Article

A proposed rupture scenario for the 1925 MW 6.5 Santa Barbara, California, earthquake

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Abstract

The 29 June 1925 Santa Barbara earthquake is among the largest 20th century earthquakes in southern California. The earthquake also predated the installation of strong motion and local monitoring instruments in southern California; some instrumental data are, however, available from long-period instruments at regional and teleseismic distances. The current catalog moment magnitude is MW 6.8. Initial intensity magnitudes (MI) estimated from original Coast and Geodetic Survey intensity assignments were lower (MI 6.3). In this study we assign modified Mercalli intensity values at 239 locations, including 144 specific locations within the city of Santa Barbara for which detailed damage information is available. Comparing the reinterpreted intensities with Did You Feel it? intensities for recent events in California, we estimate MW = 6.5, with a plausible range of 6.3–6.6. We further consider reported instrumental amplitudes to estimate an instrumental moment magnitude of MW = 6.6 ± 0.5. Our preferred final estimate is MW 6.5. Based on available constraints including aftershock locations inferred from data recorded on portable instruments, we propose that the earthquake nucleated east of the city of Santa Barbara, closer to the coast than previously estimated, and ruptured unilaterally ~30 km to the west, possibly along the south-dipping Mesa-Rincon Creek, and the More Ranch fault systems. Contrary to suggestions made in earlier studies (e.g. Willis, 1925a), relatively high intensities ~50 km west of Santa Barbara can then be explained by directivity rather than involvement of the Santa Ynez fault. Finally, we discuss the possibility that the earthquake was triggered by the larger MW = 6.6 Clarkston, Montana earthquake the previous day or induced by oil production in the Summerland oil field.

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... Several small-to-moderate size earthquakes have occurred in the Santa Barbara channel over the last century. The epicenter of the 29 June 1925 (M w ≈6.5) earthquake is thought to have been located just east of Santa Barbara (e.g., Willis, 1925;Hough and Martin, 2018). Although instrumental records were not available to determine fault plane solutions, it is considered to have ruptured the Mesa-Rincon Creek thrust faults in the northern most Santa Barbara channel (Hough and Martin, 2018) or portions of the North Channel, Pitas Point, or Red Mountain faults (e.g., Archuleta et al., 1997;Kamerling et al., 2003;Nicholson, Sorlien, Kamerling, and Hopps, 2017). ...
... The epicenter of the 29 June 1925 (M w ≈6.5) earthquake is thought to have been located just east of Santa Barbara (e.g., Willis, 1925;Hough and Martin, 2018). Although instrumental records were not available to determine fault plane solutions, it is considered to have ruptured the Mesa-Rincon Creek thrust faults in the northern most Santa Barbara channel (Hough and Martin, 2018) or portions of the North Channel, Pitas Point, or Red Mountain faults (e.g., Archuleta et al., 1997;Kamerling et al., 2003;Nicholson, Sorlien, Kamerling, and Hopps, 2017). The 13 August 1978 M w 5.6 earthquake occurred southwest of Santa Barbara on an oblique reverse fault with aftershocks indicating a north-dipping, northwest-striking fault plane (Lee et al., 1978;Corbett and Johnson, 1982). ...
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... The results of this study illustrate that the application of the BW97 method, or other statistical approaches (e.g., Gasperini et al., 1999) requires careful consideration of original data, especially with azimuthally unevenly distributed (Hough and Martin, 2018) and or sparse data sets (Meltzner and Wald, 1999;Szeliga et al., 2010). An optimal (L2 norm) fit to the intensity data may yield a location that is inconsistent with key observations, as we suggest was the case for E-24. ...
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... The application of statistical approaches (e.g., Bakun and Wentworth, 1997;Gasperini et al., 1999) is also limited by the lack of intensity prediction equations (IPEs) unique to the region. Furthermore, the sensitivity of these approaches to data such as ours with 30 or fewer observations and with poor azimuthal distribution is well known (Meltzner and Wald, 1999;Szeliga et al., 2010;Hough and Martin, 2018). Instead, we select provisional epicentral locations near the locations where the highest intensities were documented for both the 31 January (2.0°N, 102.8°E; dark blue star, Fig. 4a) and the 7 February (1.9°N, 103.8°E; black star, Fig. 4b) earthquakes. ...
