Seismicity and rates of relative motion on the plate boundaries of Western North America

Transcription

1 Geophys. J. R. asir. Soc. (1983) 72,59-82 Seismicity and rates of relative motion on the plate boundaries of Western North America R. D. Hyndman and D. H. Weichert Pacific Geoscience Centre, Earth Physics Branch, Department of Energy, Mines and Resources, PO Box 6000, Sidney, British Columbia V8L 4B2, Canada Received 1982 April 4;in original form 1981 October 21 Summary. The consistency of earthquake data and plate tectonic models and other estimates of fault slip, may be tested by estimating rates of motion from the earthquakes using the concept of seismic moment. The contribution of individual events may simply be summed, but a generally better estimate of long-term average slip rate is obtained by integration over magnitudefrequency of occurrence relations. Estimates of fault motion rates associated with earthquakes are possible within about a factor of 2 using this approach if the major sources of uncertainty are given careful consideration; e.g. incompleteness and inaccuracies in the earthquake data; empirical moment-magnitude relations and the effect of their stochasticity; fault widths or depth extents; the recurrence relations; maximum magnitudes and the form of truncation at the maximum magnitude. A formulation for the recommended magnitude density truncation is developed. Application of the latter method to the earthquake data of the offshore transform faults of the Juan de Fuca ridge system, the Queen Charlotte fault zone and the northern Vancouver Island area in each case gives good agreement with rates from plate tectonic models. For the southern San Andreas fault and Gulf of California area there is also good agreement with previous estimates obtained by summing the contributions of individual events. However, the displacement rate in the margin convergence zone of southern British Columbia, Washington and Oregon computed from the seismicity is at least a factor of 10 lower than from plate models and from other convergence estimates, and primarily aseismic slip is suggested. The fault motions as a function of time computed from the seismicity records have also been plotted and compared to the longterm average rates. The plots permit estimates of the minimum present accumulated elastic strain, and show if there are any temporal relations among earthquake displacements on different fault zones. htroduc tion A basic understanding of the origin and nature of earthquakes in a region and detailed evaluation of the associated seismic risk requires development of valid tectonic models. Tectonic

2 60 R. D. Hyndman and D. H. Weichert models can be tested with earthquake data, first, through the correlation between the pattern of hypocentres and particular faults, fault zones and plate boundaries that can be mapped and studied. Secondly, the fault motion parameters and other characteristics of the earthquake records can be compared to the fault orientations and directions of motion from the tectonic model. Finally, the magnitude of fault displacements or average rates of motion estimated from the earthquake record can be compared to those from the model. The latter comparison is the subject of this article. The fault displacements associated with earthquakes may be eshated through the concept of seismic moment (e.g. Brune 1968). Here, we present refinements to the method of estimating average fault slip rates from the historical seismicity and then apply the method to the plate boundaries of western North America, especially those around the Juan de Fuca plate. The seismicity data are for a period of less than 100 yr while the plate tectonic models are derived primarily from data with a time resolution of the order of lo6 yr. Thus, general agreement between rates of motion from the two types of data will suggest that our plate tectonic models for the present are essentially correct and that the available earthquake data are representative of much longer time periods. Finally we compute the fault motions as a function of time from the historical earthquake records and compare them with the estimated PUGET SOUND UAN DE FUCA CA LlFORNlA I or fault zones are: (1) Dellwood-Wilson, (2) Revere-Dellwood, (3) Sovanco, (4) Nootka, (5) Blanco, (6) Gorda, (7) Mendocino, (8) Sandspit, (9) Beaufort.

3 Fault motion from seismicity 61 average rates. The present deficit in motion compared to the long-term average is an indicator of the elastic strain available for release in earthquakes. The plots of fault motion with time can also show temporal relations among earthquake displacements on different fault zones. For earthquake data and plate tectonic models to give the same rates of fault motion, a number of general conditions should be satisfied. (1) The plate tectonic models derived mainly from marine magnetic data on seafloor spreading rates that have a time resolution of about 0.5 Ma and from the orientations of transform faults, must be valid for the recent period of the seismicity data; i.e. there must have been no very recent changes in plate motions and the motion must be steady. (2) The available historical seismicity data must be representative of that for the much longer period of the data used to obtain the plate models; i.e. the seismicity for a particular fault zone must be statistically stationary over times of several Ma, or at least the seismicity record must be representative of the long-term average. This condition may not be met in some areas of the world where cycles of earthquake activity over periods of hundreds of years have been suggested based on long historical records (Lee, Wu & Jacobsen 1976; Ambraseys 1970; Bolt & Miller 1971). (3) The quality of the earthquake data set (i.e. completeness of detection, accuracy of magnitude estimation and epicentral accuracy) must be adequate for quantitative analysis. (4) The parameters relating earthquake data to fault displacements or regional strain (i.e. moment-magnitude relation, maximum magnitude, fault width, rigidity) must be adequately known for all of the areas. If the parameters are poorly known but are the same for all of the faults, the ratio of motion on different faults can still be estimated from the seismicity. The rate of motion on one fault can then be determined from the rate and the seismicity of another fault of similar type and tectonic environment. (5) All of the relative plate motions must occur through earthquake displacements; i.e. there must be no aseismic motion. It is important to emphasize that the slip rates estimated through the seismic moment include only the motion associated with earthquakes. Creep motion is evident on parts of several continental fault systems (e.g. Savage & Burford 1971; Walcott 1978). However, the data of Davis & Brune (1971) suggest that for the majority of transform faults around the globe, slip is primarily seismic. Plate tectonic slip rates The present plate tectonic regime of the west coast of North America involves relative motion of three main lithospheric plates, the large Pacific and America plates and the intervening Juan de Fuca plate (Fjg. 1) (e.g. Atwater 1970; Tobin & Sykes 1968). The Juan de Fuca plate has recently been shown to be made up of two parts, a small northern segment called the Explorer plate and the main Juan de Fuca plate to the south (Riddihough 1977; Hyndman, Riddihough & Herzer 1979; Keen & Hyndman 1979; Riddihough, Currie & Hyndman 1980). There also is evidence that the southernmost part of the Juan de Fuca plate is moving independently (called the Gorda South plate by Riddhough 1980). The Queen Charlotte transform fault system lies along the edge of the continental shelf from southern Alaska to the southern end of the Queen Charlotte Islands. It is the boundary between the Pacific and America plates. The part of this fault zone lying to the north of the Queen Charlotte Islands (called the Chicagof-Baranof fault zone by Von Heune, Shor & Wageman 1979) is oriented parallel to the present relative motion vector from global models, between the Pacific and America plates (Minster & Jordan 1978; Chase 1980). The part of the fault zone off the Queen Charlotte Islands (see Chase & Tiffin 1972) differs in strike by about 20" from the estimated Pacific-America motion vector. There may be an uncertainty

