An empirical bayes estimator of seismic events using wavelet packet bases

An empirical Bayes (EB) estimator is constructed to denoise a time series containing quarry blasts in New England. This estimator is portable and can be used more generally to denoise seismic events. The EB estimator uses adaptive wavelet packet analysis (WPA) for transformation selection via an EB approximation to the standard entropy functional. We compare this basis selection method to the discrete wavelet transform (DWT) and best basis selection via Stein’s unbiased risk estimator (SURE). The relation of sparsity of representation to quality of estimation over a range of signal-to-noiserations (SNR) for synthetic quarry blast events is demonstrated. For functions with sparse representations, we have found that, at moderate SNR, WPA significantly out performs DWT. The EB best basis performs similarly to SURE best basis, thereby lending credence to the EB method. Finally, we compare DWT and WPA. methods for denoising quarry blast events recorded in New England.