Displacement-Length Scaling of Faults on Earth, Mars, and Beyond

Journal of Structural Geology, 2006

Displacement-length (D/L)scaling relations for normal and thrust faults from Mars, and thrust faults from Mercury, for which sufficiently accurate measurements are available, are consistently smaller than terrestrial D/L ratios by a factor of about 5, regardless of fault type (i.e. normal or thrust). We demonstrate that D/L ratios for faults scale, to first order, with planetary gravity. In particular, confining pressure modulates:

Journal of Structural Geology, 2009

We measure throw distributions for graben-bounding normal faults from two areas on Mars to investigate fault growth, displacement-length (D max-L) scaling, and extensional strain using a complementary suite of techniques. Faults in the northern plains are inferred to be restricted at 2-3 km depth, as shown by a transition from linear scaling, with D max-L ratios of w1 Â 10 À3 , to nonlinear scaling for faults >50 km long. On the Alba Patera volcano, faults conform to linear D max-L scaling, with a D max-L ratio of w6 Â 10 À3 , consistent with more deeply penetrating faults that are not restricted at depth. These grabens accommodate larger extensional strains (w0.84%) than the faults in the northern plains (w0.23%), with a temporal change from regionally distributed to localized deformation and associated increases in D max-L ratio, extensional strain, and perhaps down-dip fault height. The results suggest that both spatial and temporal variations in extensional strain and displacement-length scaling relations, along with fault restriction, are recorded by Martian fault populations.

Faults have been identified beyond the Earth on many other planets, satellites, and asteroids in the solar system, with normal and thrust faults being most common. Faults on these bodies exhibit the same attributes of fault geometry, displacementlength scaling, interaction and linkage, topography, and strain accommodation as terrestrial faults, indicating common processes despite differences in environmental conditions, such as planetary gravity, surface temperature, and tectonic driving mechanism. Widespread extensional strain on planetary bodies is manifested as arrays and populations of normal faults and grabens having soft-linked and hardlinked segments and relay structures that are virtually indistinguishable from their Earth-based counterparts. Strike-slip faults on Mars and Europa exhibit classic and diagnostic elements such as rhombohedral push-up ranges in their echelon stepovers and contractional and extensional structures located in their near-tip quadrants. Planetary thrust faults associated with regional contractional strains occur as surface-breaking structures, known as lobate scarps, or as blind faults beneath an anticlinal fold at the surface, known as a wrinkle ridge. Analysis of faults and fault Planetary Tectonics, edited 457 458 Planetary Tectonics

Icarus, 2002

Laser Altimeter (MOLA). The absence of rift-flank uplift at the NTR is consistent with an elastic thickness, T e , of 20 km or greater at the time of rift formation. The maximum resolved shear stresses on bounding faults due to this topography do not therefore exceed 20 MPa, similar to the inferred strength of terrestrial faults. Elastic thickness estimates at VM are mostly around 50 km or greater. Therefore, for canyon widths of ∼400 km, the bounding faults of VM, if present, must be able to withstand stresses of up to approximately 100 MPa. However, if the fault-controlled sections of the canyons do not exceed 150 km in width, as suggested by geomorphological analysis, the fault strength required is only 20 MPa.

Geophysical Research Letters, 2006

Current stress solutions for Mars match the long wavelength signal of present day topography and gravity but fail to match many surface faults, including the normal faults in northern Claritas Fossae north to Tantalus and Alba Fossae. A deviatoric stress field associated with horizontal gradients of gravitational potential energy (GPE) provides an excellent fit, as measured by objective functions, to many of the normal faults in the western Martian hemisphere as well as wrinkle ridges circumferential to Tharsis; $70% of the faults have a misfit 0.1. The fit of faults to the GPEderived stress field reflects the thermal state of the planet at the times of faulting, and suggests that at such times elastic thicknesses and membrane stresses were small, and topography was supported by buoyancy forces.

