EXTENSIONAL BOUDINAGE OF COOLING LITHOSPHERE

A planetary process investigated by Maria Zuber early in her career was the deformation of viscous layered lithosphere in compression and extension. Starting with a single strong layer with power-law creep rheology over a weaker substrate, she systematically explored the wavelengths and growth rates of instabilities leading to boudinage and folding, extending the semi-analytic, infinitesimal perturbative methods of Fletcher [1974] to multiple layers representing differing crust and mantle rheologies and continuous strength envelopes. Such methods placed constraints on the thermal structure and tectonic history of Earth, Venus, and Mars. As finite element methods became available on workstations, she and her colleagues considered the behavior of layered rheologies and growth of faults in finite extension.

Following the discovery of 150-250-km-wavelength cross-grain gravity lineations in the Pacific Plate [Haxby, 1986], some attempted to explain these as extensional instabilities under plate driving forces [Winterer and Sandwell, 1987], while others proposed small-scale convection as the underlying mechanism [e.g., Buck and Parmentier, 1986]. Plate motions, mantle rheology, stress, and thermal state in the past are poorly constrained. Whether diffuse extension or small-scale convection or some other mechanism is the prime source of the short wavelength undulations remains an open question [Wessel and Bercovici, 1996; Sandwell and Fialko, 2004; Forsyth et al., 2006].

In any case, finite-amplitude deformation of a cooling, extending lithosphere does not lend itself to simple analytic models, and is complicated by the coupling of thermal and density anomalies to finite strain with Coulomb strength envelopes under gravitational loads. Such a regime may exist not only at mid-ocean ridges but in transient spreading centers of the terrestrial planets and icy moons.

This paper will show that a multi-layer approximation to young oceanic lithosphere tends to have the highest growth rates of instabilities at wavelengths 4x lithospheric thickness, casting doubt on the extensional boudinage mechanism for wavelengths in excess of 150 km. Model strength envelopes that achieve the observed Pacific Plate wavelength have low growth rates. We also review the results of finite-element models for a case applicable to the oceanic problem.