The electrical conductivity of the Moon: an application of inverse theory

Hobbs, B. A.

doi:10.1111/j.1365-246x.1977.tb04217.x

Cited by 14 publications

(9 citation statements)

References 10 publications

(16 reference statements)

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“…To adjust the errors, first consider what type of response the spectral expansion (or any other method) might be expected to achieve. As stated elsewhere (Hobbs 1977), response functions are inherently smooth with respect to frequency -even if the models are discontinuous. Thus the final response will be a smooth function of frequency which fits the data values, perhaps in some least squares sense.…”

Section: T H E M E a S U R E O F Fitmentioning

confidence: 98%

“…These replaced errors, { aCf;)], are used only as an aid to stability in the model fmding procedure. For model interpretation, the original errors may be used or slightly refined as in Hobbs (1977). Unfortunately, the choice of / 3 is somewhat subjective, but its value is not critical and its choice is considered more fully in the numerical applications.…”

Section: T H E M E a S U R E O F Fitmentioning

confidence: 99%

“…Using the same method as in Hobbs (1977), the Fr6chet kernel for y may be determined as F ( y ; r , w) = -2d2~oio~2(r) /~(1)~,(1). (20) The real part of F is the Fr6chet kernel for the logarithm of the apparent resistivity, the imaginary part is that for the phase of &.…”

Section: F R E C H E T K E R N E L F O R I N V E R S E P R O C E D U R Ementioning

confidence: 99%

“…Here an alternative method is considered to those of Oldenburg and Parker, one that is objective and produces smooth parameter distributions. It was shown in Hobbs (1977) that for conductivity models fitting some lunar magnetic data, a discontinuous model was less well resolved than a model in which the conductivity was continuous and smooth. This situation may also apply to magnetotelluric data.…”

Section: Introductionmentioning

confidence: 99%

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Automatic model for finding the one-dimensional magnetotelluric problem

Hobbs

1982

Geophysical Journal International

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A method is described for finding a resistivity model that fits given magnetotelluric data in the one-dimensional case. The procedure is automatic and objective in that no a priori model structure is imposed. Starting with a uniform half space derived directly from the data, the procedure gradually transforms the half space to one with a continuous and smooth resistivity distribution whose response fits the measured data. The method is illustrated b y application to two magnetotelluric data sets.

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Section: T H E M E a S U R E O F Fitmentioning

confidence: 98%

Section: T H E M E a S U R E O F Fitmentioning

confidence: 99%

Section: F R E C H E T K E R N E L F O R I N V E R S E P R O C E D U R Ementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Automatic model for finding the one-dimensional magnetotelluric problem

Hobbs

1982

Geophysical Journal International

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“…These values are consistent with other investigations of the lunar induction problem. The infinite summations in equations (2) and (8) were truncated to n = 5,yielding adequate accuracy for the frequencies being considered (Hobbs 1977). Fig.…”

Section: Calculationsmentioning

confidence: 99%

Limitations on the parameters of the solar wind in modelling lunar electromagnetic induction

Hobbs¹,

Parker

1978

Geophysical Journal International

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A striking feature of the day-side response of the Moon to periodic fluctuations in the solar wind is the rapid rise, and subsequent fall, in the amplitude of the transfer function as the inducing field frequency increases. This behaviour can be characterized by the amplitude values at the two frequencies 24 and 40mHz. Before the response of a conductivity model representing the Moon can be calculated at a given frequency, the parameters (u, 0) (where u is the solar wind speed and 0 is the angle between the solar wind velocity and the magnetic field propagation direction) have to be specified. By applying some results due to Parker (1972) to the above two data points, we have determined constraints on the parameter space (u, 0). In particular, we determine the region of the (u, 8) space in which conductivity models may be found that satisfy our data pair. Outside this region, there are no conductivity models satisfying the data pair, and hence many (u, 0) values are inconsistent with the original data and the model assumptions.

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The Global Conductivity Structure of the Moon

Mittelholz

Grayver

Khan

et al. 2021

Preprint

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Magnetic sounding is a powerful tool to explore the interior of planetary bodies through the electrical conductivity structure. The electrical conductivity structure of the lunar mantle has previously been derived from surface magnetic field measurements as part of the Apollo 12 mission and concurrent magnetometer data acquired from orbit through the Explorer 35 satellite. Here, we derive the first global conductivity structure using only satellite magnetometer data collected by the recent Lunar Prospector and Kaguya Selene satellite missions. We show that the field in the geomagnetic tail exhibits a simple geometrical structure and can be well described by a single spherical harmonic of degree and order one. Employing this information about the inducing field geometry and assuming a potential representation of the field in the geomagnetic tail, we derive a frequency-dependent transfer function and invert it for a global one-dimensional (1-D) electrical conductivity profile. Our global transfer function shows striking similarity with the local one obtained from joint analysis of Apollo 12 and Explorer 35 magnetometer data. This indicates the lack of local variations at the Apollo 12 landing site compared to the globally-averaged upper to mid-mantle electrical conductivity structure.

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The electrical conductivity of the Moon: an application of inverse theory

Cited by 14 publications

References 10 publications

Automatic model for finding the one-dimensional magnetotelluric problem

Automatic model for finding the one-dimensional magnetotelluric problem

Limitations on the parameters of the solar wind in modelling lunar electromagnetic induction

The Global Conductivity Structure of the Moon

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