Tectonophysics, 2013

Following an earthquake in a fault zone, commonly the co-seismic rupture length and the slip are measured. Similarly, in a structural analysis of major faults, the total fault length and displacement are measured when possible. It is well known that typical rupture length-slip ratios are generally orders of magnitude larger than typical fault length-displacement ratios. So far, however, most of the measured co-seismic ruptures and faults have been from different areas and commonly hosted by rocks of widely different mechanical properties (which have strong effects on these ratios). Here we present new results on length-displacement ratios from 7 fault zones in Holocene lava flows on the flanks of the volcano Etna (Italy), as well as 10 co-seismic rupture lengthslips, and compare them with fault data from Iceland. The displacement and slip data from Etna are mostly from the same fault zones and hosted by rocks with largely the same mechanical properties. For the co-seismic ruptures, the average length is 3657 m, the average slip 0.31 m, and the average length-slip ratio 19,595. For the faults, the average length is 6341 m, the average displacement 73 m, and the average lengthdisplacement ratio 130. Thus, the average rupture-slip ratio is about 150-times larger than the average length-displacement ratio. We propose a model where the differences between the length-slip and the length-displacement ratios can be partly explained by the dynamic Young's modulus of a fault zone being 10 1-2-times greater than its static modulus. In this model, the dynamic modulus controls the length-slip ratios whereas the static modulus controls the length-displacement ratio. We suggest that the common aseismic slip in fault zones is partly related to adjustment of the short-term seismogenic length-slip ratios to the long-term length-displacement ratios. Fault displacement is here regarded as analogous to plastic flow, in which case the long-term displacement can be very large so long as sufficient shear stress concentrates in the fault.

Geophysical Research Letters, 2002

Rates of deformation are estimated from exposed normal faults within the Tempe Terra extensional province, Mars, through an analysis that incorporates fault segment linkage and utilizes regional observations of displacementlength relationships measured from Mars Orbiter Laser Altimeter topographic data. Moment rates (from 10 14-10 16 N-m/yr), strain rates (10 À12-10 À11 yr À1) and rifting velocities ($0.003 mm/yr) are comparable to rates of deformation on stable plate interiors of Earth. The calculated low rates of rifting may result from the poorly constrained timing of deformation on Mars. Cumulative moment release estimates decrease linearly with time from Noachian ($1 Â 10 25 N-m) to Early Hesperian ($6 Â 10 24 N-m) and Late Hesperian-Early Amazonian ($1 Â 10 24). These results indicate that a portion of Tharsisrelated deformation remained localized within the Tempe Rift throughout much of Martian history, and provide important constraints for models of Martian mantle convection.

Following an earthquake in a fault zone, commonly the co-seismic rupture length and the slip are measured. Similarly, in a structural analysis of major faults, the total fault length and displacement are measured when possible. It is well known that typical rupture length -slip ratios are generally orders of magnitude larger than typical fault length-displacement ratios.

Journal of Structural Geology, 1992

lt is observed that the amount of displacement (d) on a fault is proportional to the mapped trace length L. The exact form of the fault scaling relationship, i.e. d = f(L), is still a subject of some disagreement. A number of workers have interpreted data from individual data sets as indicating a linear relationship between d and L. However, these individual data sets have large scatter and a limited range of scale, so their interpretations are not fully conclusive. Other workers have interpreted combinations of different data sets, taken together, and concluded that the d vs L scaling relationship is non-linear. Fault growth models, however, indicate that the scaling relationship should depend on rock properties so correlations using combined data sets may be questionable.

Geophysical Research Letters, 2005

1] We analyze the magnitudes and distributions of displacements on normal faults that are contained within a five layer marly-limestone/silty-clay sedimentary sequence. Observations of bedding plane exposures of the wellexposed mechanically isolated faults reveal a systematic strong decrease in the displacement gradient related to the horizontal lengthening of faults growing at constant height. Because mechanically heterogeneous sequences produce populations of vertically restricted faults having a large range of aspect ratios (length/downdip height), much of the scatter on a displacement-length diagram can be attributed to nonlinear growth paths. Our results demonstrate the significant influence of layering on fault scaling relations, growth, and maximum dimensions.