Michele L. Cooke

Community Fault Model (CFM) for Southern California

We present a new three-dimensional model of the major fault systems in southern California. The model describes the San Andreas fault and associated strike- slip fault systems in the eastern California shear zone and Peninsular Ranges, as well as active blind-thrust and reverse faults in the Los Angeles basin and Transverse Ranges. The model consists of triangulated surface representations (t-surfs) of more than 140 active faults that are defined based on surfaces traces, seismicity, seismic reflection profiles, wells, and geologic cross sections and models. The majority of earthquakes, and more than 95% of the regional seismic moment release, occur along faults represented in the model. This suggests that the model describes a comprehen- sive set of major earthquake sources in the region. The model serves the Southern California Earthquake Center (SCEC) as a unified resource for physics-based fault systems modeling, strong ground-motion prediction, and probabilistic seismic hazards assessment.

Fracture localization along faults with spatially varying friction

Opening-mode splay fractures have been observed within clusters near fault tips. The spatial distribution of splay fractures along faults influences fluid flow and lends insight into the mechanical processes of faulting. Slip gradients along faults produce stress concentrations which promote the development of opening-mode splay fractures along faults. Since the slip distribution depends on the distribution of frictional strength along faults, spatial variations in the frictional properties may influence fracture localization. Variations in friction coefficient along faults can reduce the stress singularities at fault tips and promote the development of multiple fractures inwards from the fault tips. The conditions that promote splay crack localization are examined using analytical and numerical fault models. Single splay fractures develop at locations of abrupt friction coefficient change and/or at fault tips when the friction coefficient near the tips is less than a critical value. Fault models with linearly increasing friction coefficient toward the fault tip promote the development of multiple splay fractures within broad zones near the tip.

Role of shale thickness on vertical connectivity of fractures: application of crack-bridging theory to the Austin Chalk, Texas

Abstract Contrasting material properties of alternating chalk and shale layers control vertical connectivity of fractures. Our field observations within the Austin Chalk, Texas indicate that: (1) the majority of vertical fractures occur in chalk layers and abut against contacts with shale layers, (2) thicker shale layers have greater resistance to fracture propagation than thinner shale layers. From these observations we hypothesize both the resistance of shale to fracturing and the thickness of shale layers may inhibit fracture propagation across the shale and into the next chalk layer. We model crack propagation within a three-layered system (brittle chalk:fracture resistant shale:brittle chalk). The modeled crack extends across the shale, but closing tractions applied to the crack segment within the shale layer simulate resistance of shale to fracturing. The crack-tip lies a short distance within the unfractured chalk layer simulating a coplanar flaw with potential to propagate. If the stress intensity factor at the flaw exceeds the chalk fracture toughness, the crack propagates, thereby bridging and eventually rupturing the shale layer. For any chalk thickness, there is a critical shale thickness above which fractures cross the shale layer and below which fractures arrest at shale. Finite Element Method (FEM) analysis evaluates the influence of shale ductility within the chalk: shale: chalk system. Although remote and fluid pressure driven fractures produce identical stress intensity factors in elastic chalk/shale systems, lower driving stresses are required to propagate fluid pressure driven fractures through a system ductile shale layers than fractures under remote tension.

Bedding-plane slip in initial stages of fault-related folding

Abstract Frictional slip along bedding planes contributes to fault-related folding of layered rocks. We use numerical experiments to investigate the deformation of frictional bedding planes near dipping faults under layerparallel contraction and extension. Within the numerical experiments, contraction boundary conditions produce asymmetric anticlines and extension produces asymmetric synclines. The fold shape may be used to infer dip of the underlying fault in situations where the fault may not be observable. Additionally, sense of slip along bedding planes may indicate proximity to the fault tip. Under uniform remote tectonic strain, fault slip induces deformation in both the hangingwall and the footwall. At depths as shallow as 1 km there is no significant difference between fold amplitudes in the hangingwall and the footwall; this result is contrary to many kinematic models currently in use. Kinematic models of fault-related folds commonly include the development of flat-ramp and flat-ramp-flat fault geometries which may be attributed to initial ramp thrusting and later flat development. Our mechanical models show that fault flats may be produced from fault ramps due to slip along frictional bedding planes near the thrust fault tips. Our numerical experiments also evaluate joint initiation; joints perpendicular to bedding are promoted in extensional environments. We compare the results of the mechanical model to kinematic models of fault-propagation folds and conclude that mechanical models offer important insights to better understand the folding process.

