[Paper Review] High Resolution Long- and Short-Term Earthquake Forecasts for California

Maximilian J. Werner, Agnès Helmstetter+2 more|ArXiv.org|Oct 26, 2009

earthquake and tectonic studies39 references4 citations

TL;DR

This paper presents two high-resolution earthquake forecasting models for California: a time-independent model for 5-year forecasts of m≥4.95 quakes using adaptive kernel smoothing of small events (m≥2) and a negative binomial count distribution, and a time-dependent ETAS model for next-day forecasts of m≥3.95 quakes with magnitude-dependent triggering and Omori-Utsu decay. The short-term model achieves a probability gain of ~6.0 over the long-term model, demonstrating significant predictive improvement.

ABSTRACT

We present two models for estimating the probabilities of future earthquakes in California, to be tested in the Collaboratory for the Study of Earthquake Predictability (CSEP). The first, time-independent model, modified from Helmstetter et al. (2007), provides five-year forecasts for magnitudes m > 4.95. We show that large quakes occur on average near the locations of small m > 2 events, so that a high-resolution estimate of the spatial distribution of future large quakes is obtained from the locations of the numerous small events. We employ an adaptive spatial kernel of optimized bandwidth and assume a universal, tapered Gutenberg-Richter distribution. In retrospective tests, we show that no Poisson forecast could capture the observed variability. We therefore also test forecasts using a negative binomial distribution for the number of events. We modify existing likelihood-based tests to better evaluate the spatial forecast. Our time-dependent model, an Epidemic Type Aftershock Sequence (ETAS) model modified from Helmstetter et al. (2006), provides next-day forecasts for m > 3.95. The forecasted rate is the sum of a background rate, proportional to our time-independent model, and of the triggered events due to all prior earthquakes. Each earthquake triggers events with a rate that increases exponentially with its magnitude and decays in time according to Omori's law. An isotropic kernel models the spatial density of aftershocks for small (< 5.5) events. For larger quakes, we smooth early aftershocks to forecast later events. We estimate parameters by optimizing retrospective forecasts. Our short-term model realizes a gain of about 6.0 over the time-independent model.

Motivation & Objective

• To develop and test high-resolution, probabilistic earthquake forecasts for California suitable for prospective evaluation in CSEP.
• To improve long-term forecasting by modeling seismicity clustering and count variability beyond Poisson assumptions, using a negative binomial distribution.
• To extend and calibrate a time-dependent ETAS model for one-day forecasts across all of California, incorporating magnitude-dependent triggering and spatial smoothing of aftershocks.
• To enhance spatial forecast evaluation by modifying likelihood tests to condition on observed event counts, increasing spatial resolution and robustness.
• To assess the predictive performance of both models against CSEP testing standards, using retrospective forecasts optimized on data up to April 2009.

Proposed method

• The long-term model uses adaptive spatial kernel smoothing of m≥2 earthquakes to estimate future m≥4.95 event probabilities, with optimized bandwidth and a universal tapered Gutenberg-Richter magnitude distribution (mc=8.0).
• The model replaces Poisson count assumptions with a negative binomial distribution to better capture temporal variability in seismicity, improving consistency with retrospective data.
• The short-term model is an extended ETAS model where each earthquake triggers aftershocks with rate increasing exponentially with magnitude and decaying in time via Omori’s law (u(t) ∝ 1/(c+t)^p).
• Background seismicity is modeled as a spatially heterogeneous Poisson process, with spatial distribution derived from the long-term model, and rate estimated from data.
• Spatial smoothing of early aftershock locations is applied to forecast later aftershock sequences, particularly for larger events (≤5.5).
• Model parameters are optimized via retrospective forecasting performance, and likelihood-based tests are modified to condition on observed event counts to improve spatial resolution and sensitivity.

Experimental results

Research questions

• RQ1 Can high-resolution spatial forecasts of large earthquakes (m≥4.95) in California be improved by using the locations of small events (m≥2) through adaptive kernel smoothing?
• RQ2 Does modeling the number of earthquakes per time interval with a negative binomial distribution yield better consistency with observed seismicity than a Poisson assumption in long-term forecasts?
• RQ3 Can a time-dependent ETAS model with magnitude-dependent triggering and Omori-Utsu decay provide significantly better one-day forecasts (m≥3.95) than a time-independent model?
• RQ4 How does conditioning likelihood tests on observed event counts improve the spatial resolution and reliability of forecast evaluation?
• RQ5 To what extent do models based solely on past seismicity outperform or compare to models incorporating tectonic or geodetic data, especially over longer timescales?

Key findings

• The time-independent long-term model, using adaptive kernel smoothing of m≥2 events and a negative binomial count distribution, passed retrospective number consistency tests, unlike the original Poisson-based forecast.
• The modified likelihood test, conditioned on observed event counts, increased spatial resolution and reduced sensitivity to event count fluctuations, improving forecast evaluation accuracy.
• The time-dependent ETAS model achieved a probability gain of approximately 6.0 over the time-independent model in one-day forecasts, indicating strong predictive performance.
• Smoothing early aftershock locations to forecast later ones significantly improved the forecast of larger aftershock sequences, especially for events ≤5.5 in magnitude.
• The use of small events (m≥2) to forecast larger quakes (m≥3.95) proved effective in the short-term model, supporting the hypothesis that seismicity clustering is a key driver of short-term hazard.
• The models outperformed baseline Poisson forecasts, particularly in capturing temporal variability and clustering, validating the use of branching processes for earthquake forecasting.