Processing approach

The PEF's 332#332 and 338#338 are determined from windows of the data file that are particularly representative of each. It is essential to have good design windows for the two PEF's, representative of the two components 343#343 and 344#344. We determine only one PEF for the entire data file, thus assuming (perhaps unwisely) stationarity. Using the PEF's 332#332 and 338#338, we perform an iterative inversion to determine signal and noise models 347#347and 348#348 with the fitting goal ():  

 349#349 (144)

where

350#350

We solve the following least squares inverse formulation of equation ():   with as defined by (). The estimated noise 353#353and signal 354#354 are then computed by

355#355 (145)

The weighting factor 12#12 in equation () is crucial to this process. As 356#356, 357#357 is given too little importance in the inversion relative to 358#358 and 359#359 is polluted with large amounts of noise. Physically, 12#12 represents the magnitude difference between the two distinct physical processes that make up the electroseismic response. These two proceses are: the generation of electromagnetic energy by an oscillating electric dipole (observed from a distance, called the interface response), and the generation of an electric field within a passing seismic wave (measured directly, called the coseismic field).

Because the fitting goal does not include a term for 345#345,any background noise remaining in the data after pre-processing simply falls into the residual. This is necessary because 345#345 is difficult to model, and acceptable because 360#360. Convolution of the PEF's with the data is accomplished using the helix of ().

To summarize the processing sequence:

1.

Frequency filtering and 60 Hz removal

2.

Second time derivative and other preprocessing steps described later

3.

Determine 332#332 and 338#338 from windows of data file

4.

Iteratively solve the inverse problem of equation (). Output 361#361.