupled pre- and post-earthquake tide-gauge readings made by U.S. Coast and Geodetic Survey, and by numerous estimates of relative changes in tide levels by local residents. The major area of uplift is about 800 km long and trends north – east from southern Kodiak Island to Prince William Sound, and east –west to the east of Prince William Sound. The maximum measured uplift on land is 10 m at the south – west end of Montague Island and more than 15 m offshore from Montague Island. Holdahl and Sauber (1994) improved upon earlier geodetically derived coseismic slip models by inverting simultaneously vertical and horizontal geodetic, tide gauge, and geologic data for a more detailed distribution of coseismic slip by using the fault geometry inferred from other geophysical informa-
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tion. They examined the hypothesis that there were regions of high slip separated by regions of more moderate slip. Johnson et al. (1996) used all the data used by Holdahl and Sauber (1994). In Fig. 1, the observed vertical displacement field is shown. Excluding Prince William Sound area, we have a maximum value of about 3 m and a minimum value of about 2 m; but a maximum vertical coseismic displacement of 10 m is reached in the Montague Island zone. In the Kodiak area, a maximum displacement between 1 and 2 m is observed. Plafker (1965) considered the presence of two smaller faults in the Montague Island zone: they produced secondary dislocations, much more superficial in respect to the main dislocation. The additional coseismic deformation, observed in the Prince William Sound area, is due to the presence of the two secondary dislocations. There are no contour lines between Kodiak Island and the Aleutian Trench Axis due to the presence of the sea.
3. The model Let us consider an elastic, homogeneous and isotropic half-space, occupying the region x3 z 0 in a Cartesian coordinate system, and assume that the fault surface is a rectangle belonging to a half-plane intersecting the Earth’s surface with a dip angle d. The x3 axis is parallel to the fault strike and contains the projection of the bottom side of the fault surface on the Earth’s surface. The depth of the bottom side of the fault surface is D.
Due to inhomogeneity of friction on faults, dislocation surfaces have usually irregular shapes. In order to take this into account, we assume that the fault rupture is the consequence of the failure of a large number of small square asperity units (Fig. 2). In the case of a rectangular dislocation, the displacement field at the Earth’s surface can be obtained by available analytical solutions (Okada, 1985). From the solution for a square dislocation, it is easy to obtain the analytical solution for any dislocation with a polygonal contour. As a consequence, it is possible to model the effect of dislocations with any shape by employing suitably small asperity units (e.g. Dragoni, 1988; Santini et al., 2000). In order to retrieve the slip distribution associated with the 1964 Alaska earthquake, we implement the following procedure. The slip distribution (or dislocation surface) is the effect of the failure of a corresponding distribution of square asperity units and is obtained on the basis of the fault geometry, the focal mechanism and the seismic moment of the 1964 Alaska earthquake. The aftershock distribution is not taken into account at this stage. The procedure is made of the following steps: 1. Individuation of the fault plane, using geological constraints and the total seismic moment. According to the calculated focal mechanism (Savage and Hastie, 1966), the type of fault movement is that of a thrust fault, with a dip angle of 9j; the dislocation area is 75,000 km2 and the average slip is about 14 m.
Fig. 2. Model for the fault plane of the 1964 Alaska earthquake.
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2. The subdivision of the fault surface in n = 120 square asperity units, with a side d equal to 25 km: this number is chosen in order that, with a slip amplitude U in the order of 1 m, the failure of an asperity unit releases a seismic moment corresponding to the typical magnitude (Mw c 6.5) of the largest aftershocks of the Alaska earthquake (Kasahara, 1981). 3. The use of a Monte Carlo method in order to generate a large number of possible slip distributions; the calculation of the vertical surface displacement for each slip distribution and the comparison with the available displacement data, in order to minimize the misfit between the predicted and observed data. The slipping area (dislocation) of the fault is obtained assuming that each asperity unit has two possible states: locked or slipping. 4. The use of a chi-square test for each asperity (or slip) distribution, with the calculation of the chisquare value (as described below in this paragraph) which determines how long the Monte Carlo program has to run. 5. The assignment to each dislocation unit of the amount of slip which minimizes the chi-square value; the association of this value with the corresponding asperity (or slip) distribution.