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... Our reinterpreted intensity distribution provides a missing puzzle piece for the larger picture of California's maximum historically observed earthquake intensities. Other big pieces are already in place: intensities have been revisited in recent years for the large events of Fort Tejon in 1857, Hayward in 1868, Owens Valley in 1872, Laguna Salada in 1892, San Francisco in 1906, and Santa Barbara in 1925, as well as many moderate historic events (Meltzner and Wald, 1999;Martindale and Evans, 2002;Hough and Elliot, 2004;Bundock, 2008a, 2008b;Hough and Hutton, 2008;Hough and Martin, 2018). These reinterpretations, combined with DYFI data for more recent events, will eventually produce a uniform shaking dataset with which earthquake hazard map performance can be assessed. ...
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Following the Northridge, California, earthquake of 17 January 1994, the Humboldt Earthquake Education Center (HEEC) conducted a telephone survey of approximately 6000 adults from within the felt region to study the earthquake's effects on individual households. We tabulate human responses to the earthquake and observations of the earthquake's effects on inanimate objects from the HEEC survey as a function of independently assigned U.S. Geological Survey Modified Mercalli (USGS MM) intensity for the same communities. Human responses and subjective judgments about the severity of shaking, when averaged over a large number of samples, are useful discriminants of the levels of strong ground motion up to those associated with USGS MM intensity VII, notwithstanding that individual human responses and subjective judgments are notoriously unreliable. A threshold of strong ground motion corresponds to USGS MM intensity of about VII, above which over 40% of respondents described the earthquake as "violent" and most people reported difficulty standing, furniture displaced, and some damage to their homes. Even at intensities VIII and IX, however, relatively few people (about 15%) described their reaction as "panic" and only about 12% reported major damage to their homes. The HEEC phone-survey data show that, in communities of low to moderate shaking, USGS MM intensities estimated from a single postal questionnaire are quite robust. At USGS MM intensity of V and below, 88% of USGS MM intensities determined from postal questionnaires are within one intensity unit of intensities determined from the more numerous HEEC telephone survey data for the same community. We introduce the concept of a community decimal intensity scale (CDI) based on telephone-survey data and calibrated to agree on average with the USGS MM intensities. The CDIs are more regularly distributed than the USGS MM intensities and show much less scatter when plotted as a function of epicentral distance. CDIs show promise as a tool for comparing regional attenuation, for delineating variations in shaking strength within areas mapped as a single MM zone, and for rapid preliminary intensity estimates utilizing electronic media.
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The 21 October 1868 Hayward, California, earthquake is among the best-characterized historical earthquakes in California. In contrast to many other moderate-to-large historical events, the causative fault is clearly established. Published magnitude estimates have been fairly consistent, ranging from 6.8 to 7.2, with 95% confidence limits including values as low as 6.5. The magnitude is of particular importance for assessment of seismic hazard associated with the Hayward fault and, more generally, to develop appropriate magnitude–rupture length scaling relations for partially creeping faults. The recent reevaluation of archival accounts by Boatwright and Bundock (2008), together with the growing volume of well-calibrated intensity data from the U.S. Geological Survey “Did You Feel It?” (DYFI) system, provide an opportunity to revisit and refine the magnitude estimate. In this study, we estimate the magnitude using two different methods that use DYFI data as calibration. Both approaches yield preferred magnitude estimates of 6.3–6.6, assuming an average stress drop. A consideration of data limitations associated with settlement patterns increases the range to 6.3–6.7, with a preferred estimate of 6.5. Although magnitude estimates for historical earthquakes are inevitably uncertain, we conclude that, at a minimum, a lower-magnitude estimate represents a credible alternative interpretation of available data. We further discuss implications of our results for probabilistic seismic-hazard assessment from partially creeping faults.
Article
The “revised magnitudes”, M, converted from Gutenberg's unified magnitude, m, and listed by Richter (1958) and Duda (1965) are systematically higher than the magnitudes listed by Gutenberg and Richter (1954) in Seismicity of the Earth. This difference is examined on the basis of Gutenberg and Richter's unpublished original worksheets for Seismicity of the Earth. It is concluded that (1) the magnitudes of most shallow “class a” earthquakes in Seismicity of the Earth are essentially equivalent to the 20-sec surface-wave magnitude, M_s; (2) the revised magnitudes, M, of most great shallow (less than 40 km) earthquakes listed in Richter (1958) (also used in Duda, 1965) heavily emphasize body-wave magnitudes, m_b, and are given by M = 1/4 M_s + 3/4 (1.59 m_b - 3.97). For earthquakes at depths of 40 to 60 km, M is given by M = (1.59 m_b − 3.97). M and M_s are thus distinct and should not be confused. Because of the saturation of the surface-wave magnitude scale at M_s ≃ 8.0, use of empirical moment versus magnitude relations for estimating the seismic moment results in large errors. Use of the fault area, S, is suggested for estimating the moment.