Stratigraphic controls on vertical fracture patterns in Silurian dolomite, northeastern Wisconsin

Vertical opening-mode fractures are mapped on quarry walls to assess the stratigraphic controls on fracture patterns in the relatively undeformed Silurian dolomite of northeastern Wisconsin. Our two-stage study uses maps of vertical fractures to assess the effectiveness of various types of stratigraphic horizons (e.g., organic partings or cycle-bounding mud horizons) in terminating opening-mode fractures. First, the mechanical stratigraphy of the exposures is interpreted from the observed fracture pattern. Both visual inspection and a newly developed quantitative method are employed to identify effective mechanical interfaces. The two methods show similar results, confirming the validity of qualitative visual inspection. The second stage of our study stochastically predicts mechanical stratigraphy and subsequent fracture pattern from empirical relationships between the observed sedimentary stratigraphy and the interpreted mechanical stratigraphy. For example, 63% of cycle-bounding mud horizons within the inner-middle and middle shelf facies associations serve as mechanical interfaces. These empirical percentages are input to a Monte Carlo analysis of 50 stochastic realizations of mechanical stratigraphy. Comparisons of the stochastically predicted and interpreted mechanical stratigraphy yield errors ranging from 13 to 33%. This method yields far better results than assuming that all stratigraphic horizons act as mechanical interfaces. The methodology presented in this article demonstrates an improved prediction of fracture pattern within relatively undeformed strata from both complete characterization of sedimentary stratigraphy and understanding mechanical controls on fracturing.

Fracture propagation paths under mixed mode loading within rectangular blocks of polymethyl methacrylate

Mixed mode I + III loading of a fracture front results in out-of-plane propagation into echelon stepping fractures. Because a planar fracture geometry is the exception rather than the rule, and because the introduction of even a minor component of mode II or III loading is known to promote out-of-plane propagation, an understanding of mixed mode fracture growth is imperative to analyze fracture behavior. We have loaded cracks in mixed mode I + III within polymethyl methacrylate (PMMA or Plexiglas) rectangular blocks resembling conceptual fracture mechanics models of mixed mode loading and have analyzed the resulting geometries. The observed angle of twist of echelon fractures from the parent crack plane increases with the ratio KIII/KI and falls below theoretical predictions. Fracture propagation paths depend not only on the load ratio applied but also on sample geometry, loading configuration, and interaction among growing fractures. Sample geometry and loading configuration are approximately accounted for using analytical determinations of the stress intensity factors. We propose that interaction among growing fractures may contribute to the discrepancy between theoretically predicted twist angles and those observed in these and other mixed mode I + III experiments. Analysis of these experimental results has motivated the design of a new sample and loading configuration to test the propagation paths of uniformly loaded mixed mode I + III fractures.

Why blind thrust faults do not propagate to the Earth's surface: Numerical modeling of coseismic deformation associated with thrust‐related anticlines

High fault-tip stress concentrations are associated with coseismic slip on blind thrust faults and suggest that these structures should readily propagate to the Earths surface. Seismic profiles of blind-thrust-related earthquakes reveal diffuse zones of aftershocks surrounding the fault tip which are attributed to inelastic deformation, such as flexural-slip or extensional fracturing. The complex interaction between blind thrust faults and secondary structures may control the evolution of blind thrust systems. The influence of bedding-plane slip on fault propagation is simulated with numerical models using the boundary element method. We use two parameters to estimate the tendency for thrust fault propagation, (1) the mode II stress intensity factor and (2) the maximum Coulomb stress near the fault tip. Calculations from both analyses suggest that shallow thrust faults may exhibit an increased tendency to propagate as a result of interaction with the Earths surface and slip along bedding planes above the fault tip and a decreased tendency to propagate due to slip along bedding planes at or below the fault tip. Our results demonstrate that the magnitude and style of inelastic deformation in active fault systems control fault propagation.

