An Envelope-Based Paradigm for Seismic Early Warning

We present a waveform envelope-based paradigm for seismic early warning. As suggested by theoretical scaling relations and as observed from data, acceleration saturates with increasing magnitude at a faster rate than does velocity or displacement. Thus, ratios of velocity or displacement to acceleration should be indicative of the magnitude of an earthquake. We introduce an evenlope-based parameterization of ground motion, where the observed ground motion envelope is decomposed into independent P-wave, S-wave, and ambient noise envelopes. The body wave envelopes, in turn, are parameterized by a rise time, an amplitude, a duration, and two decay parameters. We apply this parameterization to a database of over 30,000 records of horizontal and vertical acceleration, velocity, and displacement recorded on digital Southern California Seismic Network stations within 200 km of 80 regional events ranging in magnitude from M2.0 to M7.3. We derive attenuation relationships that account for magnitude-dependent saturation for vertical and horizontal acceleration, velocity, and displacement for P- and S-wave amplitudes, obtain station corrections relative to the mean hard rock response, and use these relationships to examine trends with magnitude and distance of ratios of different components of ground motion. An important consequence of our parameterization is the insight it provides into P-wave characteristics. We find that various ratios of P-wave velocity and displacement to acceleration are indicative of magnitude, and may have potential as another quick method to estimate magnitude for seismic early warning.