amount of slip for each slipped asperity unit, with the total seismic moment maintained constant. Also in this case we use a chi-square test in order to determine the quality factor of the slip distributions calculated by Monte Carlo simulations; it determines the goodness of the fit with the observed geodetic data (Plafker, 1965). The nonuniform slip model gives of course a better chi-square value. The Monte Carlo method (Metropolis and Ulam, 1949) in employed with the aim of testing the performances of a large set of a priori possible distributions of asperity failures on the fault plane. The asperity distribution is selected from a large number of random distributions on the fault. The depths of the fault top and bottom are, respectively, equal to 12.2 and 51.3 km. We generated a set of 25,000 random slip distributions, yielding a seismic moment equal to M0V and calculated the surface vertical displacement u3 using analytical formulae given by Okada (1985). We p employ the symbol u3,k to indicate the vertical displacement predicted by the model at the generic k-th point at the Earth’s surface. It is given by a sum over the n square asperity units:
As a further, qualitative check on the obtained slip distribution, we shall consider the aftershock distribution of the 1964 Alaska earthquake and examine the aftershock location with respect to the dislocation surface. In more detail, we first work out a dislocation surface having the area of the rectangular model of Savage and Hastie (1966); the distribution of the corresponding slipped asperity units, obtained by the procedure described above, has an irregular shape. Assuming a uniform slip, we obtain a maximum value of surface vertical displacement equal to about 3 m and a minimum value of about 2 m: these values, comparable to those calculated by Savage and Hastie, give a qualitatively good fit with the geodetic data by Plafker (1965). Then the shape of the dislocation surface is retained as a constraint for the variable slip inversion, where for each slipped unit cell the slip value is allowed to vary. We consider a variable slip within the determined dislocation surface, determining the
In order to compare the displacement values predicted by the model with the values observed by Plafker (1965), we consider a square grid covering the Earth’s surface in the fault region. The grid side is equal to 600 km and the distance from each point of the grid to one of the surrounding points is equal to 30 km, implying that the total number of points is N = 21 21 = 441. We indicate the observed values of vertical displacement at the k-th point of the Earth’s o surface by the symbol u3,k . The v2 value is calculated for each slip distribution according to the formula
up3;k ¼
n X
up3;j
ð3Þ
j¼1
2
v ¼N
1
N ðuo up Þ2 X 3;k 3;k k¼1
rok
ð4Þ
in units of meters, where rok is the standard deviation of the observations. In order to find the best shape of the dislocation surface, we choose the slip distribution having the smallest v2 value. When we consider a variable slip on this surface, in the set of 25,000 distributions gener-
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ated by Monte Carlo method we retain as acceptable the subset of slip distributions, corresponding to 1% of the total number, having the smaller v2 values. For them there is at least a 99% probability of finding a worse solution. We define v992 the minimum of v2 values associated with the 1% of better distributions: in our case, v992 = 0.50. In the subset, we retain as the best solution the one for which the slip is a function as smooth as possible of the position on the fault. In a previous paper (Santini et al., 2000), we studied the displacement fields produced by dislocations with irregular shapes. We now apply this methodology to the inversion of displacement data surveyed by Plafker (1965), including the offshore extrapolation inferred
by him (Fig. 1). Holdahl and Sauber (1994) used earlier Johnson and Satake’s (1993) results to introduce a priori information for the offshore region. In particular, we try to reproduce the fault asperities and the slip distribution of the Alaska 1964 dislocations, showing that geodetic data can be interpreted in terms of complicated asperity distributions on a fault plane.
4. Uniform slip model Among the first papers dealing with dislocation modelling of the 1964 Alaska earthquake, the most complete work is that of Savage and Hastie (1966). The authors use geological data by Plafker (1965) and
Fig. 3. Comparison between the models ‘‘MOD2’’ and ‘‘MOD3’’ by Savage and Hastie (1966) and the contour of our model. In order to compare the sizes of rectangles, our fault model has been rotated; the geographic coordinates are given in Fig. 1. An asperity unit, 25 25 km2, is shown in the lower left corner.
