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![GLTFM applied to the Mojave section of the San Andreas fault (Pallett Creek record). (a) Hazard rate history plot. The dashed lines indicate how hazard is estimated to accumulate between earthquakes (solid lines). Rotated numbers after earthquake indicate R value. Numbers below earthquake indicate years of residual strain after earthquake, for example, 128 yr after the 1812 earthquake. Best‐fitting GLTFM parameters and paleoseismic record mean, standard deviation (SD), and coefficient of variation (CV) indicated. (b) Estimated interevent time distribution for current quiescent period. Mean (μ), standard deviation (σ), and loglikelihood (LL) indicated for different models. (c) Corresponding 30‐year earthquake forecasts with current 30‐year forecast indicated. The color version of this figure is available only in the electronic edition.]()
![GLTFM applied to the Mojave section of the San Andreas fault (Pallett Creek record) only up to and including the 1812 earthquake. (a) Hazard rate history plot. The dashed lines indicate how hazard is estimated to accumulate between earthquakes (solid lines). Rotated numbers after earthquake indicate R value. Numbers below earthquake indicate residual strain after earthquake. GLTFM estimates 128 yr of residual strain remaining after the 1812 earthquake. (b) Estimated interevent time distribution for the quiescent period after 1812. Mean (μ), standard deviation (σ), and loglikelihood (LL) indicated for different models. (c) Corresponding CDFs. The probability of earthquake occurring within 45 yr is much higher for GLTFM due to the residual strain. The color version of this figure is available only in the electronic edition.]()
![Uncertainties of post‐1812 Pallett Creek forecasts. Histograms show the number of simulations (out of 1000) for a given probability that an earthquake will occur within 45 yr after the 1812 earthquake. (a) Lognormal results. (b) BPT results. (c) Weibull results. (d) GLTFM results. GLTFM shows a broad distribution between 20% and 70% indicating that an earthquake occurring soon is much more likely than for the other models. The color version of this figure is available only in the electronic edition.]()
![Estimating earthquake probabilities. (a) Pallett Creek paleoseismic record of past earthquakes (Scharer et al., 2011, listed in Table S1). (b) Histogram of interevent times (gray bars) and estimated probability distributions for interevent times for exponential, lognormal, and Brownian passage time (BPT) models. The lognormal and BPT models have a coefficient of variation (CV) of 0.54. Also shown is the long‐term fault memory (LTFM) presented in this article. (c) Conditional probability of an earthquake (EQ) in the next 30 yr given the 1857 date of the last earthquake. The color version of this figure is available only in the electronic edition.]()
![Earthquake forecasts after recent Pallett Creek sequence earthquakes. (a) Pallett Creek paleoseismic record with the four most recent earthquakes labeled. (b) Estimated probability density functions (PDFs) for interevent time until the next earthquake after the 1339 earthquake. AICc, empirical mean (μ), and standard deviation (σ) indicated for each model. Vertical dashed line indicates when the next earthquake actually occurred. (c) Cumulative distribution functions (CDFs) for models in panel (b). Probability of earthquake occurring within 169 yr (the actual observed interevent time) is indicated. (d) PDFs after the 1508 earthquake. (e) CDFs after the 1508 earthquake. (f) PDFs after the 1812 earthquake. (g) CDFs after the 1812 earthquake. (h) PDFs after the 1857 earthquake for the current quiescent period. Vertical dashed line indicates the year 2022. (i) Estimated 30 yr earthquake probabilities with the year 2022 indicated. The color version of this figure is available only in the electronic edition.]()
![Comparisons of Weibull and LTFM. (a) Pallett Creek interevent time cumulative hazard plot for Weibull distribution with 1σ uncertainties of the interevent times indicated. (b) Comparison of best‐fitting Weibull distribution and β=2 Weibull distribution to the long‐run LTFM‐LR interevent time distribution. Interevent time mean (μ) and standard deviation (σ) are indicated. (c) Corresponding hazard‐rate functions for PDFs in panel (b). The color version of this figure is available only in the electronic edition.]()
