Phased Array Analysis Incorporating the Continuous Wavelet Transform

ABSTRACT Nonlinear block thresholding of the continuous wavelet transform (CWT) of 2D phased array signals offers high time-resolution solutions for analyzing seismograms of local and regional seismic events. An initial denoising step on an array ensemble reveals the regions of the scale-time plane that contain high signal-to-noise arrivals. Individual seismic phase arrivals in ensemble, denoised seismograms can be partitioned using scale-time gating in which CWT wave packets of an individual seismic phase on the scale-time plane for a reference array element are time-correlated with all other elements to find an optimum time shift for the phase across all elements. The seismic phase is then clipped out of the CWT of each array element using this optimal time shift for further analysis. The seismogram can be separated into component seismic waves for a detailed view of wave characteristics such as slowness and arrival azimuth using conventional frequency–wavenumber methods. However, the process can be taken further using the CWT of each phase to construct high time-resolution signal beams over the CWT scale. Local explosion data from the 2016 Incorporated Research Institutions for Seismology (IRIS) Wavefields Community Experiment in northern Oklahoma are used to demonstrate these techniques in separating surface-wave modes and body waves and to examine the scattering of regional phases. High-resolution CWT processing in the 1–3 Hz band for northern Oklahoma reveals horizontal Rayleigh-wave refraction and multipathing. Rayleigh-wave phase-velocity dispersion measurements are used to construct a 1D velocity model under the IRIS experiment. Scale-time gating helps expose near-source surface reflections from a local M 3.6 earthquake that are used to verify the 4 km source depth obtained from a published regional moment tensor solution.