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225
Fig. 4. (a) Uniform slip distribution of asperities on the fault plane. (b) Surface vertical displacement produced by a dislocation with the slip distribution as seen in Fig. 6a. (c) The misfit: v2 = 0.54.
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Fig. 5. (a) Variable slip distribution of asperities on the epicentral zone of the fault plane. (b) Surface vertical displacement produced by a dislocation with the slip distribution as seen in Fig. 7a. (c) The misfit: v2 = 0.52.
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Fig. 6. (a) Variable slip distribution of asperities on the total fault plane. (b) Surface vertical displacement produced by a dislocation with the slip distribution as seen in Fig. 8a. (c) The misfit: v2 = 0.47.
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Fig. 7. (a) Main dislocation (long green line in the section) and secondary dislocations (shallower dark green lines and deeper dark green line in the Montague Island zone). (b) Surface vertical displacement produced by the main dislocation, with the slip distribution as seen in Fig. 8a, and the secondary dislocations, with uniform slip = 5 m. (c) The misfit: v2 = 0.43.
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a uniform slip modelling approach, in order to constrain three fault models. Here we consider two of them, that we call MOD2 and MOD3 (Fig. 3). They are grossly consistent with the observed vertical displacement and the calculated seismic moment. However, MOD2 (L = 600 km, W = 125 km) gives a reasonable seismic moment, but it does not determine a good fit to the vertical displacement; MOD3 (L = 600 km, W = 200 km) gives a reasonable fit of the vertical displacement, but it does not produces a suitable seismic moment. As a starting point, we assume a uniform slip of the fault (U = 14 m) and approximate the fault with a single fault surface whose parameters were defined on the basis of earthquake focal parameters (Stauder and Bollinger, 1966), geologic and geodetic studies (Plafker, 1969, 1972; Savage and Hastie, 1966; Hastie and Savage, 1970), and seismicity studies (Algermissen et al., 1969). The model yields the slip distribution shown in Fig. 4a. This distribution corresponds to v2 = 0.54, and so we consider it fairly good. The rupture does have an irregular shape, with a larger eastern lobe. The top of the ruptured area is at about 12 km depth, with a maximum length of 600 km. The average dislocation width is about 125 km. In Fig. 4b, we show calculated vertical displacement. Plafker (1965) predicted a possible uplift in the Aleutian and Alaskan ranges: this appears to be confirmed by our model. We define as misfit the difference between the observed and calculated displacements. It is shown in Fig. 4c where it is possible to note that the largest difference is located in the Montague Island zone. Since the misfit is about 10%, we conclude that the displacement field calculated by the uniform slip model provides a reasonable fit to the Plafker data. In particular we confirm, as in the Holdahl and Sauber (1994) model, that the top of the fault plane cannot be deeper than 20 km in order to maintain a reasonable fit.
229
The following constraints are assumed: (1) the total geodetic moment is equal to the seismic moment M0V obtained for the uniform slip case, and (2) the shape of the dislocation is maintained equal to that shown in Fig. 4a. We perform a large number of Monte Carlo simulations allowing asperity units to undergo variable amounts of slip. As a first trial, we condition the Monte Carlo program to maintain uniform the slip in the western part of the fault; this determines a larger slip in the epicentral zone of the fault plane (Prince William Sound asperity). However this yields a minimum v2 value equal to 0.52>v992, as shown in Fig. 5a. In Fig. 5b, we show the calculated vertical displacement. The misfit is shown in Fig. 5c where it is possible to note that the largest differences are located in the Montague Island and Kodiak Island zones. The latter discrepancy is presumably due to the presence of a second slip area near the western end of the fault. If we run the Monte Carlo program without any condition we obtain a minimum v2 value equal to 0.47 < v992, corresponding to the distribution shown in Fig. 6a. In Fig. 6b, we show the calculated vertical displacement for this case. The misfit is shown in Fig. 6c where it is possible to note that after the presence of another slip area near the western end of the fault
5. Variable slip model We now redistribute the slip on the fault in order to infer the variable slip distribution over the dislocation area as determined in the previous section for the uniform slip.
Fig. 8. Histogram showing the distribution of shocks as a function of time after the great 1964 Alaska earthquake. The green bars indicate the aftershocks occurred inside the dislocation area and the red bars indicate events occurred inside the unbroken asperities. Note that all events occurred inside the asperities after year 1970.