![LTFM uncertainty analysis. (a) Plot of LTFM Pallett Creek negative log‐likelihood values for different N and D combinations. Best‐fitting parameters are indicated by orange X. Gray contours indicate 68% and 95% confidence intervals. Stars indicate parameter combinations used in panel (b). (b) Corresponding 30 yr earthquake forecasts for the parameter combinations. Thick orange line corresponds to the LTFM best‐fitting parameters (orange X in panel a). Thin gray lines correspond to the randomly sampled LTFM parameter combinations. Labeling indicates LTFM parameter combination shown in panel (a). The solid pink line is the best‐fitting BPT forecast and light pink lines are 200 randomly sampled BPT forecasts based on its estimated parameter uncertainty. The color version of this figure is available only in the electronic edition.]()
![LTFM realizations of Pallett Creek record. Possible Markov state and corresponding earthquake probability histories for the Pallett Creek record for the best‐fitting maximum‐likelihood estimation (MLE) parameters. Three different initial starting states (300, 200, and 50) are shown (indicated by the orange, blue, and red lines, respectively). The three curves converge after the first three earthquakes indicating how any residual strain at the start of the record is shortly eliminated. The color version of this figure is available only in the electronic edition.]()
![Layer, earthquake, and recurrence PDFs for the Pallett Creek (PC) site, using both peat accumulation and layer-ordering constraints (thick solid lines) and using only layer-ordering constraints (thin solid lines). See Figure 3 for further explanation of the features of this figure.]()
![The distribution of peat-bearing layer ages at the Pallett Creek (PC) site. Those layers labeled in bold were used to define the peat accumulation rate for each interval as described in our companion article (Hilley and Young, 2008). Those layers lying within each interval spanned by the noted bounding layer ages are assumed to have formed under a constant peat accumulation rate. Note that there is significant variation in the peat accumulation rate over time.]()
![Layer, earthquake, and recurrence PDFs for the Pallett Creek (PC) site, using both peat accumulation and layer-ordering constraints (thick solid lines) and using only layer-ordering constraints (thin solid lines). See Figure 3 for further explanation of the features of this figure.]()
![Layer, earthquake, and recurrence PDFs for the Pallett Creek (PC) site, using both peat accumulation and layer-ordering constraints (thick solid lines) and using only layer-ordering constraints (thin solid lines). See Figure 3 for further explanation of the features of this figure.]()
![Location of the Wrightwood, Pallett Creek, and Pitman Canyon sites in southern California. The heavy line is the San Andreas fault; lighter lines are secondary faults in the region. The Mojave segment has been variously defined but is shown here as the straight segment between the Big Bend and the southern extent of the 1857 rupture (Sieh, 1978b). Metropolitan Los Angeles (hatchured) could experience strong ground motions if the Mojave segment ruptured alone or as part of a larger event.]()
![Peat accumulation plots for Pallett Creek and Wrightwood sites. Peat thicknesses were measured perpendicular to bedding at their thickest point. Measurements were compiled from mapped exposures and reported sample thicknesses. Thicknesses were plotted at the mean dates of their ordering constrained date distributions (dotted lines, Figs. 2, 3). Average peat accumulation rates were estimated where multiple dates define segments by drawing straight lines through the circles. Higher rates (smaller minimum time separation constraints) were used at “growth spurts” where the average rate would otherwise force nearby layer dates into unlikely posterior distributions. For Wrightwood a single rate of 15 yr/cm was applied because the available data do not justify a more detailed model. Pallett Creek peat accumulation resolvably varied with time. Both sites experienced slow accumulation from A.D. 350–600. Event W14 occurred during this slow period and is poorly resolved as a result.]()
![Wrightwood and Pallett Creek event date distributions. Dashed plots are events using ordering-constrained layer date distributions (dotted, in Figs. 2 and 3); solid lines show events from fully constrained layer distributions and peat thickness partitioning at the event horizon. Events W1812, W1857, and P1857 are shown as historic. Dates under the event names are the mean of the ordering-only and fully constrained event distributions, respectively. The heavy underbars indicate previously published two-sigma date ranges from Fumal et al. (1993) and Sieh et al. (1989). The vertical scale varies from event to event to give each distribution the same peak height.]()