4 62 R. D. Hyndman and D. H. Weichert of 10" in this estimate but the global models all seem to require a small component of convergence. Earthquake mechanism solutions (e.g. Wickens & Hodgson 1967) and microseismicity (Hyndman & Ellis 198 I), however, suggest primarily strike-slip motion on a vertical fault zone just seaward of the coast. Additional motion may occur on one or more inland faults on, or east of, the Queen Charlotte Islands and there may be a component of underthrusting beneath the Islands. However, only very recently has the accuracy of epicentres become sufficient to determine if individual events are on the main offshore fault or on inland faults such as the Sandspit. Therefore, we have estimated the total motion from the seismicity of the whole region as well as making a rough estimate of the motion on the inland faults. Plate models indicate right-lateral relative motion of the whole Queen Charlotte fault system of about 55 mm 6' (see review in Riddihough 1977). To the south, the Juan de Fuca ridge system is modelled as a series of spreading centres (Tuzo Wilson, Dellwood, Explorer, Juan de Fuca and Gorda), offset by transform fault segments (Dellwood-Wilson, Revere-Dellwood, Sovanco, Blanco and Mendocino) (Fig. 1). The oceanic lithosphere between the edge of the continent and the Dellwood-Wilson and Revere-Dellwood transform faults and Dellwood and Tuzo Wilson spreading centres (i.e. 'Dellwood/Winona Block') appears to be moving very slowly relative to the America plate (see Riddihough et al. 1980; Davis & Riddihough 1982). Thus, the fault slip and ridge spreading rates along this boundaxy should be close to the Pacific-America rate of 55 mm a-'. There may be a small amount of motion between the Dellwood/Winona Block and the main Explorer plate to the south-west (Davis & Riddihough 1982). The Explorer ridge and Sovanco transform fault rates of motion are given by the Pacific- Explorer plates relative motion estimated from the magnetic anomaly pattern to be 42 mm 6' (Riddhough 1977; Riddhough et al. 1980). The left-lateral Nootka transform fault separates the Explorer plate from the main Juan de Fuca plate (Hyndman et al. 1979). The fault has had a complex history but its present rate of motion is estimated to be between 25 and 35 mm a-' (Hyndman et al. 1979; Riddihough 1977). The Juan de Fuca ridge and Blanco transform fault separate the Pacific plate from the main Juan de Fuca plate. The rate of relative motion across the boundary decreases from about 60 mm a-' at the north end of the ridge to about 56 mm a? in the south (Riddihough 1977, 1980). The spreading rate across the northern Gorda ridge is similar but the rate across the southern portion may be only 24 mm a-'. There is about 24 mm 6' across the Mendocino transform fault and another 32 mm 6' on a subparallel Gorda fault just to the north (Riddihough 1980) so that the combined rate is about 56 mm a-'. Along the continental margin, estimated rates of convergence with the North America plate are less than 10 mm a-' for the Dellwood/Winona Block (Davis & Riddihough 1982), about 5-15 mm a-l for the Explorer plate (north of the Nootka fault zone) and mm 6' decreasing to the south, for the Juan de Fuca plate (Riddihough 1977) (see also Atwater 1970; Silver 1971; Chase, Tiffin & Murray 1975; Riddihough & Hyndman 1976). Oblique convergence is predicted along a portion of the continental margin north of the Nootka fault zone so the orthogonal component of convergence is less. For the Gorda South plate (Riddihough 1980) the motion may be parallel to the margin at a rate of about 32 mm 6'. In our study we have considered only the Puget Sound, southern Georgia Strait area where the seismicity is greatest. We also have computed the average rates of motion on the southern part of the San Andreas fault system and in the Gulf of California from the seismicity for comparison with the above zones, In both of these latter areas, rates of motion and seismicity have previously been related using slightly different techniques (e.g. Reichle, Sharman & Brune 1976; Ander-

5 Fault motion from seismicity 63 son 1979; Brune 1968). Like the Queen Charlotte fault zone, both areas mark the Pacific- America plate boundary. The San Andreas system is very complex because motion occurs on many strands across a broad zone. In the northern portion of the system the seismicity may not have been stationary or steady in time over the period for which earthquake data are available and fault creep occurs in some parts, but in the southern portion the seismicity does appear to have been stationary and no creep is observed (Anderson 1979). We have assumed in the latter region that the total motion on all the identified land faults equals the relative plate motion at a rate of about 56 mm a-', although some motion may occur on offshore faults and deformation in the adjacent Basin and Range probably is important. The Gulf of California zone is made up of an enechelon series of long transform faults offset by short spreading segments (e.g. Larson 1972). The rate from plate models is about 58 mm a-' (Minster & Jordan 1978; Chase 1980) although some motion again may occur on offshore faults. All of the estimated rates of motion from plate models are given in Table 1. Other plate convergence estimates In addition to estimates from plate tectonic models, estimates of Juan de Fuca-America convergence are available from repeated geodetic measurements and from estimates of sediment deformation along the margin. Savage, Lisowski & Prescott (198 1) reported geodetic measurements of strain across southern Puget Sound for the interval They find at N71 E compression of microstrain yr-'. Their array roughly corresponds to the zone of high seismicity and extends about 100 km in the direction of compression so the total shortening rate is about 13 mm a-'. In south-central Washington over a distance of 60km they find compression at a rate of 0.04It 0.01 microstrain yr-' at N54"E. Table 1. Fault zone data. Fault zone 1 Queen Charlotte 2 Sandspit 3 Dellwood area faults 4 Sovanco 5 Nootka 6 Blanco 7 Mendocino and Corda South' 8 N. Vancouver Is. 9 Puget Sound 10 S. San Andreas 11 Gulf of calif. Plate boundary Pacific- America Pacific- America (subsidiary) Pacific -Dellwood Block Pacific -Explorer Explorer-Juan de Fuca Pacific-Juan de Fuca Pacific-Juan de Fuca Explorer -Juan de Fuca Juan de Fuca- America Pacific- America Pacific- America Lengthldepth (km) 850 X X X X X 3 350x4 280 X X x X x4 Mx 8.5 I.o I I.2 Mo (X 10") o Plate model 55? ? Rates (mm yr) Seismicity * * Note different relation for convergence zone. See text.