Article
Over 480 earthquakes from central and eastern North America having instrumental mb magnitudes and maximum Modified Mercalli intensities (I0) were examined using exploratory data analysis techniques and modeled with robust estimation methods (91 of those earthquakes also have felt area data). A previously undocumented distinct offset of magnitudes is observed between Modified Mercalli intensities VI and VII in both the central and eastern North America data set and a separate western North American catalog of earthquakes. The offset is most probably a characteristic of the Modified Mercalli scale and brings into question the often assumed linear relationship between magnitude and intensity. (In particular, linear regression models could not accurately estimate magnitudes for larger, I0 = VII or VIII, events.) Instead, robust estimates of center and spread for individual intensity interval distributions are recommended. In studies where conversion of intensity to magnitude for groups of earthquakes is required (e.g., studies involving the Gutenberg-Richter recurrence relation), the underlying distribution of magnitudes (or its approximation) for each intensity should be used. Linear regression models using I0 and/or felt area (and several transformations were tested. The robust linear regression models m b = 2.48 + 0.0769 log 2 ( F A ) and m b = 2.16 + 0.0219 l 0 2 + 0.0596 log 2 ( F A ) (where FA is felt area in square kilometers) proved to be the most accurate magnitude estimation models for central and eastern North America earthquakes. A comparison of regional felt area models indicates that regional differences in attenuation of seismic waves may exist between central and eastern North America that becomes apparent only for events of sufficient magnitude. Those differences appear as larger felt areas for earthquakes of central North America as compared to earthquakes of eastern North America.
Article
The 5.1 M_L Santa Barbara earthquake of 13 August 1978 occurred at 22h54m 52.8s UTC. The epicenter was located 3 km southeast of Santa Barbara at 34° 23.9′N latitude and 119°40.9′W longitude with a focal depth of 12.7 km. The main shock was followed between 13 August and 30 September by 373 aftershocks that were located with the Caltech-USGS array. The aftershock zone extended 12 km WNW from the epicenter and was 6 km wide in the N-S direction, and it had a very clear temporal development. During the first 20 min of activity, all the aftershocks were located in a cluster 7 km WNW of the main shock epicenter. During the next 24 hr, the aftershock zone grew to 11 km in the WNW direction and 4 km in the N-S direction. During succeeding weeks, the zone extended to 12 by 6 km. This temporal-spatial development relative to the main shock epicenter may indicate that the initial rupture propagated 7 km unilaterally to the WNW, and the initial rupture plane may have been considerably smaller than the eventual aftershock zone. This smaller area suggests that the stress drop may have been significantly greater than that derived from the final aftershock zone. In cross section, the aftershock hypocenters outline a nearly horizontal plane (dipping 15° or less) at 13 km depth. The main shock focal mechanism indicates NNE-SSW compression and vertical extension. The preferred fault plane strikes N80°W and dips 26°NNE, indicating north-over-south thrusting with a component of left-lateral movement. Focal mechanisms for 40 aftershocks also indicate compression in the general N-S direction. For most of these events, the north-dipping nodal plane dips between 7° and 45°, with most dipping 25° or more, which is significantly steeper than the plane delineated by the hypocenters themselves. These observations are consistent with a tectonic model in which much of the slip during the Santa Barbara earthquake occurred on a nearly horizontal plane. The after shocks then might represent movement on a complex series of imbricate thrust faults that flatten into the plane of primary slip. Hence, the Santa Barbara earthquake may be taken as evidence for mid-crustal horizontal shearing in the western Transverse Ranges.