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Fig. 9. (a) Aftershocks epicentres (green dots are the events with Mw z 6) and the distribution of asperities (red area). (b) Post-1965 events (red dots with Mw z 6 and bleu dots with Mw z 6.5) and the dislocation surface (green area).
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(Kodiak asperity), only one is left in the Montague Island zone. Finally, we take into account the two small secondary dislocations surveyed by Plafker (1965) in the Montague Island zone (Fig. 7a): it has been hypothesized that they became active as a consequence of the main dislocation. The fault along the south –east side of the island was informally named the Patton Bay Fault; the one on the north – west side of the island, the Hanning Bay Fault. In order to calculate vertical and horizontal displacements connected to the 1964 main shock, we superimpose the secondary dislocations of Montague Island to the effects of the main dislocation. In doing so, we obtain a minimum v2 value equal to 0.43 corresponding to the slip distribution on the main dislocation shown in Fig. 6a plus the two secondary dislocations with uniform slip equal to 5 m. Fig. 7b shows a maximum of displacement in correspondence of Montague Island. Fig. 7c shows that the superimposition of the effects of the main dislocation, with two principal asperities, and of the secondary dislocations on the two minor faults gives a better fit between observed and calculated vertical displacements, as noted by previous papers (Holdahl and Sauber, 1994; Johnson et al., 1996). The low v2 value indicates a good approximation. We calculate also the horizontal displacement produced by the main dislocation, with the nonuniform slip distribution shown in Fig. 6a, and by the secondary dislocations. The maximum displacements are
231
again observed in correspondence of Montague Island. We cannot show the horizontal displacement field because we did not have the possibility to compare our predicted data with a well-constrained set of observed data.
6. Post-1964 seismicity In Fig. 8, we point our attention to the Alaska seismicity after the 1964 main shock up to year 1999. The green bars indicate the aftershocks that occurred inside the main shock dislocation area, and the red bars indicate seismic events that occurred inside the surrounding asperities. We have plotted post-1964 events with a magnitude greater than 6.0: it can be seen that after 1970, all seismic events occurred inside the asperities. As a further test of the slip distribution obtained by the Monte Carlo simulation, we consider the seismicity that occurred in the area after the great Alaska earthquake. In Fig. 9a, we can see the 1964 aftershocks (from NEIS data). We consider only the shocks having magnitude Mw z 6. For earthquakes with magnitudes between 6.0 and about 6.6 (the maximum value in this period), the depth values range between 10 and 50 km (Table 1). It is possible to note that most of the early aftershocks are concentrated within the dislocation area obtained in our model.
Table 1 NEIS seismological parameters of aftershocks (until December 31, 1964) Category
Year
Month
Day
Time
Lat – long
Depth (km)
Mw
USHIS USHIS USHIS USHIS USHIS USHIS USHIS USHIS USHIS USHIS USHIS USHIS USHIS USHIS USHIS USHIS
1964 1964 1964 1964 1964 1964 1964 1964 1964 1964 1964 1964 1964 1964 1964 1964
3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4
28 28 28 28 28 28 28 28 30 30 4 4 4 5 12 16
45,407.9 71,022 90,100.9 95,256 103,538 122,050 144,737.3 144,914.2 21,806.8 70,933.8 84,030.8 174,609 175,944 12,214 12,431.2 192,656.7
59.80 – 149.40 58.83 – 149.29 56.42 – 152.01 59.72 – 146.47 57.17 – 152.45 56.45 – 153.94 60.36 – 146.61 60.51 – 146.70 56.65 – 152.82 59.89 – 145.66 56.52 – 152.56 56.30 – 154.40 56.51 – 154.33 56.28 – 153.34 56.60 – 152.20 56.41 – 152.90
25 17 23 30 26 25 12 10 22 13 19 24 22 24 22 25
6.1 6.2 6.2 6.2 6.3 6.5 6.3 6.5 6.6 6.2 6 6.5 6.13 6 6.25 6.63
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Table 2 NEIS seismological parameters of post-1964 events (from year 1965 to 1999) Category
Year
Month
Day
Time
Lat – long
Depth (km)
Mw
USHIS USHIS USHIS USHIS USHIS USHIS PDE PDE PDE PDE PDE PDE PDE PDE PDE PDE PDE