6 64 R. D. Hyndman and D. H. Weichert If this deformation is assumed to be associated with the seismicity zone that extends over a width of about 300 km from central Washington to the coast (see Weichert & Hyndman 1981) excluding the high seismicity hget Sound area, the shortening rate is very approximately 12 mm 6'. Under this assumption, and assuming that the rate is continuous and does not represent elastic strain buildup the total compression is the order of 25 mm a-' in a roughly ENE direction across Washington. An additional measure of part of the convergence between the Juan de Fuca plate and North America is the deformation of deep sea sediments along the continental margin. The estimates have a large uncertainty and range from 7 to 27 mm a-l (Silver 1972; von Heune & Kulm 193; Barnard 1978). These rates probably refer to the rate of underthrusting right at the margin, and hence should be added to the continental compression discussed above to give the total plate convergence rate. The different data are very approximate and are from very different time intervals, but it is significant that the sum is similar to the approximately 40 mm a-l convergence from plate models.?he region oi northern Vancouver Island has high seismicity but the activity probably only indirectly reflects a plate boundary. Slawson & Savage (1979) have estimated horizontal motion on the Beaufort Range fault (Fig. 1) associated with the 1946, M, = 7.3 event of over 1 m by re-triangulation surveys. However, other large events do not appear to be on this fault and the origin of the stress that generates the events is not clear (Rogers 1976, 1979). The stress may be associated with the Nootka transform fault which cuts the oceanic lithosphere that descends beneath this region and to the different margin convergence rates to the north and south, or it may arise from the obliqueness of the convergence (e.g. Rogers 1979). There is some evidence that strain associated with the Nootka fault may be expressed by continental shelf structures such as the Apollo structure (Yorath 1980). The earthquakes appear to be in the overlying continental lithosphere (see Rogers & Hasegawa 1978) and the Beaufort fault is orthogonal to the Nootka transform fault so some form of complex stress coupling is required between the oceanic and continental lithospheres. There are no other direct estimates of deformation except for the re-surveying mentioned above, but the Nootka fault zone motion and margin convergence rates range from about 15 to 46 mm a-l so earthquake deformation could be up to these rates. Some of the northerly events of the region may be associated with the northern edge of the Explorer plate (see Riddlhough et az. 1980; Davis & Riddihough 1982). Earthquake data We have estimated fault slip rates from the observed seismicity for each major segment of the boundaries of the Juan de Fuca plate system and the adjacent Queen Charlotte fault zone. The minimum size of area or length of fault that can be treated separately depends on the accuracy of the epicentres and on the number of events in the data sets. The area must be much larger than the epicentral uncertainty so that the majority of the events that were located in the area actually occurred in it, and there must be enough events to provide an adequate statistical sample of the seismicity in the area. The fault zones or areas of Table 1 and Fig. 3 have been chosen as having adequate independent data. Note that the areas are much wider than the boundaries themselves to allow for inaccuracies in event locations. Several areas have also been grouped to study the effect of a larger number of events in a data set. The southern San Andreas system and the Gulf of California have also been included for comparison with the northern transform fault zones. The earthquake data for the northern plate boundaries were taken from the Canadian Earth Physics Branch earthquake data file. Data for the Blanco and Mendocino transform

7 Fault motion from seismicity 65 faults are from the US. Geological Survey NEIS file. The San Andreas data are from Anderson (1979) and the Gulf of California data from Reickle et al. (1976). The data in the Canadian file are described by Milne et al. (1978). The magnitudes used are generally local ML or equivalent except for the few largest events for which only surface Wave magnitude M, is available. For a few earthquakes only body wave magnitude mb was available. These were converted to equivalent ML as described below. Magnitude uncertainties are the order of 0.25 unit for most of the events that define the recurrence relations. The uncertainty in epicentres is as much as 100 km and commonly 50 km for events prior to 1951 but is about 20km for most recent events. Estimates of the magnitudes for complete detection as a function of time based mainly on a study by C. C. Rogers (1981, private communication), are given in Table 2. For the offshore areas they are based on seismograph types and distribution, for the land areas, felt-report data is also considered. For the Mendocino-Corda fault zones Berkeley ML magnitudes from the NEIS file were used along with M,, generally Pasadena magnitudes, for some of the larger and older events. For the few earthquakes for which only body wave magnitudes were available, mb was converted to equivalent M,. For the Blanco fault zone only mb was available for most events since These were converted to equivalent MLmagnitudes.M,magnitudes were used for the few older and larger events. The estimates of the magnitudes for complete detection as a function of time are similar to those in Milne et al. (1978) except that for the Blanco zone the minimum magnitude from the beginning of 1964, is taken as 5.0 rather than 4.0 From 1963 there was routine reporting with mb magnitudes of events in the area. The southern San Andreas fault system data set of Anderson (1979) usesmlmagnitudes. He provides estimates of detectability as a function of time. In the Gulf of California data st of Reichle et al. (1976), mbmagnitudes have been converted to equivalent M,, except for the few larger events for whichm,values were available. To convert mb magnitudes to equivalent M, (or M,) we have employed an empirical relation based on the events for which both magnitudes are available. Fig. 2 shows a compilation of data for the oceanic transform faults of our study area, from the Earth Physics Branch file and from the NEIS file, including M, as well as ML magnitudes. Also shown is the q, :M, relation of Reichle et al. (1976) that provides a good fit and that we have used for conversion. We note that the mb :ML data alone which are mainly for events of magnitude less than 5 could equally well be fitted by a constant difference, the mb being about 0.4 unit higher. The relation of Reichle et al. is consistent with the data of Marshall & Basham (1972) but gives ML estimates much higher than the mb :M, relation recommended by the IASPEI Committee on Magnitude (Bath 1968) or that given by Richter (1958) and lower than relations from some other local studies (e.g. Gibowicz 1972). The choice of a particular 'Table 2.Estimated magnitudes for complete detection as a function of time. 8 Queen Charlotte and Sandspit Dellwood Sovanco Nootka Blanco Mendocino N. Vancouver Is. hget Sound 9 S. San Andreas 10 Gulf of California ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

