A Harmonic and Statistical Analysis of the Topography of the Earth, Moon, and Mars

Citation

Bills, Bruce Gordon (1978) A Harmonic and Statistical Analysis of the Topography of the Earth, Moon, and Mars. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/SM57-8B66. https://resolver.caltech.edu/CaltechTHESIS:04092012-114720525

Abstract

In chapter I a global lunar topographic map is derived from Earth based and orbital observations supplemented in areas without data by a linear autocovariance predictor. Of 2592 bins, each 5° square, 1380 (64.7% by area) contain at least one measurement. A spherical harmonic analysis to degree 12 yields a mean radius of (1737.53 ± 0.03) km (formal standard error) and an offset of the center of figure of (1.98 ± 0.06) km toward (19 ± 2)° S, (194 ± 1)° E. A Bouguer gravity map is also presented. It is confirmed that the low-degree gravity harmonics are caused primarily by surface height variations and only secondarily by lateral density variations.

In chapter II a series of models of the lunar interior are derived from topographic, gravitational, librational and seismic data. The moon departs from isostasy, even for the low-degree harmonics, with a maximum superisostatic stress of 200 bars under the major mascon basins. The mean crustal thicknesses under different physiographic regions are: mascons, 30-35 km; irregular maria, 50- 60 km; and highlands, 90-110 km. A significant correlation between lunar surface chemistry and crustal thickness suggests that regions of thicker crust are more highly differentiated. A possible mean composition consistent with our model is an anorthositic crust, underlain by a predominantly forsterite upper mantle which grades into a refractory rich lower mantle surrounding a pyrrhotite core.

In chapter III a model of martian global topography is obtained by fitting a spherical harmonic series of degree 16 to occultation, radar, spectral and photogrammetric measurements. The existing observations are supplemented in areas without data by emperical elevation estimates based on photographic data. The mean radius is (3389.92 ± 0.04) km . The corresponding mean density is (3.933 ± 0.002) g cm^(-3). The center of figure is displaced from the center of mass by (2.50 ± 0.07) km towards (62 ± 3)° S, (272 ± 3)° W. The geometric Flattening [f_g = (6.12 ± 0 .04) 10^(-3) ] is too great and the dynamic flattening [f_d (5.22 ± 0 .03) 10^(-3)] is too small for Mars to be homogeneous and hydrostatic. It is confirmed that, similar to the Moon, the martian low-degree gravity harmonics are produced primarily by surface height variations and only secondarily by lateral density variations. Maps of the global topography and Bouguer gravity are presented. These are interpreted in terms of a crustal thickness map which is consistent with gravity, topography and recent preliminary Viking seismic results. Using plausible density contrasts and an assumed zero crustal thickness at Hellas, the inferred minimum mean crustal thickness is (28 ± 4) km.

In chapter IV it is shown that the topographic variance spectra of the Earth, Moon, Mars and Venus are all very similar. The variance per harmonic degree V(H;n) decreases roughly as the inverse square of the degree, or more precisely V(H;n) ≐ V(H;O)/(n)(n+1). On the Earth and Moon this relationship has been confirmed down to scale lengths as small as L ≐ 100 m. At the other end of the spectrum, the variance appears to be deficient relative to this model for scale lengths greater than L ≐ 2000 km. The most satisfactory explanation for this phenomenon appears to be a simple equilibrium between constructional or "tectonic" processes which tend to roughen the surface uniformly at all scales, and destructional or erosive processes which tend to smooth the surface preferentially at small scales. The deficiency in the low-degree variances is attributable to visco-elastic deformation.

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