Robust estimation of seismic coda shape

• We present a new method for estimation of seismic coda shape. It falls into the same class of methods as non-parametric shape reconstruction with the use of neural network techniques where data are split into a training and validation data sets. We particularly pursue the well-known problem of image reconstruction formulated in this case as shape isolation in the presence of a broadly defined noise. This combined approach is enabled by the intrinsic feature of seismogram which can be divided objectively into a pre-signal seismic noise with lack of the target shape, and the remainder that contains scattered waveforms compounding the coda shape. In short, we separately apply shape restoration procedure to pre-signal seismic noise and the event record, which provides successful delineation of the coda shape in the form of a smooth almost non-oscillating function of time. The new algorithm uses a recently developed generalization of classical computational-geometry tool of alpha-shape. The generalization essentially yields robust shape estimation by ignoring locally a number of points treated as extreme values, noise or non-relevant data. Our algorithm is conceptually simple and enables the desired or pre-determined level of shape detail, constrainable by an arbitrary data fit criteria. The proposed tool for coda shape delineation provides an alternative to moving averaging and/or other smoothing techniques frequently used for this purpose. The new algorithm is illustrated with an application to the problem of estimating the coda duration after a local event. The obtained relation coefficient between coda duration and epicentral distance is consistent with the earlier findings in the region of interest.

Nyckelord

Time-series analysis; Image processing; Body waves

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