8 66 R. D. Hyndman and D. H. Weichert Can. Seis. Service EPB File I * *,'/ Q.7.. / 3 I/ / / / / / / / / / / / 6- NEIS File...O *P., I I 1 I I I I I Figure 2. A comparison of the mb and ML/M, magnitude estimates for the offshore fault zones from the Earth physics Branch and NEIS data files. The open circles are for M,, the solid dots for ML. The linear relation is from Reichle et QZ. (1976). relation will have a significant effect on the results only for the Blanco fault zone and for the Gulf of California where only mb magnitudes are available for most events. There appears to be a systematic difference between the M, and ML magnitudes at small magnitudes. However, they are in general agreement at the larger magnitudes, and the contribution of the M,magnitudes to the recurrences generally is small so the difference should not affect the moment estimates significantly. The majority of the empirical moment-magnitude relations have been obtained using California ML magnitudes. The Canadian ML are computed using the same procedures but it is still important to ensure that the CanadianMLare equivalent. There are very few offshore events for which there are both Canadian and Berkeley,ML estimates. However, the similarity of the two relations with mb (Fig. 2) gives us confidence that the CanadianMLestimates are equivalent to those from California. We have assumed that all of the observed offshore seismicity occurs on the transform faults and that the spreading ridges are aseismic. Little seismicity and a limitation of the events to small magnitudes is a characteristic of most ridges with moderate to fast spreading

9 Fault motion from seismicity 67 rates around the world. The Juan de Fuca and Explorer ridges both appear to be largely aseismic. There is some seismicity in the area of the Dellwood spreading centre (e.g. Riddihough et al. 1980; Hyndman & Rogers 1981) and on the Gorda ridge but most is probably associated with the adjacent transform faults. Fault motion and seismic moment The average slip u on a discrete fault during an earthquake is proportional to the seismic moment Mo, and the slip rate is proportional to the moment rate &fo MO u=- PA and s=lla where p is the rigidity and A is the fault area (Brune 1968). The equation is directly applicable to transform fault strike-slip boundaries, and is probably applicable to the main thrust fault zone of convergent boundaries where the slip is measured downdip of the fault zone (e.g. Davis & Brune 1971). In the case of a convergent (or divergent) zone where there is regional strain, Anderson (1979) and Molnar (1979), following the statistical relation of Kostrov (1974) (also Chen & Molnar 1977) have shown that the convergence rate s' is given by CMO $'=- 2pA' MI3 where A'= Wx L is the cross-sectional area of the convergence zone in the plane perpendicular to the convergence direction. C depends on the orientation of the faulting with respect to the regional motion. Molnar (1979) assumed 45" faults so that C = 1.O. Anderson (1979), however, estimatedcempirically to be 0.75 using the data of Chen & Molnar (1977). We have used C= 0.75 for the Puget Sound area. The fault zone lengths L for most of our areas are quite well defined but the fault widths W (i.e. the vertical extent of the seismogenic layer for vertical faults) must be estimated. For the oceanic transform faults, including the Gulf of California, which cut young and thus thin and hot lithosphere, we have taken W = 3 km for the shorter faults, i.e. about 150 km long, and W= 4 km for the longer faults, i.e. about 300 km long. The minimum W of 3 km is chosen from the probable depth of hydrothermal cooling of the crust near a spreading centre. It is also possible that the maximum W is determined by oceanic events being limited to the crust, perhaps by serpentinization of the mantle along the fault zones. The thickness of overlying sediment on young crust may also be important to the thermal regime and thus the thickness of the seismogenic layer. The lithosphere cools away from spreading ridges so the thickness of the seismogenic layer should increase with age (see Burr & Solomon 1978). On the Juan de Fuca ridge system microearthquake studies have shown events from just below the seafloor to a depth of about 4km (Hyndman & Rogers 1981). Since significant earthquakes probably cannot be supported by the fractured high porosity uppermost crust we have taken a minimum fault width of 3 km. It may be that the maximum depth increases with magnitude but we have no data to support this possibility. Similar or slightly larger values of fault width were estimated by Brune (1968) for the Chain, Romanche and St pads transform faults, although he suggested smaller values for some other faults. Reichle et at. (1976) estimated 3 km for fault width in the Gulf of California. Burr & Solomon (1978) estimated W indirectly, generally to be 1-2 km for a variety of oceanic transform faults.

10 89 at Pennsylvania State University on September 18, 2016 Downloaded from Figure 3. Seismicity of the Juan de Fuca plate region showing the earthquake areas associated with each boundary. The data compilation is by G. C. Rogers and includes all events from available data fiies. In the Queen Charlotte fault zone, at least one side of the fault appears to be cold thick continental lithosphere, so the fault width should be considerably greater. Near the midpoint of the Queen Charlotte fault, Hyndman & Ellis (1981) observed a maximum depth for microearthquakes of about 25 km. High seismic velocity basement is at a depth of about 3 km on the seaward side of the fault and no very shallow events were observed, so we have taken a fault width of 22 km. We have used the same value for the Sandspit and nearby faults although W may be slightly greater there since the continental lithosphere further inland probably is colder. We have taken a somewhat smaller fault width of 15 km for the southern portion of the San Andreas'fault system (e.g. Thatcher, Hileman & Hanks 1975; Anderson 1979), and 30 km for central Vancouver Island (e.g. Rogers & Hasegawa 1978).

