Series and parallel transformations of the magnetotelluric impedance tensor: theory and applications

Romo, J. M.; Gómez‐Treviño, Enrique; Esparza, Francisco J.

doi:10.1016/j.pepi.2004.08.021

Cited by 11 publications

(15 citation statements)

References 26 publications

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“…We compare our solution to the joint inversions by deGroot‐Hedlin & Constable (1993) and Romo et al (2005). These solutions are respectively A, B and C of Fig.…”

Section: Resultsmentioning

confidence: 99%

“…4. A and B are from deGroot‐Hedlin & Constable (1993) and C is from Romo et al (2005). The horizontal and vertical scale of the three models is the same as our model in Fig.…”

Section: Resultsmentioning

confidence: 99%

“…Being able to use bounds for regularization is a great advantage over other inverse codes (e.g. deGroot‐Hedlin & Constable 1990; Rodi & Mackie 2001; Oldenburg & Ellis 1993; Smith & Booker 1991; Romo et al 2005). We can place the same bound on the entire region, as we have done here.…”

Section: Resultsmentioning

confidence: 99%

“…In contrast, there are many purely numerical methods for finding a 2‐D MT regularized solution (e.g. deGroot‐Hedlin & Constable 1990; Rodi & Mackie 2001; Oldenburg & Ellis 1993; Smith & Booker 1991; Romo et al 2005). These methods can usually find a smooth solution that fits the data, but they cannot identify properties common to all models that fit the data.…”

Section: Optimization Theory In Inversionmentioning

confidence: 99%

“…The model from Romo et al (2005) is from an inversion of all 40 frequencies of the COPROD data set, instead of from only the reduced COPROD2 data set. Therefore we expect their model to possess more detail near the surface than ours; our model relies on the lower frequencies with larger skin depths.…”

Section: Coprod2 Joint Te-tm Data Inversionmentioning

confidence: 99%

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The 2-D magnetotelluric inverse problem solved with optimization

Beusekom

Parker

Bank

et al. 2010

Geophysical Journal International

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S U M M A R YThepractical 2-D magnetotelluric inverse problem seeks to determine the shallow-Earth conductivity structure using finite and uncertain data collected on the ground surface. We present an approach based on using PLTMG (Piecewise Linear Triangular MultiGrid), a special-purpose code for optimization with second-order partial differential equation (PDE) constraints. At each frequency, the electromagnetic field and conductivity are treated as unknowns in an optimization problem in which the data misfit is minimized subject to constraints that include Maxwell's equations and the boundary conditions. Within this framework it is straightforward to accommodate upper and lower bounds or other conditions on the conductivity. In addition, as the underlying inverse problem is ill-posed, constraints may be used to apply various kinds of regularization. We discuss some of the advantages and difficulties associated with using PDE-constrained optimization as the basis for solving large-scale nonlinear geophysical inverse problems.Combined transverse electric and transverse magnetic complex admittances from the CO-PROD2 data are inverted. First, we invert penalizing size and roughness giving solutions that are similar to those found previously. In a second example, conventional regularization is replaced by a technique that imposes upper and lower bounds on the model. In both examples the data misfit is better than that obtained previously, without any increase in model complexity.In magnetotelluric (MT) sounding, measurements of time-varying surface magnetic and electric fields allow us to learn about the conductivity structure of the Earth. However, the measurements are necessarily finite and uncertain and in the face of these limitations, the ultimate goal of an inversion must be to quantify the information that the measurements contain about the electrical structure of the Earth. Because the MT inverse problem is also non-linear and ill-posed, there is a paucity of rigourous methods that can extract the truly essential features of conductivity models. One such solution to the MT problem in one spatial dimension has been developed by us using optimization theory to unify the treatment of the differential equations and the inversion (Medin et al. 2007). Our method was applied to long-period observations and the question of the conductivity in the upper and mid-mantle paper. Our purpose here is to extend (as far as possible) that technique to a 2-D geometry.Our earlier work does not rely on regularization to construct a plausible model from which to draw conclusions. Instead, the observations and the differential equations are regarded as constraints in an optimization problem in which a conductivity function is minimized subject to inequality constraints that keep σ positive (for example). Subject to these constraints, bounds are sought on the average conductivity in intervals of particular geophysical interest, such as the seismic transition zone. Whereas the 1-D problem is motivated by whole-Earth issues such as ...

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“…We compare our solution to the joint inversions by deGroot‐Hedlin & Constable (1993) and Romo et al (2005). These solutions are respectively A, B and C of Fig.…”

Section: Resultsmentioning

confidence: 99%

“…4. A and B are from deGroot‐Hedlin & Constable (1993) and C is from Romo et al (2005). The horizontal and vertical scale of the three models is the same as our model in Fig.…”

Section: Resultsmentioning

confidence: 99%