Article
Seismicity rates have increased sharply since 2009 in the central and eastern United States, with especially high rates of activity in the state of Oklahoma. Growing evidence indicates that many of these events are induced, primarily by injection of wastewater in deep disposal wells. The upsurge in activity has raised two questions: What is the background rate of tectonic earthquakes in Oklahoma? How much has the rate varied throughout historical and early instrumental times? In this article, we show that (1) seismicity rates since 2009 surpass previously observed rates throughout the twentieth century; (2) several lines of evidence suggest that most of the significant earthquakes in Oklahoma during the twentieth century were likely induced by oil production activities, as they exhibit statistically significant temporal and spatial correspondence with disposal wells, and intensity measurements for the 1952 El Reno earthquake and possibly the 1956 Tulsa County earthquake follow the pattern observed in other induced earthquakes; and (3) there is evidence for a low level of tectonic seismicity in southeastern Oklahoma associated with the Ouachita structural belt. The 22 October 1882 Choctaw Nation earthquake, for which we estimate M-w 4.8, occurred in this zone.
Article
In this study, I consider the ground motions generated by 11 moderate (Mw 4.0–5.6) earthquakes in the central and eastern United States that are thought or suspected to be induced by fluid injection. Using spatially rich intensity data from the U.S. Geological Survey “Did You Feel It?” system, I show the distance decay of intensities for all events is consistent with that observed for tectonic earthquakes in the region, but for all of the events, intensities are lower than the values predicted from an intensity prediction equation that successfully characterizes intensities for regional tectonic events. I introduce an effective intensity magnitude MIE, defined as the magnitude that on average would generate a given intensity distribution. For all 11 events, MIE is lower than the event magnitude by 0.4–1.3 magnitude units, with an average difference of 0.82 units. This suggests stress drops of injection‐induced earthquakes are systematically lower than tectonic earthquakes by an estimated factor of 2–10. However, relatively limited data suggest intensities for epicentral distances less than 10 km are more commensurate with expectations for the event magnitude, which can be reasonably explained by the shallow focal depth of the events. The results suggest damage from injection‐induced earthquakes will be especially concentrated in the immediate epicentral region.
Article
The Santa Barbara earthquake of 13 August 1978, provides an opportunity to perform a broadband investigation of body waves for a well-recorded, moderate size (M_L = 5.1) event. The long- and short-period teleseismic body waves are modeled in the time domain to construct a source time function which is consistent in the period range of 1 to 20 sec. The long-period records indicate an overall duration of 6 sec while the short-period records reveal the fine-scale character of the slip history consisting of two sharp pulses separated by about 1 sec. The source mechanism determined from this analysis is a moderately dipping (30°NE) thrust with significant left-lateral slip. The moment was determined to be 1.1 × 10^(25) dyne-cm. The earthquake was also reasonably well recorded on accelerographs in the near-field. The modeling of the strong motion displacements was a two step procedure: (1) the displacements were modeled alone, and (2) in an attempt to achieve consistency between the local and far-field time functions, the qualitative features of the teleseismic short-period time function were used to predict the displacements. If the two sources in the short-period time function are allowed to have different mechanisms, the displacements can be modeled quite well. This suggests that the overall faulting process was rough, and the multiple source character suggested at high frequencies is due to high-stress drop asperities. The two sources are modeled as asperities separated by 1.5 km; the first source has a mechanism consistent with the teleseismic solution while the second source is more steeply dipping. The total moment determined from the strong motion data is 3.5 × 10^(24) dyne-cm or one-third the long-period moment. This is consistent with other recent studies which suggest that the high-frequency strong ground motion is controlled by the distribution of asperities even though the sum of their moments may be small compared to the overall moment. This study also shows the importance of teleseismic short periods in predicting the local displacements.
Article
The central matter of this investigation is the commonly held belief that eastern North America (ENA) earthquakes are felt to much greater distances, at all levels of intensity, than their western U.S. (WUS) counterparts of the same source strength. By comparing the areas enclosed by Modified Mercalli intensities I to III (felt), IV, V, I and VII for ENA and WUS earthquakes at the same source strength, it is found that this proposition is mostly false at damaging levels of ground motion. -from Authors
Article
Seismological observations local to the 1927 earthquake suggest an epicenter for it near 34.6°N, 120.9°W. These observations include S-P times for the immediate aftershocks recorded at four stations in southern California; S-P times reported for the main shock at Berkeley and Lick Observatory by P. Byerly; and a time-decaying (1934 to 1969) zone of seismicity centered offshore of Point Arguello, herein identified as the aftershock zone of the 1927 earthquake. This location is approximately 40 km southwest of the teleseismic location for the 1927 earthquake recently offered by W. Gawthrop, although a location intermediate to the one proposed here and the one by Gawthrop would satisfy uncertainties associated with both locations. Even so, the location farther offshore is suggested by the near absence of strong shaking in the adjacent coastal region, which seemingly precludes a near-coastal location for an earthquake of this magnitude. Furthermore, unpublished teleseismic first-motion data of G. Stewart and analysis of the distortion of a geodetic quadrilateral by J. Savage and W. Prescott argue against a faulting mechanism for the 1927 earthquake that involves predominantly right-lateral slip on a near-coastal and northwesterly striking fault of the San Andreas type.