Evidence for temporally changing mechanical stratigraphy and effects on joint-network architecture

Previous studies of jointing in sedimentary rocks have shown that joint-network archi- tecture is controlled by mechanical stratigraphy, which is described by (1) the thickness and rigidity of stratigraphic units and (2) the nature of interfaces between beds. Using joint pattern to infer rigidity contrast between beds is complicated by the possibility that material properties of the beds may change between fracturing events. Observation of both an early bed-contained joint set and a differently oriented late throughgoing joint set in the same beds of growth strata in the Oliana anticline in the Spanish Pyrenees may reflect changing mechanical properties (i.e., via diagenesis) during the folding process. Using a Schmidt hammer, we assess the rigidity contrast between the individual units and show that the present-day contrast is not great enough to terminate joints at interfaces. This result is consistent with an interpretation that the late-stage throughgoing joints formed in strata with conditions similar to those of the present day and that the early bed-contained joints formed when the rigidity contrast between beds was significantly greater than that of the present day. For example, differential diagenesis rates between layers of differing grain size would produce temporally changing mechanical stratigraphy. We propose that changes in mechanical stratigraphy may have previously been unrec- ognized in other stratigraphic sections and that these changes affect joint-network archi- tecture and subsequent fluid-flow pathways.

San Andreas fault geometry through the San Gorgonio Pass, California

Three-dimensional numerical models are needed to investigate the role of nonvertical strike-slip fault segments on the deformation within restraining bends. Numerical models simulate geologic deformation of two alternative three-dimensional present-day configurations for the San Andreas fault through the restraining bend within the San Gorgonio Pass region (SGPR) in Southern California. Both models produce decreasing strike-slip rates southward along the San Bernardino strand of the San Andreas fault, similar to geologic data. The north-dipping San Andreas fault model better matches the available strike-slip data as well as the geologic uplift data for the southern San Bernardino Mountains than the vertical San Andreas fault model. We conclude that a north-dipping fault configuration is preferred for models of the San Andreas fault in the SGPR. The complexity of the active fault geometry at the SGPR promotes the transfer of strike slip from the San Andreas fault to the nearby but unconnected San Jacinto fault. Slip rates and uplift patterns are sensitive to fault geometry within strike-slip restraining bends.

Effects of Nonplanar Fault Topology and Mechanical Interaction on Fault-Slip Distributions in the Ventura Basin, California

To assess the control of fault geometry and mechanical interactions on fault-slip distributions in a complex natural system, we present results from three- dimensional mechanical models incorporating both nonplanar and rectangular planar representations of active faults within the Ventura basin region of southern California. We find that the incorporation of geologically constrained nonplanar fault surfaces into numerical models of active deformation results in a better match to available geologic slip-rate data than models utilizing rectangular planar fault surfaces. The model results demonstrate that nonplanar fault geometry and mechanical interactions exert a strong control on resultant slip distributions. Additionally, we find that slip rates at most locations along the surface trace of Ventura faults are not likely to rep- resent average values for the entire fault surface. We propose that results from three- dimensional mechanical models using realistic (i.e., nonplanar) fault geometry can be used to both predict slip rates at specific locations and determine whether existing site- specific slip-rate estimates are representative of average fault-slip rates. Although geo- metric irregularities along-fault surfaces should resist slip, planar faults can have lesser slip than nonplanar faults due to the differing mechanical interactions among nearby faults in the two representations. This suggests that models using simplified or planar fault geometry are likely to inaccurately simulate regional deformation. We assert that detailed knowledge of three-dimensional fault shape as well as the geometry and con- figuration of deep fault intersections is essential for accurate seismic hazard char- acterization of regions of complex faulting such as the Ventura basin of southern California.