Fault spacing in continental strike-slip shear zones

Highlights

• Strike-slip shear zones are often comprised of evenly-spaced faults.

• An analytical model is established to reveal controls on fault spacing in crust.

• Increasing brittle layer or lower crust thickness may increase fault spacing.

• Inverse relation between fault strength or lower crust viscosity and fault spacing.

• Lower crust viscosity in California, New Zealand and central Tibet is estimated.

Abstract

Strike-slip shear zones with sub-parallel arrays of evenly-spaced faults are widely observed in nature, but the controls on the spacing between major faults are unclear. We analyze a 2-D model and develop a scaling law relating the fault spacing to structural and rheological parameters in the continental crust. We find that fault spacing positively correlates with brittle-layer thickness, viscous lower crust thickness, and strength contrast between active faults and surrounding intact blocks; and is inversely correlative with lower crust viscosity. This is corroborated for either a zero-shear traction (decoupled) or a prescribed velocity (coupled) basal boundary condition in the 2-D analytical solution. The zero-shear traction boundary condition represents low viscosities in the lowermost crust or the topmost mantle that may decouple deformations from mantle flow. The prescribed velocity boundary condition emphasizes basal drag tractional forces imparted on the lower crust by a strong mantle. For a viscous layer that is thicker than half of its average fault spacing, models with either of the boundary conditions produce the same results. Otherwise, a thinner, viscous layer with a linear-velocity condition tends to produce smaller fault spacings than a no-shear model, all else being equal. These theoretical models are comparted to data from shear zones in California, the Marlborough Fault Zone in New Zealand and central Tibet. Modeling indicates that the effective viscosity of the viscous layer underlying the brittle layer in all of the selected areas is $2\times {10}^{20}$ to $4\times {10}^{21}$ Pa⋅s. The subducted oceanic plate attached to the lower crust of the eastern Marlborough Fault Zone also appears to influence fault spacing in the overriding plate.

Introduction

Strike-slip faults are important features of plate tectonics on Earth (Wilson, 1965). Finite horizontal displacements on strike-slip faults at continental plate boundaries can reach several hundreds of kilometers, e.g., San Andreas fault (SAF, California) and Alpine fault (New Zealand). It is often assumed that such major strike-slip faults (i.e., continental transform faults) cut through entire lithosphere (Roy and Royden, 2000a). In contrast to a deep-penetrating transform fault, intraplate strike-slip (transcurrent) faults are often assumed to be limited to the thickness of crust and manifest as parallel arrays of nearly uniform spacing between neighboring faults, e.g., the East Californian Shear Zone (ECSZ) and the strike-slip fault systems surrounding Tibet (Yin and Taylor, 2011). Zuza et al. (2017) observed that active fault spacing in the ECSZ is tens of kilometers while in the Tibetan Plateau it is hundreds of kilometers. Why fault spacing varies with different tectonic settings is not well understood.

The concept of stress-shadowing, which is widely used in explanations of extensional-joint spacing, was introduced by Yin et al. (2016) in the context of the mechanics of evenly-spaced faults. This mechanism was further developed by Zuza et al. (2017) to explain the spacing of faults in California and the India-Asia collision zone. Stress-shadow theory relates shear stress (${\sigma }_{xy}$) to geometrical parameters (x, distance from the fault; h, depth of the fault) through a power law according to ${\sigma }_{xy}(x)={\sigma }^{bc}+({\sigma }^{bc}-{\sigma }^f)[\frac{|x{|}^{l_1/l_2}}{{(|x{|}^{l_1}+h^{l_1})}^{1/l_2}}-1]$ where ${\sigma }^{bc}$ and ${\sigma }^f$ are the far-field stress boundary condition and the vertically-averaged stress on the fault plane respectively. However, the exact values of the power-law exponent ($l_1$ and $l_2$) are unknown. Zuza et al. (2017) calibrated the exponent using sandbox modeling and suggested a linear relationship, i.e., both exponents, $l_1$ and $l_2$, equal to one. It is not clear how sandbox results translate to other systems and how properties of the lower crust control brittle deformation patterns. Our analysis includes the effects of lower crustal flow to determine the expression of lower-crustal properties in surface strain distributions.

Roy and Royden (2000a) presented an analytic model of the deformation of a stratified, viscoelastic crust driven by basal velocity boundary conditions. Their results showed that, a strong viscosity contrast between an upper and lower crust tends to produce a wide deformation zone. A relatively weak upper crust, if it reaches the yield stress, should have a more localized deformation zone than the case of a strong upper crust. From that perspective, in the limit of pure elastic deformation, we would expect faults to develop everywhere. Since the study assumes a fixed, shallow faulting-depth without considering pressure-dependence of the yield criterion, such a conclusion may only apply to surficial faults. We note that the model of Roy and Royden (2000a) is focused on plate boundary faults and the loading is applied from the underlying mantle. This choice may not be appropriate for intracontinental transcurrent faults overlying a weak lower crust. Rolandone and Jaupart (2002) proposed a model driven from far field stresses and suggested the fault depth and vertical variations in crustal rheology control deformation patterns. They found a deep fault or large vertical rheological variations help localize deformation on a pre-defined fault zone. However, scaling relationships for fault spacing were not explicitly examined in either of the studies.

In this contribution we first develop a scaling law for the emergent fault spacing in a stratified visco-plastic model. The model is composed of a brittle upper crust and a viscous lower crust. Faults are assumed to cut through the brittle upper layer and the brittle deformation terminates in the viscous layer (Fig. 1). The difficulty for the physical model lies in deriving a functional form of shear stress ${\sigma }_{zy}$ at the bottom of a brittle layer. This basal shear stress ${\sigma }_{zy}$, in turn, influences the average shear stress ${\sigma }_{xy}$ in the brittle crust (Savage and Lachenbruch, 2003). How shear stress, ${\sigma }_{xy}$, evolves from a fault towards the far field is the basis for the stress-shadow theory used by Zuza et al. (2017). Our analytical solutions demonstrate that the basal shear stress is a function of the aspect ratios of a model. We compare our scaling theory for fault spacing against field observations from the SAF system in California, the Marlborough Fault Zone (MFZ) in New Zealand and shear zones in the central Tibet. Modeling of fault spacing enables further refinement of viscosity parameters in the lower crust beneath those shear zones. Investigating structural parameters, e.g., seismogenic thickness, viscous layer thickness, and fault spacing, also sheds light on the coupling state between shallower brittle deformation and deep dynamics.