![Recurrence intervals for (a) Pallett Creek and (b) Wrightwood. Mean recurrence intervals are shown for the best estimate (solid lines) and order-constrained (dashed lines) event dates from Figure 6.]()
![Nonparametric test for clustering at Pallett Creek and Wrightwood. Event series were chosen at random from the fully constrained pdfs of Figure 6. Horizontal increments are the fraction of the total time from event C or W14 to 1857 taken by each interval ending at the labeled event. One vertical step is taken at each event and plotted as a dotted line. Repeating the sampling 100 times results in apparent increases and decreases in line density, which reflect more or less commonly selected paths. Series that cross the 80% and 95% bounds are too clustered at that level of confidence to have derived from a Poisson distribution. The series culminating at event R would not be unusual (i.e., expected 20%–30% of the time) for a Poisson process. The long step from event R to event T illustrates the importance of the stratigraphic relations around event R to the hypothesis of clustering.]()
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1
Journal Article
Paleoseismic Event Dating and the Conditional Probability of Large Earthquakes on the Southern San Andreas Fault, California
Publisher: Seismological Society of America
Published: 01 October 2002
Bulletin of the Seismological Society of America (2002) 92 (7): 2761–2781.
...Glenn P. Biasi; Ray J. Weldon, II; Thomas E. Fumal; Gordon G. Seitz Abstract We introduce a quantitative approach to paleoearthquake dating and apply it to paleoseismic data from the Wrightwood and Pallett Creek sites on the southern San Andreas fault. We illustrate how stratigraphic ordering...
FIGURES
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Image
GLTFM applied to the Mojave section of the San Andreas fault (Pallett Creek...
in The Generalized Long‐Term Fault Memory Model and Applications to Paleoseismic Records
> Bulletin of the Seismological Society of America
Published: 01 March 2024
Figure 4. GLTFM applied to the Mojave section of the San Andreas fault (Pallett Creek record). (a) Hazard rate history plot. The dashed lines indicate how hazard is estimated to accumulate between earthquakes (solid lines). Rotated numbers after earthquake indicate R value. Numbers below
Image
GLTFM applied to the Mojave section of the San Andreas fault (Pallett Creek...
in The Generalized Long‐Term Fault Memory Model and Applications to Paleoseismic Records
> Bulletin of the Seismological Society of America
Published: 01 March 2024
Figure 8. GLTFM applied to the Mojave section of the San Andreas fault (Pallett Creek record) only up to and including the 1812 earthquake. (a) Hazard rate history plot. The dashed lines indicate how hazard is estimated to accumulate between earthquakes (solid lines). Rotated numbers after
Image
Uncertainties of post‐1812 Pallett Creek forecasts. Histograms show the num...
in The Generalized Long‐Term Fault Memory Model and Applications to Paleoseismic Records
> Bulletin of the Seismological Society of America
Published: 01 March 2024
Figure 9. Uncertainties of post‐1812 Pallett Creek forecasts. Histograms show the number of simulations (out of 1000) for a given probability that an earthquake will occur within 45 yr after the 1812 earthquake. (a) Lognormal results. (b) BPT results. (c) Weibull results. (d) GLTFM results. GLTFM
Image
Estimating earthquake probabilities. (a) Pallett Creek paleoseismic record ...
in A More Realistic Earthquake Probability Model Using Long‐Term Fault Memory
> Bulletin of the Seismological Society of America
Published: 27 December 2022
Figure 1. Estimating earthquake probabilities. (a) Pallett Creek paleoseismic record of past earthquakes ( Scharer et al. , 2011 , listed in Table S1). (b) Histogram of interevent times (gray bars) and estimated probability distributions for interevent times for exponential, lognormal
Image
Earthquake forecasts after recent Pallett Creek sequence earthquakes. (a) P...
in A More Realistic Earthquake Probability Model Using Long‐Term Fault Memory
> Bulletin of the Seismological Society of America
Published: 27 December 2022
Figure 5. Earthquake forecasts after recent Pallett Creek sequence earthquakes. (a) Pallett Creek paleoseismic record with the four most recent earthquakes labeled. (b) Estimated probability density functions (PDFs) for interevent time until the next earthquake after the 1339 earthquake. AICc
Image
Comparisons of Weibull and LTFM. (a) Pallett Creek interevent time cumulati...
