Application of fk Analysis and Entropy to Track the Transition from Spatially Coherent to Incoherent Earthquake Coda in Long Beach, California

Abstract

Online Material: Time sequences of the fk analysis for two of the largest events recorded by the Long Beach array. Seismic‐scattering theories describe high‐frequency coda waves as a combination of waves from random scatterers superimposed on direct waves from the source. The direct waves are expected to be spatially coherent whereas the scattered waves, arriving with random phase, will be spatially incoherent. Our objective is to use data from an extreme high‐resolution seismic experiment in Long Beach, California, to determine the transition from coherent to incoherent coda. The network, deployed by Nodal Seismic, comprises ∼5400 vertical component instruments, spaced every ∼100 m over an area of ∼5×7 km2. It was deployed for a period of six months with the primarily target to image the geological structure of the area for oil exploration. During the deployment, several thousand earthquakes and microearthquakes were recorded. We examine coda waves from the two largest events that occurred in the vicinity of the array. We compute frequency–wavenumber diagrams to determine the sources of coda and their evolution in time. Entropy analysis of the propagation of seismic waves through the array indicates the transition between the coherent direct body waves and the onset of incoherent coda waves. Our analysis illustrates that after the arrival of the body waves, the seismic coda is initially dominated by a dispersing wave train composed of spatially coherent body waves, forward scattered from 1D crustal layering. This is then followed by omni‐directional, spatially incoherent coda waves that can be described as scattered waves from 3D random sources. Pioneering work by Aki (1969) first recognized that coda is the result of scattering due to the random distribution of heterogeneities in the crust. In later work, Aki and Chouet (1975) developed a theoretical model of single scattering, using the Born approximation, that fits …