Geoscience Reference
In-Depth Information
Synthetic and real data comparison − E2:1809.5 s
Norm of synthetic error = 3.46e-010; Norm of thresholded synthetic error = 1.73
Real data
Full synthetic
Thresholded synthetic
2
1
0
−1
−2
5
10
15
20
25
30
(a)
Sensor position number
Full model vector for 1809.5 s
0.18
0.16
0.14
0.12
×10
−4
Zoom of full model vector for 1809.5 s
5
0.1
0.08
0
0.06
−5
0.04
200
400
600
800
1000
1200
1400
1600
1800
2000
0.02
Model vector location
0
200
400
600
800
1000
1200
1400
1600
1800
2000
(b)
Model vector location
Figure 5.23
E2 compacted inversion results and forward modeled comparison with a thresholded forward model.
a)
Comparison of
the real data with the forward model calculations using the full inverted model, and a thresholded model derived from the full
inversion model.
b)
The full model vector that was found through inversion and compaction. The inset shows the multitude of minor
dipoles spread throughout the model vector that were generated by the inversion and compaction process. (
See insert for color
representation of the figure
.)
volumetric support for the source current density). This
process results in a few (one or two) dominant dipoles
with the rest of the points in the solution containing
dipoles with very low moment magnitudes. In step 7,
we threshold the small dipoles to make them equal to
zero. Indeed, the large number of low-magnitude dipoles
represents a nonphysical solution to the inversion as
stated earlier.
To check how the thresholded solutions compare with
the measured data, we examine their differences (using
the L2 norm). In the following analysis, the forward
modeled predictions of the data are called synthetic data.
Figure 5.22 shows the comparison between the initial
inversion results after one iteration (without compaction;
Figure 5.22a and c) and the compacted solutions after
40 iterations (Figure 5.22b and d) for Events E2 and
E3, respectively. Each small cone in Figure 5.22 repre-
sents a dipole at a kernel matrix point, pointing in the
direction of the electrical current at that point, an expres-
sion of the dipole moment for the dipole positioned at
that point. The compacted inversion (Figure 5.22b and
d) results for both events show a single dipole pointing
mostly in the +
z
direction. This solution is consistent with
the hypothesis of seal leakage induced upward (+
z
direc-
tion) fluid flow based on the observations of the electrical
potential distribution (see Figure 5.19). Additionally,
according to the electrical current flow and the dynamic
fluid coupling processes described by Equations (5.29)
through (5.35), the electrical current flow is expected
to occur in the direction of the fluid flow (via the drag
of an excess of charge in the fluid flow direction with a
current flowing in the direction of the cations).