11 FmEt motion from seismicity 69 cor the convergent margin several different assumed fault widths follow from different assumptions as to the earthquake and fault distributions. The faulting can be assumed to be uniformly distributed to a depth of 60 km, the maximum observed depth of earthquakes, or to lie over a depth extent of some 10 km within the decending oceanic lithosphere. Using the data of Crosson (1981) G. C. Rogers (1981,private communication) has shown that most of the seismic moment is in the deeper probably Benioff-Wadati events and we have taken W = 10 km. However, Rogers prefers to ascribe the deep events to phase changes following McGarr (1977) so our relations between slip rate and seismic moment may not be appropriate. No continental margin thrust earthquakes have been identified in tkls region. The rigidity p for crustal rocks is about 3.3 x 10" N m-' (e.g. Brune 1968; Thatcher et al. 1975) although it may be higher, about 7.0 x 10" Nm-' for the mantle (e.g. Molnar 1979). If our assumed fault widths are correct, most of the earthquakes are in the oceanic or continental crust and we have taken 3.3 x 10". In the margin convergence zone we assume that the deep events occur in the crust rather than in the mantle of the decending oceanic lithosphere. Integral moment and maximum magnitude An estimate for the total seismic moment and thus fault slip rate over a period of time may be obtained from the sum of the estimated moments for the observed events during that period (e.g. Brune 1968; Wyss & Brune 1968; Davies & Brune 1971; Reichle et d. 1976). However, the small number of the larger events leads to a large statistical error in an average mom'ent rate estimate. The uncertainty in the magnitudes of the few largest events also leads to a significant uncertainty in the rate. More accurate estimates should be available from stable magnitude-recurrence relations. The total seismic moment per unit time is obtained by integrating the moment contributions over magnitude M in the magnitude-recurrence relation up to some maximum magnitude M,. Smith (1976) suggested this approach to estimate a regional maximum magnitude from geologically determined fault displacement. Molnar (1979) and Anderson (1979) use a similar approach to estimate earthquake recurrence intervals from plate tectonic and geological data. Similar techniques have been used for some time for stabilizmg seismic risk estimates through integration over IeLurrence relations (Cornell 1968; Anderson & Trifunac 1978; Weichert & Milne 1979; Basham, Weichert & Berry 1979). This approach requires that the recurrence relation be a valid representation of the observed seismicity, and that both a maximum magnitude and the nature of the recurrence as the maximum is approached, can be estimated. The main moment contributions come from the largest magnitudes so the form of the recurrence relation near the maximum magnitude is important. Smith (1976) integrates over magnitude and assumes a log-linear cumulative magnitude recurrence relation, but effectively truncates the magnitude density, at the maximum magnitude M, since he does not include a Dirac-delta function at M, in the density function. Anderson (1979) integrates over log-moment and tiuncates the log-moment density at some maximum log-moment. Molnar (1979) integrates over moment and explicitly truncates the cumulative moment distribution at the maximum moment, since he included a Dirac-delta function. We feel that such a spike in the density function at the maximum magnitude is not physically reasonable, and secondly consider use of the magnitude rather than moment function to be preferable (see below), so we truncate the magnitude density recurrence function. The truncated exponential distribution of Cornell & Vanmarcke (1969) that Berrill & Davis (1980) showed follows from the principle of maximum entropy is identical to the truncated density function. In addition to the above two simple truncation forms, a more gradual cut-off is suggested by physical considerations. Epicentre resolution and other practical problems generally

12 70 prevent us from considering individual faults, so we must consider the effect of having an ensemble of faults each with a different maximum magnitude (e.g. Utsu 197 I). However, we estimate that a cut-off more gradual than the density truncation, that is consistent with our data is unllkely to introduce an error of more than about 25 per cent in moment rate. Since the currently catalogued earthquake parameter is magnitude rather than moment, we prefer to integrate moment contributions over magnitude rather than over moment density. If the moment-magnitude relation were considered to be deterministic, truncation of magnitude density at M, would be equivalent to truncation at the corresponding maximum moment. However, this relation shows a considerable scatter, typically a factor of about 2, so there is not a simple one-to-one relation between moment truncation and magnitude truncation. This stochastic relationship will introduce an offset in the final moment sum rate in addition to the statistical uncertainty. This problem will be discussed later. It is convenient to write the density function as: n (M) = (Y exp (-W) R. D. Hyndman and D. H. Weichert M G M, =O M> M,. The (Y and 0 are used to distinguish the exponential coefficients from the decimal logarithm coefficients a and b, as in log n (M) = a - bm. Note that (Y is the density recurrence coefficient. It must be divided by 0 to obtain the cumulative recurrence coefficient. The moment-magnitude relation is still assumed to be deterministic with the moment Mo being given by the relation of the form Mo=Yexp6M or logmo=c+dm where, as discussed below, c is of the order of 9.O and d the order of 1.5 in SI units. From physical considerations d - b > 0 otherwise one obtains infinite moment contributions from the smallest magnitude events. All of our data also satisfy this inequality since b is always less than 1. Alternatives have been discussed in Molnar (1979). The total moment rate for truncation of the incremental or density recurrence function is then given by: For convenience in computation this may be written:. exp [2.303 (d- b)mx] Mo = (d- b) - where a and b are the commonly computed cumulative recurrence coefficients, and d and c are the moment-magnitude coefficients defined above. For comparison, the moment rate for truncation of the cumulative recurrence function is 6 exp [(A - nio =p PWX w. The latter is seen to be larger by a factor of 6/p (or d/b) which is of the order of 2. In contrast, more gradual truncation will give somewhat smaller moment rates. We have used the density truncation for the computation of the moment rates and average slip rates given in Tables 1 and 3. The maximum magnitude M, earthquake for each fault or zone can be estimated in two ways. The first is from the observed seismicity. If there are enough events in the recurrence