Article
The Lompoc earthquake of 4 November 1927 (Ms 7.0) was one of the largest offshore events in California, and the associated tsunami was recorded in Hawaii as well as on the California coast. From tsunami travel times, the source location was estimated to be well offshore at about 34.2°N, 120.75°W, consistent with recent seismic waveform analysis. Waveform modelling of the tsunami also supports an outer continental shelf location. The seismic moment is estimated to be 3×10²⁶dyne.cm, corresponding to a moment magnitude of 7.0. The tsunami computation reproduced the large tsunami in Hawaii, indicating that the observed large tsunami was due to bathymetry effects, particularly near Hilo Bay. The tsunami magnitude of 7.6 obtained from the Hawalian recordings by Abe thus appears to be an overestimate. -from Authors
Article
INTRODUCTION The most common information available immediately following a damaging earthquake is its magnitude and the epicentral location. However, it is also desirable to know the extent of the felt area, and, more important, the range of shaking experienced and the areal extent of strongest shaking. For most of the United States, there is insufficient seismic strong-motion station coverage to portray quickly and accurately the extent of strong shaking. Seismic intensity has been traditionally used worldwide as a method for quantifying the shaking pattern and the extent of damage for earthquakes. Though developed prior to the advent of today's modern seismometric instrumentation, seismic intensity scales nonetheless provide a useful framework to describe, in a simplified fashion, the complexity of ground motions and the extent and nature of the damage. A limitation of traditional intensity mapping has been the long time required to generate a detailed seismic intensity map, typically weeks...
Article
A modest but noteworthy Mw 5.9 earthquake occurred in the Bay of Bengal beneath the central Bengal fan at 21:51 Indian Standard Time (16:21 UTC) on 21 May 2014. Centered over 300 km from the eastern coastline of India, it caused modest damage by virtue of its location and magnitude. However, shaking was very widely felt in parts of eastern India where earthquakes are uncommon. Media outlets reported as many as four fatalities. Light damage was reported from a number of towns on coastal deltaic sediments, including collapsed walls and damage to pukka and thatched dwellings. Shaking was felt well inland into east‐central India and was perceptible in multistoried buildings as far as Chennai, Delhi, and Jaipur at distances of ≈1600 km. The purpose of this report is to make available the newly collected intensity dataset and to present preliminary analysis of this noteworthy recent earthquake. We further show that the intensity distribution provides evidence for a high-stress drop source. These results bear out the observation made two decades ago by Hanks and Johnston (1992, p. 20): “[Our] results suggest that it should be a fairly simple matter to infer a high-stress-drop event from intensity data alone, provided that an instrumental M0 or Mw value is known separately.” Our study illustrates the potential value of carefully determined intensity data for investigations of earthquake source properties, especially when instrumental recordings are sparse. We suggest it may in fact be a more robust way to estimate stress drop than conventional approaches, which require correction of attenuation to estimate pulse width or corner frequency (e.g., Anderson, 1986); the estimate is then cubed to estimate stress drop (Madariaga, 1976). Lastly, we discuss potentially important implications of our results for efforts to characterize probabilistic seismic hazard in the Himalayan region
Article
This paper outlines the re-computation and compilation of the magnitudes now contained in the final ISC-GEM Reference Global Instrumental Earthquake Catalogue (1900-2009). The catalogue is available via the ISC website (www.isc.ac.uk/iscgem/) and lists in a comma separated format the location and magnitude parameters (with corresponding uncertainties) of global large earthquakes. In this work we report on the procedures adopted to obtain the final magnitude composition of the nearly 20,000 earthquakes processed. We have made every effort to use uniform procedures of magnitude determination throughout the entire period of the catalogue. The re-computation of the surface wave MS and short-period body-wave mb values benefitted from new hypocentres (Bondár et al., 2015), previously unavailable amplitude-period data digitized during this project (Di Giacomo et al., 2015), and a more reliable algorithm for magnitude estimation based on a 20% alpha-trimmed median magnitude (Bondár and Storchak, 2011). In particular, for MS until the end of 1970 we have processed an unprecedented amount of data and obtained several thousands of station magnitudes not available before.
