A probabilistic approach for estimating the separation between a pair of earthquakes directly from their coda waves

Coda wave interferometry (CWI) can be used to estimate the separation between a pair of earthquakes directly from the coda recorded at a single station. Existing CWI methodology leads to a single estimate of separation and provides no information on uncertainty. Here, the theory of coda wave interferometry is revisited and modifications introduced that extend the range of applicability by 50% (i.e., 300-450 m separation for 1-5 Hz filtered coda waves). Synthetic experiments suggest that coda wave separation estimates fluctuate around the actual separation and that they have an increased tendency to underestimate the actual separation as the distance between events increases. A Bayesian framework is used to build a probabilistic understanding of the coda wave constraints which accounts for both the fluctuations and bias. The resulting a posteriori function provides a conditional probability distribution of the actual separation given the coda wave constraints. It can be used in isolation, or in combination with other constraints such as travel times or geodetic data, and provides a method for combining data from multiple stations and events. Earthquakes on the Calaveras Fault, California, are used to demonstrate that CWI is relatively insensitive to the number of recording stations and leads to enhanced estimates of separation in situations where station geometry is unfavorable for traditional relative location techniques.