in A More Realistic Earthquake Probability Model Using Long‐Term Fault Memory
> Bulletin of the Seismological Society of America
Published: 27 December 2022
Figure 8. Comparisons of Weibull and LTFM. (a) Pallett Creek interevent time cumulative hazard plot for Weibull distribution with 1 σ uncertainties of the interevent times indicated. (b) Comparison of best‐fitting Weibull distribution and β = 2 Weibull distribution to the long‐run
Image
LTFM uncertainty analysis. (a) Plot of LTFM Pallett Creek negative log‐like...
in A More Realistic Earthquake Probability Model Using Long‐Term Fault Memory
> Bulletin of the Seismological Society of America
Published: 27 December 2022
Figure 9. LTFM uncertainty analysis. (a) Plot of LTFM Pallett Creek negative log‐likelihood values for different N and D combinations. Best‐fitting parameters are indicated by orange X. Gray contours indicate 68% and 95% confidence intervals. Stars indicate parameter combinations used
Image
LTFM realizations of Pallett Creek record. Possible Markov state and corres...
in A More Realistic Earthquake Probability Model Using Long‐Term Fault Memory
> Bulletin of the Seismological Society of America
Published: 27 December 2022
Figure 10. LTFM realizations of Pallett Creek record. Possible Markov state and corresponding earthquake probability histories for the Pallett Creek record for the best‐fitting maximum‐likelihood estimation (MLE) parameters. Three different initial starting states (300, 200, and 50) are shown
Image
Layer, earthquake, and recurrence PDF s for the Pallett Creek ( PC ) site,...
in Deducing Paleoearthquake Timing and Recurrence from Paleoseismic Data, Part II: Analysis of Paleoseismic Excavation Data and Earthquake Behavior along the Central and Southern San Andreas Fault
> Bulletin of the Seismological Society of America
Published: 01 February 2008
Figure 7. Layer, earthquake, and recurrence PDF s for the Pallett Creek ( PC ) site, using both peat accumulation and layer-ordering constraints (thick solid lines) and using only layer-ordering constraints (thin solid lines). See Figure 3 for further explanation of the features of this figure.
Image
The distribution of peat-bearing layer ages at the Pallett Creek ( PC ) sit...
in Deducing Paleoearthquake Timing and Recurrence from Paleoseismic Data, Part II: Analysis of Paleoseismic Excavation Data and Earthquake Behavior along the Central and Southern San Andreas Fault
> Bulletin of the Seismological Society of America
Published: 01 February 2008
Figure 6. The distribution of peat-bearing layer ages at the Pallett Creek ( PC ) site. Those layers labeled in bold were used to define the peat accumulation rate for each interval as described in our companion article ( Hilley and Young, 2008 ). Those layers lying within each interval spanned
Image
Layer, earthquake, and recurrence PDF s for the Pallett Creek ( PC ) site,...
in Deducing Paleoearthquake Timing and Recurrence from Paleoseismic Data, Part II: Analysis of Paleoseismic Excavation Data and Earthquake Behavior along the Central and Southern San Andreas Fault
> Bulletin of the Seismological Society of America
Published: 01 February 2008
Figure 7. Layer, earthquake, and recurrence PDF s for the Pallett Creek ( PC ) site, using both peat accumulation and layer-ordering constraints (thick solid lines) and using only layer-ordering constraints (thin solid lines). See Figure 3 for further explanation of the features of this figure.
Image
Layer, earthquake, and recurrence PDF s for the Pallett Creek ( PC ) site,...
in Deducing Paleoearthquake Timing and Recurrence from Paleoseismic Data, Part II: Analysis of Paleoseismic Excavation Data and Earthquake Behavior along the Central and Southern San Andreas Fault
> Bulletin of the Seismological Society of America
Published: 01 February 2008
Figure 7. Layer, earthquake, and recurrence PDF s for the Pallett Creek ( PC ) site, using both peat accumulation and layer-ordering constraints (thick solid lines) and using only layer-ordering constraints (thin solid lines). See Figure 3 for further explanation of the features of this figure.
