** Next:** Real Electroseismic data
** Up:** Haines and Guitton: Electroseismics
** Previous:** Introduction

We begin by testing the processing approach on simple synthetic data
containing three interface response events, three coseismic
arrivals, and a small amount of random noise (Figure
a). For our first processing example we chose models
for the PEF
estimation (Figure c and d) that simply
contain amplitude-normalized versions of the events in the synthetic
data, plus random noise. For the noise model, this choice is not entirely unrealistic;
horizontal geophone data collected with electroseismic data closely
resembles the coseismic noise in the electroseismic record Garambois and Dietrichz (2001) and
could be used in this capacity. For the signal model, this choice is
rather unrealistic, as we would generally be looking for previously
unknown interface
response signal that might be entirely obscured by coseismic and
background noise. The purpose of this first example is to verify that
the method is effective, and this is demonstrated by the final result
shown in Figure b. Virtually all of the coseismic
noise has been removed, leaving only the interface response energy.
**NS_1fig
**

Figure 1 a) Simple synthetic data, with
horizontal interface response events created using equation
(1) and an arbitrary velocity function. Coseismic
noise is created with the same velocity function. b) Result after
non-stationary PEF signal/noise separation. c) Normalized version
of synthetic interface response, used as model used for the
estimation of the signal PEF's. d) Normalized version of coseismic noise,
used as model for the estimation of the noise PEF's.

Our second synthetic processing example (Figure a)
employs the same data and noise model as Figure , and
a more general signal model. We use the amplitude pattern predicted
by equation (1) to produce a model for signal PEF
estimation (Figure c). We normalize the
amplitude pattern in the time direction so that the PEF estimation
equally considers deeper and shallower parts of the amplitude
pattern. Because we use one-dimensional PEF's
Haines and Guitton (2002), this choice of signal model is quite
reasonable. If we were to use two-dimensional signal PEF's, we could
not use this model as the PEF's would be trying to model waveform
information that is not present in the model. An alternative option would be to
use the amplitude pattern (Figure c) to scale
synthetic wavelets, and then to estimate 2-D signal PEF's on that
model. But this approach would lose some generality as we would have
to assign particular arrival times to those arrivals, and is not
necessary since we find one-dimensional PEF's to be at least as
effective as two-dimensional PEF's. The final result (Figure
b) is nearly as good as that of Figure
b, and shows that the generality of this choice of
signal model does not bring with it a significant degradation of the
final result.

**NS_3fig
**

Figure 2 a) Synthetic data, same as Figure
a. b) Result after signal/noise separation. c)
Model used for estimation of signal PEF's,
based on equation (1). d) Normalized version of
coseismic noise, used as model for estimation of noise PEF's.

Our third synthetic example (Figure ) adds an
important element of realism to the synthetic data. Electroseismic
data is collected using electrode dipoles pounded into the Earth. The
coupling of these electrodes with the ground is hardly uniform and
results in amplitude variations between adjacent traces. We simulate
this coupling variation by multiplying each trace of the synthetic by a
random scalar (between 0.7 and 1.0), producing the data shown in Figure
a. We use the same signal and noise models as in the
previous example (Figure ), and obtain the result shown in Figure
b. This result contains more remnant coseismic noise
than the previous examples, but the interface response energy is
significantly stronger, and would dominate a stack of
the gather.

**NS_4fig
**

Figure 3 a) Synthetic data, same as Figure
a, but each trace is multiplied by a random number
to simulate the imperfect electrode coupling that impacts
electroseismic data. b) Result after signal/noise separation. c)
Model used for estimation of signal PEF's,
based on equation (1). d) Normalized version of
coseismic noise, used as model for noise PEF estimation.

** Next:** Real Electroseismic data
** Up:** Haines and Guitton: Electroseismics
** Previous:** Introduction
Stanford Exploration Project

7/8/2003