Geoscience Reference
In-Depth Information
Initial inversion solution
E2: 1809.5s
Compacted inversion solution
x
0
0
-0.1
-0.1
-0.2
-0.2
0.3
0.3
0.3
0.3
0.2
0.2
0.2
0.2
0.1
0.1
0.1
0.1
Y
-position (m)
X
-position (m)
Y
-position (m)
X
-position (m)
(a)
00
(b)
00
Initial inversion solution
E3: 1851.11s
Compacted inversion solution
x
0
0
-0.1
-0.1
-0.2
-0.2
0.3
0.3
0.3
0.3
0.2
0.2
0.2
0.2
0.1
0.1
0.1
0.1
Y
-position (m)
00
X
-position (m)
Y
-position (m)
00
X
-position (m)
(c)
(d)
Figure 5.22
Gradient based inversion results showing the initial and compacted dipole inversion for Events E2 and E3. In these cases, the
compact inversion of Events E2 and E3 yields one dipole that dominates the response through a higher magnitude. Note that Event E3 is
localized at a shallower depth than Event E2, showing that the causative source is moving closer to the top surface of the block in the
vicinity of Hole 9.
a)
Event E2 results of the source distribution after inversion.
b)
Same after 40 iterations in compacting the support of
the source.
c)
and
d)
Same for Event E3. (
See insert for color representation of the figure
.)
cylindrical surfaces centeredaroundHole9. Eachcylindri-
cal surface (radii = 0.0105, 0.0125, and 0.0145 mm) con-
tains 10 z-axis levels with 4.4 mm spacing between levels
and 12 points in the
x
5.3.6 Results of the inversion
5.3.6.1 Results of the gradient-based inversion
For phase 1 of the inversion, the model vector (2187 × 1
elements) represents the current dipole moment (magni-
tude in A m) at the 729 dipole positions in the model (at
each location, the current dipole moment is characterized
by three components along
x
-,
y
-, and
z
-axes). The initial
model vector solution of the gradient inversion process
generates dipoles with finite moments in every dipole
position in the inverted model vector, and as such, these
dipoles are distributed throughout the dipole point
matrix positioned within the volume of the block (the
COMSOLMultiphysics model of the block). The resulting
dipole moments are mathematically consistent with the
electrical potential distribution in the data. The compac-
tion process changes the dipole moments, reducing the
magnitude of most of the dipoles in the process (reduced
y
plane at each
z
-axis level equally
spacedat 30degree increments (seedetails inFigure5.27).
The kernel matrix was computed in the same way as the
coarse kernel matrix and resulted in a kernel matrix that
was (360 × 3) × 32 or 1080 × 32 elements. The GA we
used is the one found in the MATLAB (Global Optimiza-
tion Toolbox, MathWorks (R2012a) (
http://www.math-
works.com/products/g
lobal-optimization/functionga.m;
see for details
http://www.mathworks.com/products/
global-optimization/description4.html). It should be
noted that COMSOL Multiphysics renumbers the dipole
points during its internal geometry point scan, and the
dipole numbers listed here are aligned with this COMSOL
point sequence.
-
