global electromagnetic induction in the moon and planets - MTNet

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256 P. Dyal and C. W. Parkin, Induction in the Moon I.0 IO~ 0 8 DYAL AND ~O6 DISTANCE FROM CENTER, km 0 500 000 500 740 10 ~ PARKIN(I972)~~ E10 3 b 0 I0~ 204 - 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 .0 - R/Rm I I I I -‘ Fig. 6. Range of electricalconductivity profiles (Dyal et al., 0 200 400 600 1972b) which give radialresponse time-dependentcurvesf(t) TIME, sec that fallwithin theerror barsof Fig. 5.-A step-function input mag. Fig. 5. Normalized transientresponse data, showing f(t)- netic field, modified by an initialramp inputof 15-sec risetime, decay characteristics of theradial component of the total sur- is used in theanalysis. Theinformation at shallowdepths is limface field BAX after arrival of a step transient which changes itedby theuncertainty in therisetime of the interplanetary magthe externalmagnetic field radial componentby an amount netic field;that at largedepths is limitedby the sensitivity of the ~BEx,here normalized to one. Theshape of the curve illus- surface magnetometer. The superimposeddashedline shows trates time characteristics of the decayof the induced poloidal the results of a three-layer Moon approximation. - eddy-current fieldB~ Although the driving field is still approximatedby a data curve puts fairly restrictivelimits on the conducspatially uniform field, this procedure provides a tivity in this region. Deeper than 170 km, the conducbetter model for the very short timeresponse. tivity is seen to rise from about lO33mho/m to The theoretical response curves corresponding to a 10—2 mho/m at R/Rm = 0.45. This is in general agreelarge number of lunar conductivity profiles have been ment with the three-layer model of Dyal and Parkin compared with the data of Fig. 5. It is found that a (1972). However, we note that conductivities greater range of monotonic conductivity profiles, defining the than 10—1.5 mho/m for R/Rm
P. Dyal and C. W. Parkin, Induction in the Moon 257 - - - proximationused so far, this would change the nor- the conductivity profile in Fig.6, using the expression malization of the response curve (Fig. 5), but not its for the electrical conductivity as a function of tempershape, and hence it does not change a(r). The effects ature given by England et al. (1968) for olivine and of the confinement of the induced poloidal field to peridotite: the cavity region bounded by the solar wind have a .. = 55 exp(—0.92/kT)+ 4~10~exp(—2.7/kT) been modeled by a superconducting laboratory ex- ohvine periment which will be discussed in section 3.1. (19) a . . = 3.8 exp(—0.81/kT)+ l0~exp(—2.3/k~ 2.1.4. Internal lunar temperature calculations pmlotite Once a planetary electrical conductivity profile has been determined, an internal temperature distribution in mho/m (20) can be inferred if the material composition is known (In the above expressions, kTis in eV.) These conductiv- (see Rikitake, 1966). For cases where electrical con- ities are assumed to be independent of pressure below ductivity is independentof pressure to a first approxi- 50 kbar (England et al., 1968) and independent of fremation, the conductivity of minerals can be expressed quency below 10 Hz (Keller and Frischknecht, 1966). in terms of temperature T as follows: For the example of a peridotite Moon, a temperature profile that rises sharply to 850—1050°K atR/Rm a a. exp (—E./kT) 1 (18) ~ 0.95 and then gradually to 1200— 1500°Kat R/Rm = 0.4 is suggested by the data. At depths greater than R/Rm = 0.4 the temperature could be higher than where E 1 are the activation energies of impurity, intrinsic, and ionic modes, expressed in electron volts; a1 are 1 500°K. material-dependent constants; and k is Boltzmann’s constant. It should be emphasized that the electrical 2.2. Fourier harmonic-analysts technique conductivity a(a, E, T) is a strong function of the ma- The harmonic method, as applied to the Moon, is terial composition; therefore, uncertainties in know- based on the assumption that any global induced field ledge of the exact composition of the sphere limits the is excluded from the oncoming solar wind by currents accuracy of the internal-temperature calculation, induced in the highly conducting solar plasma; it is as- We calculate lunar temperature profiles (Fig. 7) from sumed that in effect the solar wind completely confines the induced field in the lunar interior and in a thin region above the lunar surface. By assuming this DISTANCE FROM CENTER, km sheath region is very thin, the confinement current is 6000 500 1000 500 740 considered to be a surface current for theoretical treatment; this provides a boundary condition of total con- 1400 finement by a spherical current around the whole Moon, permitting solution of Maxwell’s equations be- 1200 low and on the lunar surface. This spherical confinement case is then applied to magnetometer data meas- T, K 000 ured on the lunar sunlit side. (Basictheoretical devel-. opment of harmonic solutions can be found in several eco - ~~OLI VINE references including Schubert and Schwartz, 1969; ~~PERIDOTITE Sifi and Blank, 1970.) 600 The harmonic analytical technique requires calculating frequency-dependent “transfer functions” which R/Rm are defined as follows: Fig.7. Temperatureestimates for assumed lunar compositions bE,(f) + b~1(f) + b71(f) of pure peridotite and olivine, calculated from theelectrical A,(f) = b (f) (21) conductivity profile of Fig.6. Ez
Page 1 and 2: Physics of theEarth and Planetary I
Page 3 and 4: P. Dyal and C. W. Parkin, Induction
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Page 11 and 12: TABLE I Lunar surface remanent magn
Page 13 and 14: TABLE II Inductiveresponse times of
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