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| Titel |
Three-dimensional Complex Resistivity Modelling and Inversion with Topography |
| VerfasserIn |
Kaijun Xu, Jianping Li, Zhan Liu |
| Konferenz |
EGU General Assembly 2011
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 13 (2011) |
| Datensatznummer |
250045567
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| Zusammenfassung |
| The characteristic of complex resistivity on rock and ore has been recognized by
people for a long time. Generally we have used the Cole-Cole Model(CCM) to
describe complex resistivity. It has been proved that the electrical anomaly of
geologic bodies can be quantitative estimated by CCM parameters such as direct
resistivity(Ï0),chargeability(m),time constant(Ï) and frequency dependence(c). Thus it is
very important to obtain the complex parameters of geologic body. There are some
drawbacks in traditional complex resistivity inversion methods. For example, most of
these inversion methods are based on the hypothesis about apparent resistivity and
true parameters. The hypothesis will lead to some obvious error for the result of
inversion. In addition, the traditional methods can’t inverse the geometry parameters. In
order to enhance the veracity and reasonably of the complex resistivity data, the
effect of topography should be taken into account. As a result, in this paper we
study the methods on the frequency-domain electromagnetic three-dimensional(3D)
modelling and inversion of complex resistivity with topography by volume integral
equation.
First of all, on the basis of analysis about the complex resistivity mathematical models,
the topography is regarded as anomalous bodies; and then, the CCM is introduced into the 3D
electromagnetic modelling. The 3D electromagnetic responses of the surface electric dipole
are computed by volume integral equation. In modelling, it is to separate the electromagnetic
field into a primary and a secondary field to avoid a source singularity. In addition, the
modelling uses the Gaussian quadrature and continued fraction to calculate the integral of
Bessel function. The benchmark results of the modelling indicated that these methods are
feasible and accurate.
As to the surface electric dipole source, the modelling results of 3D complex resistivity
show that the values of secondary electric and magnetic field are not constant with complex
resistivity parameters changes. In general, the absolute values of secondary electric and
magnetic field increase with the rise of the complex resistivity parameters(m,Ï,c),
and the influence of m is more prominent among these parameters. In addition the
topography can cause great influence on the horizontal component of secondary electric
field, but it has little influence on the horizontal component of secondary magnetic
field.
At last, in this paper we develop the sensitivity matrix that reflects the rate of real
measurement field to the CCM parameters. It is achieved that the complex resistivity 3D
electromagnetic inversion with topography using conjugate gradient algorithm based on
electric dipole source. The conjugate gradient algorithm doesn’t need to compute the
sensitivity matrix but directly computes the sensitivity matrix or its transpose multiplying an
arbitrary vector. Thus this algorithm efficiently reduces the computation of the inversion. The
inversion results of complex resistivity parameters verify the validity and stability of
conjugate gradient inversion algorithm.
The results of theoretical calculation examples indicate that the modelling and inversion
of the 3D complex resistivity with topography are feasible. |
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