Image
Location of the Wrightwood, Pallett Creek, and Pitman Canyon sites in south...
in Paleoseismic Event Dating and the Conditional Probability of Large Earthquakes on the Southern San Andreas Fault, California
> Bulletin of the Seismological Society of America
Published: 01 October 2002
Figure 1. Location of the Wrightwood, Pallett Creek, and Pitman Canyon sites in southern California. The heavy line is the San Andreas fault; lighter lines are secondary faults in the region. The Mojave segment has been variously defined but is shown here as the straight segment between the Big
Image
Peat accumulation plots for Pallett Creek and Wrightwood sites. Peat thickn...
in Paleoseismic Event Dating and the Conditional Probability of Large Earthquakes on the Southern San Andreas Fault, California
> Bulletin of the Seismological Society of America
Published: 01 October 2002
Figure 4. Peat accumulation plots for Pallett Creek and Wrightwood sites. Peat thicknesses were measured perpendicular to bedding at their thickest point. Measurements were compiled from mapped exposures and reported sample thicknesses. Thicknesses were plotted at the mean dates of their ordering
Image
Wrightwood and Pallett Creek event date distributions. Dashed plots are eve...
in Paleoseismic Event Dating and the Conditional Probability of Large Earthquakes on the Southern San Andreas Fault, California
> Bulletin of the Seismological Society of America
Published: 01 October 2002
Figure 6. Wrightwood and Pallett Creek event date distributions. Dashed plots are events using ordering-constrained layer date distributions (dotted, in Figs. 2 and 3 ); solid lines show events from fully constrained layer distributions and peat thickness partitioning at the event horizon
Image
Recurrence intervals for (a) Pallett Creek and (b) Wrightwood. Mean recurre...
in Paleoseismic Event Dating and the Conditional Probability of Large Earthquakes on the Southern San Andreas Fault, California
> Bulletin of the Seismological Society of America
Published: 01 October 2002
Figure 7. Recurrence intervals for (a) Pallett Creek and (b) Wrightwood. Mean recurrence intervals are shown for the best estimate (solid lines) and order-constrained (dashed lines) event dates from Figure 6 .
Image
Nonparametric test for clustering at Pallett Creek and Wrightwood. Event se...
in Paleoseismic Event Dating and the Conditional Probability of Large Earthquakes on the Southern San Andreas Fault, California
> Bulletin of the Seismological Society of America
Published: 01 October 2002
Figure 8. Nonparametric test for clustering at Pallett Creek and Wrightwood. Event series were chosen at random from the fully constrained pdfs of Figure 6 . Horizontal increments are the fraction of the total time from event C or W14 to 1857 taken by each interval ending at the labeled event
Journal Article
The San Andreas Fault Paleoseismic Record at Elizabeth Lake: Why are There Fewer Surface‐Rupturing Earthquakes on the Mojave Section?
Publisher: Seismological Society of America
Published: 27 April 2021
Bulletin of the Seismological Society of America (2021) 111 (3): 1590–1613.
... misaligned with the regional plate motion. The Frazier Mountain, Elizabeth Lake, Pallett Creek, Wrightwood, and Pitman Canyon paleoseismic sites are located on this relatively linear surface trace of the San Andreas fault between fault bends. Our paleoseismic investigations at Elizabeth Lake document 4–5...
FIGURES
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Includes: Supplemental Content
Journal Article
Evidence for Large Earthquakes on the San Andreas Fault at the Wrightwood, California, Paleoseismic Site: a.d. 500 to Present
Publisher: Seismological Society of America
Published: 01 October 2002
Bulletin of the Seismological Society of America (2002) 92 (7): 2726–2760.
... chronologies at Pallett Creek and sites to the northwest suggests that approximately the same part of the fault that ruptured in 1857 may also have failed in the early to mid-sixteenth century and several other times during the past 1200 years. Records at Pallett Creek and Pitman Canyon suggest...
FIGURES
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