1965 1965 1966 1968 1969 1970 1974 1974 1974 1978 1982 1983 1983 1986 1986 1999 1999
9 12 4 4 11 3 8 8 8 4 9 7 9 6 9 5 12
4 22 16 23 24 11 1 1 1 12 6 12 7 19 12 7 7
143,250.2 194,121.6 12,714.1 202,914.6 225,149.6 223,832.4 50,759 55,538.2 75,956.9 34,203.5 74,854.99 151,003.4 192,205.15 90,909.21 235,715.61 141,352.36 1949.61
58.29 – 152.50 58.35 – 153.13 56.93 – 153.61 58.69 – 149.93 56.14 – 153.66 57.39 – 153.97 56.52 – 152.32 56.67 – 152.10 56.63 – 152.26 56.42 – 152.69 56.84 – 151.59 61.03 – 147.29 60.98 – 147.50 56.33 – 152.91 56.20 – 153.40 56.42 – 152.94 57.36 – 154.51
30 38 23 22 28 16 10 33 33 14 33 37 45 16 31 20 40
6.8 6.88 6.25 6.3 6 6.4 6.1 6.3 6 6.6 6 6.4 6.2 6.4 6.3 6.2 6.5
In Fig. 9b, we can see the post-1965 events (always NEIS data). The magnitudes range between 6.0 and about 6.9 and the depths range between 10 and 50 km (Table 2). It appears that most of the seismic events that occurred after 1965 are located within the areas that remained asperities in our model. Fig. 9 and Tables 1 and 2 show the locations and attributes of significant, post-1964 earthquakes; the location accuracy is different if the horizontal or vertical position is considered. In the case of horizontal position, 100 m is the nominal precision of the reported coordinate values. In the case of vertical position, the nominal precision is 1 km. However, the actual accuracy is considerably less: it depends upon numerous factors including imprecision of the velocity model of the Earth, uneven distribution of seismic stations, and imprecisions in the computational algorithm. Even if the actual uncertainty of hypocentre location is greater than the nominal values, it is however much smaller than the size of the asperity units considered in the model (25 25 km2).
7. Conclusions The interpretation of geodetic measurements in terms of nonuniform slip is nowadays commonly employed in modelling seismic sources. The displacement at the Earth’s surface connected with fault slip is
remarkably affected by inhomogeneity of slip on the fault. Moreover, the asperities which remain unbroken in the main shock are the probable candidates for aftershocks and subsequent seismicity in the source region. In the present paper, we considered the slip distribution on the fault plane of the 1964 great Alaska earthquake. Assuming first a uniform slip, we obtained a best fit of surface coseismic deformation for a dislocation surface with an irregular shape. The agreement with observations is improved by redistributing fault slip on the dislocation surface at constant seismic moment. The results show the previous finding that the slip distribution of the great Alaska earthquake was essentially made of two dislocation areas with a higher slip, the Prince William Sound and the Kodiak asperities. The presence of a large area with high slip (average slip f 24 m) below Prince William Sound zone and a smaller area with a medium slip (average f 18 m) below the town of Kodiak is confirmed, as found by Christensen and Beck (1994), Holdahl and Sauber (1994), and Johnson et al. (1996). Analysis of the post-1964 seismicity in the rupture region shows a strong correlation between the larger earthquakes (Mw z 6) and the distribution of locked asperities following the 1964 event, which can be considered as an independent test of the validity of the model. In particular, we do not find slip values higher than 25 m for any of the patches, and we determine
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two separate high-slip zones: one correspondent to the Prince William Sound asperity, and one ( f 18 m slip) to the Kodiak asperity. The slip distribution connected with the 1964 shock appears to be consistent with the following seismicity in the region. The early aftershocks (during year 1964) are mostly located within the coseismic area, while the following earthquakes (1965 –1999) are located close to the fault plane but outside of regions of highest slip, often in the vicinity of the border. The present distribution of asperities on the fault can be seen as an indicator of the location where future medium-size earthquakes are likely to occur (Dmowska and Lovison, 1992).
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