Article
[1] Analysis of numerous case histories of earthquake sequences induced by fluid injection at depth reveals that the maximum magnitude appears to be limited according to the total volume of fluid injected. Similarly, the maximum seismic moment seems to have an upper bound proportional to the total volume of injected fluid. Activities involving fluid injection include (1) hydraulic fracturing of shale formations or coal seams to extract gas and oil, (2) disposal of wastewater from these gas and oil activities by injection into deep aquifers, and (3) the development of Enhanced Geothermal Systems by injecting water into hot, low-permeability rock. Of these three operations, wastewater disposal is observed to be associated with the largest earthquakes, with maximum magnitudes sometimes exceeding 5. To estimate the maximum earthquake that could be induced by a given fluid injection project, the rock mass is assumed to be fully saturated, brittle, to respond to injection with a sequence of earthquakes localized to the region weakened by the pore pressure increase of the injection operation, and to have a Gutenberg-Richter magnitude distribution with a b-value of 1. If these assumptions correctly describe the circumstances of the largest earthquake, then the maximum seismic moment is limited to the volume of injected liquid times the modulus of rigidity. Observations from the available case histories of earthquakes induced by fluid injection are consistent with this bound on seismic moment. In view of the uncertainties in this analysis, however, this should not be regarded as an absolute physical limit.
Article
We present a method that uses macroseismic intensity data to assess the location, physical dimensions, and orientation of the source of large historical earthquakes. Intensity data contain a great deal of information that can be used to constrain the essential characteristics of the seismic source. In particular, both the seismological theory and its practice suggest that the orientation of the source of significant earthquakes is reflected in the elongation of the associated damage pattern. A plausible and easily manageable way of describing a seismic source is by representing it as an oriented “rectangle,” the length and width of which are obtained from moment magnitude through empirical relationships. This rectangle is meant to represent either the actual surface projection of the seismogenic fault or, at least, the projection of the portion of the Earth crust where a given seismic source is likely to be located. The systematic application of this method to all the M > 5.5 earthquakes that occurred in the central and southern Apennines (Italy) in the past four centuries returned encouraging results that compare well with existing instrumental, direct geological, and geodynamic evidence. The method is quite stable for different choices of the algorithm parameters and provides elongation directions that in most cases can be shown to be statistically significant. In particular, the resulting pattern of source orientations is rather homogeneous, showing a consistent Appennines-parallel trend that agrees well with the NE-SW extension style of deformation active in the central and southern portions of the Italian peninsula.
Article
At the heart of the conundrum of seismogenesis in the New Madrid Seismic Zone is the apparently substantial discrepancy between low strain rate and high recent seismic moment release. In this study we revisit the magnitudes of the four principal 1811-1812 earthquakes using intensity values determined from individual assessments from four experts. Using these values and the grid search method of Bakun and Wentworth (1997), we estimate magnitudes around 7.0 for all four events, values that are significantly lower than previously published magnitude estimates based on macroseismic intensities. We further show that the strain rate predicted from postglacial rebound is sufficient to produce a sequence with the moment release of one Mmax6.8 every 500 years, a rate that is much lower than previous estimates of late Holocene moment release. However, Mw6.8 is at the low end of the uncertainty range inferred from analysis of intensities for the largest 1811-1812 event. We show that Mw6.8 is also a reasonable value for the largest main shock given a plausible rupture scenario. One can also construct a range of consistent models that permit a somewhat higher Mmax, with a longer average recurrence rate. It is thus possible to reconcile predicted strain and seismic moment release rates with alternative models: one in which 1811-1812 sequences occur every 500 years, with the largest events being Mmax∼6.8, or one in which sequences occur, on average, less frequently, with Mmax of ∼7.0. Both models predict that the late Holocene rate of activity will continue for the next few to 10 thousand years.