A proposed triggering/clustering model for the current WGCEP Karen Felzer USGS, Pasadena Seismogram from Peng et al., in press

Terminology Aftershock = Any earthquake triggered by another earthquake, over any time, distance, magnitude difference. Background Seismicity = All non- aftershocks.

Outline Background: Triggering in WGCEP 2002 Justification: Why aftershocks should be given a larger role. The empirical ETES/Aftershock triggering model. Comparison of ETES with the STEP model Preliminary results: ‘Forecasting’ the years Preliminary results: Forecasting aftershock scenarios for The Big One.

Background

Earthquake interaction modeling in WGCEP 2002 Only effects of the1906 and Loma Prieta earthquakes were modeled. The effect of 1906 was modeled on all Bay Area faults using BPT step (Brownian Passage Time) and the Reasenberg et al. (2003) empirical models. The effect of the Loma Prieta earthquake on two neighboring sections of the SAF was modeled using BPT step.

We propose to avoid the large uncertainties in physical models and parameters by using Omori’s Law and other empirical aftershock statistics directly. The aftershock statistics we use have been thoroughly tested against California data. Proposed Change: Replace BPT step with empirical aftershock statistics

WGCEP 2002 modeled the potential earthquake interaction behavior initiated by the 1906 and Loma Prieta Earthquakes only. We propose to forecast the stress triggering effects of all catalog M≥2.5 earthquakes, using an ETES-style model (Ogata 1988, Felzer et al. 2002, Helmstetter et al. 2006). Because the cumulative triggering effects of smaller earthquakes are significant, using all M≥2.5 earthquakes should produce more accurate results. Proposed Change: Model the aftershocks of many more earthquakes

The Bay Area stress shadow WGCEP 2002 was greatly concerned with accurately modeling of the post 1906 (or post-1927!) Bay Area Quiescence. The empirical Bay Area quiescence models employed by WGCEP 2002 can be incorporated into our model by modifying the background seismicity rate.

Justification

Why have such a large aftershock component in the time-variable model? Landers, M 7.3 Big Bear, M 6.4 Hector Mine, M 7.1 Superstition Hills, M 6.7 Northridge, M 6.7 Bakersfield, M 5.8 (1952) Morgan Hill, M 6.2 Cape Mendocino, M 7.1 (1992, aftershock of 1991 Honeydew earthquake) A sample of large California aftershocks:

Detailed aftershock statistics, updated daily, produce significantly better forecasts than steady-state models Helmstetter et al forecast for 23 October, Steady state on right, ETES on left. M≥2 events given by black circles. ETES forecast agrees with earthquakes 11.5 times better than Poissonian.

But daily forecasts aren’t practical for WGCEP! We propose forecasts updated yearly -- less accurate, but better for WGCEP users and still better than steady state. Aftershock modeling also: Allows determination of the full error range on the expected annual number of earthquakes. Allows the building of earthquake sequence scenarios -- e.g. how frequently will the Big One on the SAF trigger an M 7 in the LA basin?

The ETES earthquake and aftershock triggering model: The nuts and bolts

Background seismicity Aftershocks of pre- forecast period M≥ 2.5 earthquakes Basic Model Ingredients We solve for the expected rates of all of the following during the forecast period: Aftershocks of earthquakes occurring during forecast period No physics added!

Basic Procedure The mean, median, and full PDF of expected behavior over a region are obtained by running a large number of Monte Carlo trials in which discrete earthquakes and aftershocks are modeled. The final forecasted probability at points in space is obtained by averaging and smoothing the Monte Carlo catalogs with an inverse power law kernel.

Generation of background earthquakes Background earthquakes are placed randomly according to seismicity rates and magnitude distributions specified in spatial grid cells. Background rates may be taken directly from the time-independent WGCEP forecast or altered to reflect long-term trends.

Generation of Aftershocks 1.The number of aftershocks, N, triggered by an earthquake of magnitude M  10 bM (Reasenberg and Jones (1989); Felzer et al. 2004). 2.Aftershock rate = (k D 10 bM )/(t+c D ) pD (modified Omori Law) where k D, c D, and p D are direct sequence Omori parameters. 3.Aftershock density varies with distance from the mainshock fault plane, r,  r (Felzer & Brodsky 2006). 4.Aftershock magnitudes are chosen randomly from the Gutenberg-Richter distribution. 5.M≥6.5 earthquakes are modeled as planes; smaller earthquakes as point sources

Direct Omori Law parameters fit the decay of direct aftershocks only Propagating the direct aftershocks of the mainshock and all aftershocks makes a full sequence

Benefits of using direct sequence aftershock parameters More accurate modeling of average aftershock sequence behavior, especially over the long term. More accurate modeling of the possible range of aftershock sequence behavior More accurate modeling of large secondary aftershock sequences.

Direct vs. Total Omori law parameters and large secondary sequences If using total rather than direct Omori law parameters (like STEP) when a large aftershock occurs the total sequence for the large aftershock must locally replaces the original sequence. In ETES, total sequences are built by adding the direct sequences of each aftershock => large secondary sequences are modeled automatically. Aftershocks w. large secondary sequence

Additional differences between STEP & ETES STEP uses sequence-specific Omori law parameters when possible. ETES uses generic parameters but self adjusts to the activity level of the total aftershock sequence. The STEP model uses spatially varying Gutenberg- Richter b value; ETES uses a uniform b value. STEP, run in real time, needs to guess at mainshock fault planes; ETES has the luxury of using known fault planes. Otherwise the two models are very similar!

Some Preliminary Results of the ETES Modeling

ETES Forecast trials, Years Monte Carlo trials done for each forecast. Catalog mainshocks used are all recorded M≥ 2.5 earthquakes from 1990 only. Background rate based on declustered M≥4 earthquakes, Gaussian smoothing.

1. Statewide simulations: PDF for total number of M≥2.5 earthquakes Simulations for the year 2001 ETES => More quiet years and more extreme years

ETES simulation agrees better with real data

2. Statewide results: Median forecast number of M≥2.5 eqs each year Correlation Coefficient = 0.5

3. Spatially varying results

Testing the ETES vs. Poissonian spatial forecasts 1) Each map is divided into 0.1 by 0.1° cells and each cell is ranked by its forecasted probability of containing an earthquake: #1 = highest probability. Map 1 Map

Map 1 Map ) For each earthquake that occurs we calculate a Signed Rank = Rank on Map 2 - Rank on Map 1 Signed rank of the example earthquake = 4 3) The list of signed ranks is evaluated with the Wilcoxon Signed Rank Statistic to see if Map 2 is statistically better than Map 1.

Wilcoxon test results, Year 2000 ETES does better, >99.9% confidence

Wilcoxon Test Results,

SAF M 7.8 Earthquake Scenario Simulations: Another application of the ETES model

Scenario #1: Aftershock Light

Scenario #2: A little more activity

Scenario #3: M 7.5 rips through Disneyland 4 days after mainshock!

Conclusions Aftershocks are the only obvious time-variant feature of seismicity -- thus should be a central part of time-variable forecasting. Given lack of understanding of aftershock physics, we propose a completely empirical/statistical model for forecasting the effect of aftershocks on the next year of seismicity. Tests indicate that our model predicts seismicity better than a steady state Poissonian at high confidence.