Electronic Supplement to
A Record of Large Earthquakes during the Past Two Millennia on the Southern Green Valley Fault, California

by James J. Lienkaemper, John N. Baldwin, Robert Turner, Robert R. Sickler, and Johnathan Brown

This supplement contains three sections:

1. Files for Oxcal models of paleoearthquake chronologies referred to in the paper.
2. Scans of the 1998 trench logs of the Lopes Ranch site.
3. Simplified method to estimate relative frequency of variable length ruptures along the Green Valley fault.

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Tables and Figure

Table S1. Recurrence Intervals for Scenario Ruptures

Table S2. Section Rupture Probabilities for the Green Valley Fault>

Figure S1. Location of the largest discontinuities on the Green Valley fault (GVF, red lines): W, Wilson Valley; S, Stone Corral; C, Berryessa connector; A, Alamo stepover. CF, Calaveras fault; SAF, San Andreas fault. Holocene active faults as in Fig. 1. BSF, Bartlett Springs fault; BF, Berryessa fault; HCF, Hunting Creek fault); WV, Wooden Valley; NGVF, SGVF (northern, southern GVF). B) To illustrate how these results could further be used to characterize the frequency and eventually likelihood of future large earthquakes, below we show a set of four scenarios that use all six simplified sources. We indicate the approximate weighting of each scenario by using the rounded result for each multisection rupture from our simple probability model.

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1. Oxcal models for paleoearthquakes of the Green Valley fault

The program Oxcal (Bronk Ramsey, 1995) calibrates radiocarbon data to calendar years and provides estimates of the ages of earthquakes. Lienkaemper and Bronk Ramsey (2009) describe the use of Oxcal for modeling the age of paleoearthquakes sequences.

Oxcal Model Files

Download / View: Mason.oxcal [Plain Text; 2 KB]. Mason Rd site four event Oxcal model.

Download / View: MasonLopesE1.oxcal [Plain Text; 2 KB]. Mason four event model using E1 age from Lopes model.

Download / View: Lopes.oxcal [Plain Text; 1 KB]. Lopes Ranch three event model.

Download / View: LopesMasonCombo.oxcal [Plain Text; 2 KB]. Combined Mason-Lopes six event model, includes ~1200 yr gap.

The Oxcal program is available at: http://c14.arch.ox.ac.uk/oxcal.html

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2. Scanned logs of 1998 Lopes Ranch trench T1

These scanned field logs accompanied an unpublished report (Baldwin and Lienkaemper, 1999) and are provided here primarily to show the locations of all dated radiocarbon samples from the 1998 trenching. Additional information about the stratigraphic section and earthquake sequence is presented in Baldwin et al. (2008)

Download: Lopes 1998 Logs [PDF; 2.7 MB]

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3. Rupture frequency model for Green Valley fault

The following simple method was originally presented by Lienkaemper (2012) to estimate possible variations of rupture frequency for the entire ~130-km-long Green Valley fault (GVF, between discontinuities W and A, Fig. S1A). We estimate rupture frequency primarily on the generic likelihood of any rupture to propagate through medium size (1-4 km) geometric discontinuities in the surface trace of the fault, based on the global historic record for surface rupture continuity (Wesnousky, 2008). Such discontinuities might be described as soft-segment boundaries in that only about half of ruptures tend to terminate at them. Lienkaemper and Brown (2009) initially developed this simple approach to estimate frequencies of variable length ruptures along the ~170-km-long Bartlett Springs fault. We approximate the propagation through each such medium sized step-over or bend as 50% probable, diminishing by an additional 50% for each subsequent discontinuity. Thus for a system with multiple such steps, the shortest ruptures are most likely and the longest ones are the least likely to occur. Wesnousky and Biasi (2011) tested this simple idea by statistical modeling of their historical rupture data set, finding that a 50% termination rate per discontinuity reasonably approximates the behavior of historical ruptures for ~1-4-km discontinuities.