13 Fault motion from seismicity 71 relation near the maximum magnitude, the truncation may be apparent in the data. For a long fault zone with a large maximum magnitude such as the Queen Charlotte, there are too few events near the maximum magnitude to define a statistically significant truncation..however, if a number of shorter fault zones with a smaller but similar maximum magnitude are combined, a statistically significant truncation is observed. For a Combination of the Wilson-Dellwood, Revere-Dellwood, Sovanco and Nootka transform faults, the maximum magnitude appears to be about 6.9 with an uncertainty of about 0.2 units (Fig. 4). For the combination of the Gulf of California faults and for the Blanco and Mendocino faults which are somewhat longer the maximum magnitude is seen to be about 7.2 (Fig. 6). One event occurring in 1922 is given in the data file to be of magnitude 7.3 in the Mendocino area. Recent relocations (Gawthrop 1978; Hanks 1979) suggest that the event may have occurred in the continental crust rather than on the Mendocino fault, and we have excluded this event. The effect of using a slightly larger M, for the Blanco and Mendocino faults compared to the northern offshore faults approximately balances the effect of using a larger W for the former. The second way in which the maximum magnitude may be estimated is from the maximum fault area for the faults within the zone and empirical relations between fault areas and magnitude or moment (Utsu & Seki 1954; Tsuboi 1956; Bath & Duda 1964; Press 1967 as in Thatcher & Hanks 1973; Kanamori & Anderson 1975; Burr & Solomon 1978; Acharya 1979). The relation log S = OM, where S is in km2 is representative of these studies although there is a considerable uncertainty. This relation and a fault width (depth extent) of 3km gives a maximum magnitude of about 6.7 for the approximately 150km long I Northern Offshore M Figure 4. The cumulative recurrence relation for the northern offshore (Dellwood-Wilson, Revere- Dellwood, Sovanco and Nootka) transform faults illustrating the truncation at the maximum magnitude. The axes are cumulative rate per annum and magnitude M. The error bars assume a Poisson distribution. The solid line gives the maximum likelihood fit for M, = 6 9. The dashed line is a linear extrapolation to the larger magnitudes.

14 72 R. D. Hyndman and D. H. Weichert Sovanco and Nootka transform faults and slightly less for the Dellwood area faults. A fault width of 4km and 1:ngth of about 300 km gives a maximum magnitude of about 7.1 for the longer Blanco, Mendocino and Gulf of California transform faults. However, there is a break in the Blanco transform (e.g. Johnson & Jones 1978) that may limit the maximum area and thus the magnitude to a smaller value. Similar unknown breaks or offsets may limit the maximum area for other of the transforms. There is thus an uncertainty of at least 0.2 in these estimated maximum magnitudes from this approach. The estimated values are given in Table 1. We note that the estimates of fault areas are used twice in our analysis, first for estimation of maximum magnitude and secondly for computing fault slip from moment. The result is that an incorrect estimate of fault area has only a small effect on the final calculated slip rate, since the errors approximately cancel. Moment-magnitude relations The seismic moments of only a very few events are available from wave spectra analyses so that moment must be estimated from empirical relations with event magnitude. Kanamori & Anderson (1975) have shown for intermediate size earthquakes that seismic moment Mo and surface wave magnitude M, are theoretically related by log Mo = c + dm,, where d is approximately 1.5. Since M, has been defined'to be a continuation of ML to larger magnitudes (e.g. Richter 1958), Mo should be similarly related to ML at least at moderate magnitudes. Empirical studies (e.g. Wyss & Brune 1968; Hanks & Wyss 1972), have shown that this relation is a good approximation for ML and M,. The scatter of points from the log-linear relation for a study of a single area is generally a factor of 2 with a maximum of 5 in Mo. Fig. 5 shows a summary of the relations from various authors. The majority of the relations are from events with ML magnitudes between 3 and 6 and are for the San Andreas fault system of California. The relations for other tectonic environments such as South African mine events (Spottiswoode & McCarr 1975) and shallow subduction zone earthquakes (Masuda & Takagi 1978; Molnar & Wyss 1972) are very similar. However, Davies & Brune (1971) have suggested that dip-slip or thrust earthquakes are less efficient generators of surface waves so that these events the relation may give values of Mo that are a factor of 2 too low. We take logmo = M (SI units) as the best single empirical relation over all magnitudes. It coincides with the relation of Thatcher & Hanks (1973) are intermediate magnitudes. Most of relations are within a factor of 2 in Mo of this relation. We recognize, however, that there may be a difference between the relation for land events and that for our offshore events. Above about magnitude 7.5 and particularly above 8.0 the M, scale begins to saturate so that the estimated moments from the above relation will be too low (e.g. Chinnery & North 1975; Kanamori 1978). The problem is not serious in our analysis, because the events in the data all have magnitudes of 8.0 or less and, because there are few very large events in our earthquake data sets, the recurrence relations are largely defined by events of magnitude less than 7. The larger events estimated from the recurrence are thus equivalent to M, (Kanamori 1978; Chinnery & North 1975) and do not suffer from saturation. Saturation is important in the method of direct summation of individual event moments (e.g. Brune 1968). The next point concerns the asymmetry of the stochastic moment-magnitude relation. The average log-moment leads to an average moment, and hence to an average displacement. that is greater than just the anti-log; by approximately the factor exp (s2/2), where s2 is the variance of the relation. This factor is exact if the log-moment is normally distributed (e.g. Cameron 1960). For an rms scatter of 0.3 in log Mo (0.69 in In Mo or a factor of 2 inmo), stochasticity results in an increase of 27 per cent in the displacement of slip rate estimates.

15 Fault motion from seismicity 73 Magnitude Figure 5. A compilation of empirical seismic moment-magnitude relations. The solid lines are for earthquakes from south-western United States, the thin dashed lines are for other areas. The thick dotted line is taken as representative log M, = M (SI units). The references are: Wyss & Brune (1968); Aki (1969); Douglas & Ryall (1972); Thatcher & Hanks (1973); Johnson & McEvilly (1974);Chinnery & North (1975); Hanks, Hileman & Thatcher (1975); Spottiswoode & McCarr (1975); Bakun & Lindh (1977); Masuda & Takagi (1978). The SI units are Newton metres (1 N m = lo' dyne cm). An rms scatter of 0.48 in log Mo (1.1 in In Mo or a factor of 3 in Mo) requires an increase of 83 per cent and for larger scatter the effect quickly becomes very large. In seismic risk calculations a similar asymmetry is now well known and is often included in calculations (e.g. McGuire 1976). We have increased the moment estimates by 27 per cent (corresponding to the above factor of 2 in Mo) and recognize that this is a significant source of uncertainty. Recurrence relations Magnitude-recurrence relations have been computed for all of the plate boundary segments of Table 1 using the technique of Weichert (1980). The technique is an extension of the maximum likelihood estimation of Aki (1965) to incorporate different minimum magnitudes for complete detection for different time periods. At large magnitudes there has been complete detection for long time periods (e.g. from 1860 or 1899). Use of these longer times minimizes statistical uncertainties. At small magnitudes there may have been complete detection only since the expansion of local seismograph networks (e.g. since 1950 or 1960) but the higher event rates produce acceptable statistical uncertainty. Following Page (1968) the computation of the incremental recurrence relation includes truncation at a maximum magnitude M, consistent with our treatment of the maximum magnitude discussed above.

