Before stacking seismograms for each grid point, cross correlation is required to align waveform. At first, we need to choose a model station's waveform to compare another waveform, and generate cross correlation between them. The principle to pick up model station is make its geographical position locate in the center of dense array as far as possible. $ csh Pick_model-station.csh # open Pick_model-station.csh to look over all commands

In a way, back-projection can be recognised as the method of grid search. First, we set up suitable grid points around epicenter, and hypothesize these points are all possible source locations. Then, seismograms are stacked for each possible source location to obtain a direct image of the source. Then sum the energy that is radiated from the given source constructively, and cancels out other energy present in the seismograms.

Before starting back-projection, we need to check seismic data firstly. Download data We recommend to download data recorded at verticle components of dense seismic stations. And convert seismic data to .SAC format. Select stations Back-projection is a form of time-reversal where we approximate the P wave Green’s function as a time-shifted delta function. This work agrees with tele-seismic arrivals between 30° and 90° where pulses are simple and amplitude variations are small.

Theory The part is an excerpt from Peter Shearer’s SCEC-ERI Back-projection Material Consider a linea set of equations relating observed data to a model: $$d = G m$$ using the conventional notation of $d$ for the data vector, $m$ for the model vector, and $G$ for the linear operator that predicts the data from the model. Our goal in geophysical inverse problems is to estimate $m$ from the observations, $d$.

Welcome. Qiang Yao (July 2018) The Back-projection of teleseismic waves has been proven efficient at resolving rupture durations and source extents of large seismic sources. It requires no prior knowledge of fault geometry, fault dimension, or focal mechanism. In addition, this observation-driven method takes advantage of the entire P wavetrain, and the calculation of synthetic seismograms is not needed. The purpose of the manual is to roughly show how our Back-projection procedure works.

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