A29. Bird, P., and D. R. Williams (1990) Lack of lateral extrusion on Venus limits thickness of the crust (abstract), Eos Trans. AGU, 71, 1423.
Lateral extrusion occurs when topographic pressures drive weak lower crust out from under high topography, thereby reducing relief. The characteristic signs of this process are internally smooth, convex highlands with relatively steep flanks, and a depression of the topographic power spectrum for wavelengths below some transition value, typically at 400-1000 km. (However, the alteration of the spectrum is subtle, because high-frequency topography persists in lowlands.)
On Venus, the form of the highlands does not match this description. Aphrodite Terra is at least as rough internally as the surrounding lowlands. Ishtar Terra is bordered by marginal ridges, hence is not uniformly convex. In addition, the topographic power spectra of Aphrodite Terra, Beta Regio, and Niobe Planitia all follow the same power-law as the whole equatorial region, with a slope of b = -3.1 (fractal dimension D = 2.45) at least down to 400 km in wavelength. Therefore, we conclude that there has been little lateral extrusion, and that most of the Moho on Venus is relatively cool.
To quantify this, we model the evolution of a typical highland topographic profile (3000 km long, radius 6051-6056 km, fractal D = 1.45) for 1 Ga, assuming a stiff diabase rheology for the crust. We consider 3 types of models:
(1) Airy compensation models, which have a 40-km variation in crustal thickness, and uniform heat flow. In this case, we find that the geothermal gradient cannot exceed 10 C/km (Q = 25 mW/m2) for a minimal 0-40 km crust on our profile. Much greater crustal thicknesses are implausible, as they would require even lower Q (e.g., 20-57 km crust on this profile requires dT/dz < 5 C/km, or Q < 12.5 mW/m2). Such models cannot fit the gravity data, which indicates deeper compensation.
(2) Pratt compensation models, which have lithospheres of 40-450 km (dT/dz = 2.5-21 C/km; Q = 6-53 mW/m2) and a crust of constant thickness on our profile. In this case, we find the crust cannot exceed 25 km. Such models can fit the gravity, but the stability of such thick lithosphere is questionable. Probably, lowlands (under 6051.5 km radius) would require Airy compensation (thinner crust) to avoid lithosphere thicknesses of over 400 km.
(3) 50/50 mixed compensation models, which have a 20 km variation in the crust on our profile, and a more modest variation in Q. If dT/dz varies from 4.5-19 C/km, (Q = 11-48 mW/m2; lithosphere 38-250 km), then the thickest acceptable crust ranges from 10-29 km on our profile.
If we consider that the mean radius of Venus lies at the low end of our model profile, then the probable maximum mean crustal thickness becomes 21 km with Pratt compensation (at modal Q = 6(!) mW/m2), or 10 km with mixed compensation (at modal Q = 11 mW/m2) or Airy compensation (at Q = 19 mW/m2).