16 74 R. D. Hyndman and D. H. Weichert The recurrence parameters are given in Table 3. For several areas, the recurrence parameters have been computed with various values ofm, to see the effect of taking different maximum magnitudes (e.g. Table 3). The oceanic transform fault areas also have been grouped together and an average M, assumed to provide more stable estimates of recurrence slope b. No systematic variation in b was observed among the different faults with crustal age or fault length. This slope was then imposed on the individual data sets. The cumulative recurrence plots with 67 per cent Poissonian confidence limits are shown in Fig. 6, along with the maximum likellhood relations for particular maximum magnitudes. Slip rates from seismicity Table 1 presents the slip or convergence rates computed from the seismicity by integration of the magnitude-recurrence relations. We estimate the uncertainty in the seismic slip to be about a factor of 2 for most of the fault zones from the main sources of error: the I I (<I J I I I I Magnitude Figure 6. Cumulative recurrence plots for each of the seismicity regions. The error bounds are 67 per cent confidence limits assuming a Poissonian distribution. The maximum likelihood recurrence lines with estimated maximum magnitudes M, are also shown. The solid lines are for b fixed at the overall offshore region value, the dashed lines are for b free in each data set. Where no dashed line is given the b values are nearly identical.

17 b lor Fault motion from seismicity 75 N. Vancouver Island I I I J Figure 6 - continued incompleteness and inaccuracies in the earthquake data set; statistical uncertainty in the recurrence relations; the maximum magnitude and the form of the truncation; the empirical magnitude-moment relation and its stochasticity ; fault width (depth extent); and the rigidity. The accuracy of the relative rates among the fault zones should be somewhat better. The estimates are only for the slip associated with the seismicity; aseismic slip or creep is not estimated. The Sandspit zone slip rate is only of order of magnitude accuracy because of uncertainties in the earthquake data set and in the maximum magnitude. The Nootka fault zone estimate also has lower accuracy than the estimates for the other transform faults because of uncertainties in the data set. The uncertainties in the estimates of seismic slip for the - northern Vancouver Island and Puget Sound zones are undoubtedly larger than a factor of 2 because of the complex and uncertain tectonic regimes and because the seismicity data are a composite of events occurring on a number of faults. In the northern Vancouver Island zone the moment rate and thus slip rate is very sensitive to the estimated maximum magnitude because of the small recurrence slope. The seismic motion estimate for the Puget Sound zone probably refers to north-south compression (see below) rather than to the main east-west component of convergent relative plate motion and underthrusting which must be occurring aseismically. Seismic moment and displacement with time Plots of seismic moment and fault slip or displacement with time can provide three types of information. First, they can indicate whether there is major elastic strain available for release as earthquake displacements on each fault zone. Cumulative individual event moments are Compared with the long-term averages obtained either through integrating over the recurrence

18 76 R. D. Hyndman and D. H. Weichert Table 3. Recurrence relations and moment rate with different values of M, for the various regions. Fault zone Cummul. a density b M, GI) x 10. M, (con.*) x 10 1 Queen Charlotte M, = 8.3 M,=@ 2 Sandspit M, == 3 Dellwood M, = 6.8 b free b restrained 4 Sovanco M, = 6.9 b free b restrained 5 Nootka M, = 6.9 b free b restrained 6 Blanco M, = 7.2 b free b restrained 7 Mendocino M, = 7.2 b free b restrained 8 N. Vancouver Is. M, = 7.3 M, = Puget sound M, == M, = S. San Andreas M,=Q M, = Gulf of CaIjf. M, = 7.2 b free b restrained OO oo *Corrected +27 per cent for effect of stochasticity. See text. Preferred values underlined o t relations, from the plate tectonic models or onshore from geological or surveying measurements. There is potential for large events if the moment release falls significantly below the long-term average. Secondly, in areas where the return time of the maximum magnitude events is estimated to be less than the duration of the seismicity record, an indication of the maximum magnitude can be obtained from the agreement between the moment rate from the individual events and that from the recurrence integration. Finally, such plots can show temporal relations among the earthquake fault displacements on the different parts of a plate boundary or on the different boundaries of a single plate. Davis & Brune (1971) found significant variations in global seismic moment release with time as did Reichle et al. (1976) for the Gulf of California. Fig. 7 shows the cumulative seismic moment using the empirical moment-magnitude relation given above arid the slip or displacement computed through the moment from individual events as a function of time for nine regions. To avoid the problem of lack of

19 Fault motion from seismicity lo ISLAND I PUGET Figure 7. Seismic moment as a function of time for the seismicity regions. The straight lines represent the moment rate from integrating the recurrence relations with different assumed maximum magnitudes. The choice of the origin at 1900 is arbitrary. Only the slopes are significant. The long-term rate lines for the preferred M, are also drawn through the peaks of the cumulative individual moment plots to illustrate the minimum magnitude of elastic deformation available at present for earthquake release. The shaded uncertainty bounds are from M, of * 0.2. The dotted lines give the plate tectonic slip rates. complete detection for the smaller magnitudes we have plotted only the moment of discrete events with magnitudes above the limit for complete detection. This limit varies with time. For the smaller magnitudes we have used the average moment or slip rate obtained from integrating the recurrence relation up to the magnitude for complete detection. Most of the moment or slip is in the larger discrete events. The moments have been multiplied by the 1.27 stochasticity correction (see above). Applying the moment-magnitude empirical relation to mdiviaua events entalls a considerably larger uncertainty (at least a faccur of 2 and perhaps a factor of 4) than applying it to recurrence relations with their inherent averaging. As an example, the moment estimates for the 1946 Vancouver Island event by Rogers & Hasegawa (1978) range from 80 x 1018N m which is close to the empirical moment-magnitude estimate, to 250 X 10l8 Nm. The straight lines in Fig. 7 are long-term averages obtained by integrating the magnitude-recurrence relations. The long-term rate lines are also drawn dashed through

