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with minor contributions from coseismic energy at ~11
and ~17 ms caused by the two seismic reflections.
Step III. The modeled coseismic and direct field
contributions (Figure 7.13b) are subtracted from the total
modeled seismoelectric signal (Figure 7.13a), emphasiz-
ing the contribution of the seismoelectric conversions
to the latter (Figure 7.13c). The conversions are revealed
to have considerable amplitudes between the start of the
time series and ~11 ms and to continue toward later times
with smaller amplitudes (>>20 ms) (Figure 7.13c).
Similar to the field data (Figure 7.10), the modeled
seismoelectric conversion (Figure 7.13c) at the water
table is small compared to conversions in the vadose zone
above it. It is highly significant that strong seismoelectric
conversions occur within the vadose zone at times
(>4 ms) when the coseismic and direct field contributions
(Figure 7.13a and b) are small or negligible. This behavior
readily explains the statistically significant relationship
between the principal amplitudes of the seismoelectric
conversions and vadose zone volumetric water
contents inferred from the field data (Figure 7.10), which
used data from times outlined by the red box in
Figure 7.13c. We may thus hypothesize that modeled
seismoelectric conversions (Figure 7.13c) should likewise
correlate well with vadose zone volumetric water
contents.
Step IV. The modeled seismoelectric conversions
(Figure 7.13c) are processed in the same way as the field
data, using Equations (7.1) and (7.2) together with
spherical correction and smoothing with a 0.25 m
running mean (Figure 7.14a). Processed seismoelectric
conversions (Figure 7.14a) are characterized by the
same inverse relationship with volumetric water content
(Figure 7.14b) as the field data. The computed seismo-
electric conversions similarly increase in amplitude over
the first ~1
4 m as volumetric water content decreases,
followed by a series of predominantly inverse major
fluctuations from ~4 to 9 m, and the final decrease or
increase in seismoelectric conversions and volumetric
water content between ~9 m and 11 m (Figure 7.14),
respectively. This allows the principal peak-to-peak
amplitudes of the seismoelectric conversions to be picked
and plotted against those of vadose zone volumetric
water contents (Figure 7.15), in exactly the same way
as we did for the field data. We obtain a statistically sig-
nificant relationship (
R
2
= 0.76) between the conversion
and water content amplitudes (Figure 7.15), which con-
firms our hypothesis. Numerical modeling is therefore
able to place the empirically inferred seismoelectric con-
version
-
volumetric water content relationship on a solid
physical grounding, as anticipated in the previous chap-
ters of this topic.
-
0.7
0
−0.7
1
2
3
4
5
6
7
8
9
10
11
Depth (m)
(a)
35
30
25
20
15
10
1
2
3
4
5
6
7
8
9
10
11
Depth (m)
(b)
Figure 7.14
Computed seismoelectric conversions andmeasured volumetric water contents versus depth.
a)
Seismoelectric conversions
from depths of 1.25
-
11.25 m using spherical correction applied and smoothed with a 0.25 m running mean.
b)
Volumetric water
content-depth profile from TDR measurements as it was indicated from the measured data.
