Utilizing Prior Information for Depth to Improve Seismic Event Discrimination

We have developed and tested a novel algorithm for estimating the depth of a seismic event in order to improve the discrimination of events. Information from the algorithm can be incorporated into a statistically based discrimination framework to determine the source of an event. The depth estimation approach differs from currently used algorithms, which use non-linear regression techniques, by using Bayesian techniques to incorporate constraints, or prior information about the depth of an event. We demonstrate this proof-of-concept algorithm with first arriving Pwaves and their associated modeled travel times. The likelihood is constructed with Gaussian errors. Depth may be constrained with a skewed distribution if characteristics of the waveforms from an event indicate that bounds on depth are appropriate. For instance, the Rg phase is present in a waveform only when an event is shallow. A high confidence Rg phase in one or more defining waveforms can lead one to assume a shallow-skewed prior distribution for the depth parameter. OBJECTIVE For many seismic events, depth and origin time are the hypocentral parameters that are most poorly constrained because of the source-receiver geometry imposed by the Earth. It is not unusual for current location algorithms to return event solutions that fit the data very well and yet have event depths that are above the surface of the earth (so called "air quakes") or well below the known limits of seismicity for a given area. The solutions are statistically valid in that the confidence bounds are large enough to encompass more realistic depths the specified percent of the time, but they are unsatisfying to seismologists. The effect of repeatedly seeing such unreasonable depth estimation is to develop a mistrust of the depth determinations in general, even when depth may be well constrained. What is needed is a means to flexibly incorporate a priori information about acceptable depth distributions. This will better constrain the hypocentral depth estimates when they are poorly controlled by the data, and let the data control the depth estimate when the data have good depth control. Our research has developed an algorithm that shows promise in achieving these depth estimation properties. The single event hypocenter location model is ti = τ + Ti(s) + ei , i=1,2,...,n (1) where ti is the arrival time at the i station, τ is the event origin time, Ti is the travel time from the event located at s = [x, y, z] to the i station, and ei ~ iid N(0, σ). Regardless of the solver used to estimate s, it is possible with the non-linear regression formulation to estimate z as a negative number (an airquake), or to get an unreasonably large estimate of the depth given known seismicity. One approach to correcting an air quake is to simply set negative estimates of z to zero (the surface). Our efforts focused on the incorporation of constraints on z in the non-linear regression formulation. Fully mature research will provide 327 27th Seismic Research Review: Ground-Based Nuclear Explosion Monitoring Technologies