20 78 R. D. Hyndman and D. H. Weichert the peaks of the cumulative individual moment plots to show the minimum magnitude of the elastic deformation available at present for earthquake release. The dotted lines give the rates from the plate tectonic models. The plots of cumulative seismic moment release with time (Fig. 7) for the offshore transform faults are relatively smooth reflecting the short return time of their maximum magnitude events. The Dellwood area exhibits a relatively steady rate, contrasted to the Blanco and Mendocino areas which have rather systematic variations in rate over time. There is no large present moment release deficit from the long-term maximum for the Dellwood, Sovanco and Blanco areas. There is an estimated moment release deficit of about 10 x 1018N m on the Nootka fault. The equivalent single event magnitude is about 6.5. On the Mendocino fault zone there is a deficit of about 20 x 1018Nm which has an equivalent single event magnitude of between 6.5 and 7.0. The conclusion of no significant present elastic strain for the Dellwood-Sovanco area is similar to that from strain energy release plots by Milne et al. (1978). The plots of moment release with time for the offshore areas show good agreement with the average rates from the recurrence relations with the assumed maximum magnitudes (straight lines on figures). The Queen Charlotte fault seismic moment plot is dominated by the magnitude 8 event of The estimated moment release deficit from the long-term maximum is about 250 x 1018Nm on this fault. The equivalent single event magnitude is about 7.5. The Sandspit fault data are difficult to evaluate because of the strong possibility that one or more of the older larger events occurring on this fault have been mislocated to the Queen Charlotte fault zone and vice versa. If the data set contains no serious mislocations, the plot suggests that the 80yr average is similar to the long-term rate. The northern Vancouver Island seismic moment release comes mainly from the several large events as expected from the small recurrence slope. The estimated present seismic moment deficit is about 20x 1018Nm which has an equivalent single event magnitude of However, since the seismicity of this area does not directly reflect relative plate motion, there is less assurance than for plate boundary faults that the short available seismicity record represents a continuing steady long-term process. The plot suggests that the 80yr average is greater than the long-term rate unless M, is greater than the 7.5 assumed. In the Puget Sound - southern Georgia Strait area, the plot is dominated by the 1949 magnitude 7.1 event. The maximum magnitude of 7.2 estimated gives a long-term rate much lower than the 80yr average. A maximum of 7.5 gives more reasonable agreement between the long-term average and the individual event plot. However, it is difficult to conceive of large enough fault areas in this region to give such large events. The estimated present moment release deficit is about lox 1018Nm which has an equivalent single event magnitude of about 6.5. The moment release deficit estimate is larger if the maximum magnitude and thus the long-term average moment release is larger. There are no really convincing correlations or time progressions among the patterns of moment release for adjacent oceanic faults. The most obvious correlation for the whole margin is for the 1949 magnitude 8.0 Queen Charlotte fault, the 1946 magnitude 7.3 Vancouver Island event and the 1949 magnitude 7.1 Puget Sound event. These events, all occurring within a 3 yr period, are the largest in the data files for each area, and all have estimated return periods of over 100 yr. Conclusions The agreement between the estimates of the transform fault zone slip rates from plate tectonic models to those we have estimated from the seismicity, is remarkably good, an average difference of 15 per cent. This is well within the estimated factor of 2 uncertainty

21 Fault motion from seismicity 79 (Table 1). There may be a small systematic bias for the northern offshore faults, the seismicity slip rates being on the average 25 per cent lower. Increasing M, by 0.2 for these faults gives excellent agreement. We have not included the northern and central portion of the San Andreas fault system where the seismicity does not appear to be stationary and there is fault creep. The results suggest that our plate tectonic models are essentially correct for the transform fault zones and that the motion on all of the transforms studied is primarily seismic. The results also suggest that the earthquake data are statistically stationary and are representative of much longer time periods. Our estimates of average slip rates from the seismicity of the southern San Andreas system and of the Gulf of California are close to those obtained from the summation of the moments of discrete events (Brune 1968; Reichle et al. 1976). However, our values should be more accurate estimates of long-term slip rates. There is a gross discrepancy along the convergent margin of Oregon, Washington and southern British Columbia. The rate of convergence from plate models and other estimates of deformation (see above) is about 40 mm yr-' while the rate from the seismicity is less than 3mmyr-', even in the highest seismicity portion of this margin around Puget Sound (Weichert &Hyndman 1981). The seismicity is much less to the south. Earthquake mechanism solutions (e.g. Rogers 1979, 1981) suggest that the discrepancy is even larger since most shallow events appear to reflect N-S compression nearly orthogonal to the convergence direction and the deeper events suggest down-dip tension. The deep events may be associated with phase changes (e.g. McGarr 1977; G. C. Rogers 1981, private communication). Keen & Hyndman (1979), Weichert & Hyndman (1981) and Rogers (1981) have suggested that the N-S compression and associated seismicity arise from the Juan de Fuca plate decending into the re-entrant corner in the continental margin. Thus, if the tectonic model of plate convergence is accepted, most of the convergence and underthrusting must be occurring by aseismic creep, or there has been a large elastic strain accumulation over the period of the seismicity data. The overall average rate of motion of about 14mma-' we estimate for the northern Vancouver Island area is roughly half that on the underlying Nootka transform fault and of convergence across the margin. It thus seems reasonable for the earthquake motion to be a reflection of stress coupling across the margin convergence zone or between the subducted oceanic and overlying continental lithospheres. The plots of cumulative seismic moment release with time (Fig. 7) permit minimum estimates of the present elastic strain available for release in earthquakes on eachfault zone. The method has a large uncertainty mainly because of the large uncertainty in applying the empirical moment-magnitude relation to individual events. For the offshore transform faults the plots suggest little strain accumulation on the Dellwood and Sovanco faults, and a moderate amount on the Nootka, Blanco and Mendocino faults. The margin fault zone plots all suggest only relatively small strain accumulations. However, the M, for Puget Sound and northern Vancouver Island areas is not significantly constrained by plate tectonic motion rates. Larger maximum magnitudes will result in larger estimates of accumulated elastic strain available for release in earthquakes. Acknowledgments We wish to acknowledge the many fruitful discussions on this subject with our colleagues at the Pacific Geoscience Centre, W. G. Milne, G. C. Rogers and R. P. Riddihough, and constructive comments by M. J. Berry and P. W. Basham. Contribution of the Earth Physics Branch 979.

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