Magnetics
is a common geophysical technique used to image
subsurface structure though variations of magnetic
properties. Three-dimensional inversion has been
used successfully to achieve quantitative interpretation
of magnetic data. However, a crucial parameter in
this process is the direction of magnetization.
The total magnetization is a vector sum of two components.
Induced magnetization is well approximated by the
inducing field direction; remanent magnetization
is commonly unknown and can have adirection significantly
different from that of the current field or a magnitude
large enough to alter the direction of total magnetization.
As a result, the magnetization direction becomes
an unknown quantity and hampers inversion and interpretation
of magnetic data.
I
present a general approach for inverting magnetic
data in the presence of strong remanent magnetization.
Two quantities, the amplitude of the anomalous magnetic
field and the total gradient, defined as the magnitude
of the gradient vector of magnetic anomaly data,
are weakly dependent upon the magnetization direction
in three dimensions. Therefore, I invert amplitude
and total gradient data directly to recover the
magnitude of magnetization without precise knowledge
of its direction.
Since
amplitude and total gradient data depend nonlinearly
upon magnetization, solution of a nonlinear inverse
problem is required. Further nonlinearity is introduced
by imposing a positivity constraint on the magnitude
of magnetization. I formulate the inversion using
Tikhonov regularization, impose positivity by using
a logarithmic barrier method, and solve the resulting
optimization by truncated Gauss-Newton method.
The
ability to invert magnetic data with little information
about the nature of remanent magnetization increases
the areas in which three-dimensional inversion of
magnetic data can be applied. In fact, it is now
possible to invert any magnetic data to some extent.
This newfound ability opens the door to quantitative
interpretation of data in a variety of practical
problems ranging from archaeological investigations,
mineral and resource exploration, and crustal and
planetary studies.
Download
the full Masters Thesis
