Redshift of Earthquakes

Schematic of waves emitted due to a rupture propagating from west (azimuth $\theta=270^{\circ}$) to east (90$^{\circ}$). a) Blue waves emitted towards the east are shortened, while the red waves traveling towards the west are lengthened. These waves undergo complex scattering (squares) before they reach the receivers (triangles), resulting in a challenging source-spectrum estimation problem. b) I have developed a signal model to factorize the measurements, effectively removes the complex scattering or path effects and directly estimates the source spectra (red-blue graphs) at the receivers. The variability of the normalized source spectrum with $\theta$ can be used to infer the kinematic rupture parameters.
The hazard assessment of earthquakes is closely related to the propagation of their associated ruptures. This research responds to numerous fundamental challenges involved in directly measuring source signals that originate from a propagating rupture. It is desirable to directly measure the source pulses at the seismometers and subsequently infer quantities that are related to the rupture propagation. However, the signals measured in place of those pulses are affected by the subsurface properties through which they propagate before reaching these stations. Thus, instead of measuring the earthquake source signal directly, each seismic station records two types of information that are convoluted into a single signal: information about the earthquake (source pulse) and information about the unknown subsurface features through which it passed (path effects). The path effects may distort the earthquake source signal, for example, due to:
  • one or more reflections off of geological layers in the subsurface;
  • intrinsic attenuation of the porous-rock medium.

Consequently, an accurate characterization of the earthquake rupture involves reliably analyzing the recorded seismograms to separate the path effects from the earthquake pulses. Current methods for separating out the two types of information rely on dubious assumptions, and may be confounded because extracting source pulse requires assumptions about the path, but conversely extracting path effects requires assumptions about the source. This research introduces to seismology a new analysis method, focused blind deconvolution (FBD), that can be used to extract source or path information without relying on traditional assumptions. Instead, this method compares data from the same source picked up by multiple receivers, and uses advanced signal processing to identify similarities and differences among the data. Similarities among the signals can be identified as source effects, while dissimilarities indicate path effects. Because it does not require the aforementioned assumptions, this method will provide more accurate and reliable source information to seismologists.

FBD factorizes the recorded spectra $|D|$, due to the Nicobar earthquake, into the source $|\hat{S}|$ and the path $|\hat{G}|$ at multiple azimuths. Note that the source spectrum exhibits frequency scaling, with higher corner frequency in the direction of the rupture propagation (indicated by an arrow) and vice versa.
Pawan Bharadwaj
Pawan Bharadwaj
Assistant Professor, Center for Earth Sciences

Pawan is an assistant professor in the Center for Earth Sciences at the Indian Institute of Science (IISc). He enjoys developing novel algorithms related to geophysical inverse problems, signal processing and machine learning.