The GVF has three medium-sized step-overs or bends (Fig. S1A) capable of stopping ~50% of ruptures (W, S, C) and a larger one (>5 km) capable of stopping all ruptures (A). The Hunting Creek fault (HCF) also includes a large (~17°) regional bend that likely acts as a fuse between the Bartlett Springs and Green Valley faults, but for simplicity we treat the Wilson Valley step-over (W) as a point of 100% termination for GVF ruptures. Although ~30% of historical rupture terminations occur elsewhere along the fault (i.e., not at geometric discontinuities, Wesnousky, 2008), we suggest that the simplifying assumption of terminating all ruptures at these step-overs (W, S, C, A) does reasonably characterize the magnitude range of most likely ruptures. This simplification allows us to compute the joint probabilities that each of the three weak discontinuities (W, S, C) are breached by a given rupture. To simplify further, we nucleate only at the four discontinuities (W, S, C, A). Using a stick diagram, Figure S1B illustrates the six combinations of the three segments that are allowed to occur with this simple approach. Because globally, unilateral rupture occurs for ~80% of earthquakes, we only allow 20% of GVF events to rupture bilaterally (McGuire et al., 2002). This simple probability model strongly favors single sections (56%; W-S, S-C, C-A) rupturing independently, followed by two section ruptures (28%). Three section, i.e., whole GVF ruptures, are much less likely (17%). This model result is generalized to develop a set of rupture scenarios (Fig. S1B), which are then used weight estimated recurrence times for each particular rupture (segment combination) and for each section as a result of all ruptures occurring on that section (Table S1).

We derive the raw recurrence intervals given Table S1 by calculating the mean slip from the seismic moment and area for each rupture using relations of Wells and Coppersmith (1994) and Hanks and Kanamori (1979) . Slip divided by the assumed long-term slip rate of 6 mm/yr gives the mean recurrence interval. To estimate rupture widths, we estimated the base of seismic zone on the GVF as 13 km for HCF and 14 km for Berryessa (BF) and SGVF sections using the microearthquake locations of Waldhauser and Schaff (2008). We have also estimated that approximately half of the seismic moment rate is relieved by creep in the upper half of the fault, modeling the depth of creep as ~5.5 km on HCF and ~6.5 km on BF and SGVF, using the method of Savage and Lisowski (1993). The raw rupture frequency estimates suggest intervals between single section ruptures of ~90-160 yr, 2-section ruptures at 130-180 yr, 3-sections at 210 yr . However, these raw values do not weight the relative likelihood of ruptures of differing lengths. When the weighting based on the modeled probability of each rupture or source is applied, the recurrence of each changes considerably, with the rare 3-section ruptures only recurring at ~1400-yr intervals.

The recurrence of rupture on any given section (Table S2) is based on the combined recurrence of all rupture lengths. It estimates that each section of the fault has a relatively similar probability of rupture, ranging from 111-198 yr on average. However, note that our 30-yr Poisson probability estimates differ considerably from UCERF2 (Working Group of California Earthquake Probabilities, 2008), partly because UCERF2 estimated probability only for M~6.7 and they had not yet recognized either the internal segment boundaries within the Hunting Creek-Berryessa fault nor the complete length of the SGVF (e.g., they used a 56 km length rather than the 77 km length used here.) Our model suggests that generally shorter Hunting Creek and Berryessa fault ruptures would tend to be much smaller than M6.7, while SGVF ruptures would tend to be M~6.7 or larger. Thus our model estimates the likelihood for large damaging (M~6.7) earthquakes as much higher on the SGVF (14% in 30 yr) than on the NGVF (2-5% in 30 yr). This result is the opposite of the UCERF2, which estimated larger more frequent ruptures on the NGVF (M~7, 8.7% in 30 yr) and on SGVF (M~6.8, 3.4% in 30 yr). All of these probability estimates are Poissonian (i.e., no time dependence assumed).

Most relevant to the discussion of our observed recurrence intervals along the SGVF, is that because of the greater fault complexity in the NGVF, occasionally longer ruptures may occur involving slip on both the NGVF and the SGVF. However, if this simple rupture frequency model is correct, these longer (two or three section) ruptures might happen on the SGVF only every several hundred years (model gives ~650 yr) and could be of significantly larger magnitude (e.g., M6.9-7.0 rather than M~6.7), possibly producing larger stress drop and thus require a much greater loading time to produce the next large SGVF earthquake. Delayed stress recovery might thus explain why the current open interval on the SGVF appears to be so much longer than the average recurrence interval.

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