Phillip G. Resor

Inverting for Slip on Three-Dimensional Fault Surfaces Using Angular Dislocations

The increasing quality of geodetic data (synthetic aperture radar interferometry [insar] dense Global Positioning System [gps] arrays) now available to geophysicists and geologists are not fully exploited in slip-inversion procedures. Most common methods of inversion use rectangular dislocation segments to model fault ruptures and therefore oversimplify fault geometries. These geometric simplifications can lead to inconsistencies when inverting for slip on earthquake faults, and they preclude a more complete understanding of the role of fault geometry in the earthquake process. We have developed a new three-dimensional slip-inversion method based on the analytical solution for an angular dislocation in a linear-elastic, homogeneous, isotropic, half-space. The approach uses the boundary element code Poly3D that employs a set of planar triangular elements of constant displacement discontinuity to model fault surfaces. The use of triangulated surfaces as discontinuities permits one to construct fault models that better approximate curved three-dimensional surfaces bounded by curved tiplines: shapes that commonly are imaged by three-dimensional reflection seismic data and inferred from relocated aftershock data. We demonstrate the method’s ability to model three-dimensional rupture geometries by inverting for slip associated with the 1999 Hector Mine earthquake. The resulting model avoids displacement anomalies associated with the overlapping rectangular dislocations used in previous models, improving the fit to the geodetic data by 32%, and honors the observed surface ruptures, thereby allowing more direct comparisons between geologic and geodetic data on slip distributions. Online Material : Hector Mine input files and file format description.

Deformation associated with a continental normal fault system, western Grand Canyon, Arizona

Reverse-drag folds are often used to infer subsurface fault geometry in extended terrains, yet details of how these folds form in association with slip on normal fault systems are poorly understood. Detailed structural mapping and global positioning system (GPS) surveying of the Frog Fault and Lone Mountain Monocline in the western Grand Canyon demonstrate a systematic relationship between elements of the normal fault system and fold geometry. The Lone Mountain Monocline, which parallels the Frog Fault, is made up of two half-monoclinal flexures: a hanging-wall fold in which dips gradually increase toward the fault over ∼1.5 km reaching a maximum dip of 25° and a footwall fold in which dips decrease away from the fault over ∼0.5 km from a maximum of 12°. The highest dips associated with folding are found where throw on the Frog Fault and a synthetic fault are at a maximum. Lower dips are found where there is less throw on the Frog Fault and antithetic faults are present. This relationship between fault and fold geometry suggests that the folding is associated with Basin and Range extension rather than Laramide contraction. Mechanical models of normal fault-related deformation predict similar patterns of folding over planar faults of finite extent and corroborate the important role of subsidiary fault geometry in the overall pattern of deformation. Application of these models in an inverse sense yields ∼1 km estimates of down-dip extent, a result that may indicate fault confinement within the sedimentary section or weakening effects associated with folding layered strata. A general analysis illustrates that reverse-drag folds of moderate dip are expected to form in association with slip on planar faults of finite extent—a result that has the potential to impact our estimates of hydrocarbon volumes, crustal extension, and earthquake hazards associated with continental normal faults.

Constraints on the evolution of vertical deformation and Colorado River incision near eastern Lake Mead, Arizona, provided by quantitative structural mapping of the Hualapai Limestone

The 12–6 Ma Hualapai Limestone was deposited in a series of basins that lie in the path of the Colorado River directly west of the Colorado Plateau and has been deformed by an en-echelon normal fault pair (Wheeler and Lost Basin Range faults). Therefore, this rock unit represents an opportunity to study the sedimentological and structural setting over which the Colorado River first flowed after integration through western Grand Canyon and Lake Mead. In this study, we quantify the structural geometry of the Hualapai Limestone and separate the deformation into syn- and postdepositional episodes. Both the Wheeler and Lost Basin Range faults were active during Hualapai Limestone deposition, as shown by thickening of strata and fanning of time lines toward half-graben faults that bound the Hualapai subbasins. The structure is characterized by a prominent reverse-drag fold and broad, shallow syncline adjacent to the Lost Basin Range fault, and a small-magnitude reverse-drag fold and short-wavelength normal-drag fold adjacent to the Wheeler fault. We find ∼450 m of throw between the footwall and hanging-wall Hualapai Limestone sections, suggesting faulting was ongoing after Hualapai Limestone deposition ceased and during Colorado River incision. To investigate a range of possible fault geometries that may have been responsible for Hualapai Limestone deformation, we compared our structural results against surface deflections calculated by a two-dimensional (2-D) geomechanical model. While nonunique, our results are consistent with a scenario in which the Wheeler fault was surface rupturing, or nearly surface rupturing throughout deposition of the Hualapai Limestone, but was inundated at ca. 6 Ma by coalescing paleolakes in Gregg and Grand Wash Basins as sedimentation kept pace with deformation. In contrast, we find evidence suggesting the Lost Basin Range fault was deeply buried by the Hualapai Limestone and likely propagated upward and laterally to break the surface sometime after 6 Ma. Therefore, we interpret the landscape over which the Colorado River first flowed to be of low relief within the terrain bounded by the Grand Wash Cliffs, the Hiller Mountains, and subtle topographic highs to the north and south of our field area. This original low-relief depositional surface was deflected into the structure exposed today by continuing deformation by the Wheeler and Lost Basin Range faults, allowing for calculation of apparent incision rates of the modern Colorado River drainage system that spatially vary between 33 and 42 m/m.y. in the hanging wall and between 108 and 115 m/m.y. in the footwall. Hanging-wall incision rate values are similar to, but faster than, a previously published point measurement, and footwall values are similar to measured incision rates in the western Grand Canyon, suggesting the Wheeler fault system may resolve as much as ∼410 m of Colorado Plateau uplift in the last 6 m.y.

Influence of Fault Geometry on the Spatial Distribution of Long‐Term Slip with Implications for Determining Representative Fault‐Slip RatesInfluence of Fault Geometry on the Spatial Distribution of Long‐Term Slip

Determining representative slip rates of active faults is essential to seismic hazard assessment and tectonic analysis. Here, we take a two-pronged approach to determine how spatially variable slip over many earthquake cycles impacts the sliprate record at potential sites of geologic investigation near releasing stepovers. First, we use 2D parametric models to estimate the probability that a point measurement is representative of the average slip-rate for continuous strike-slip faults and those with a range of releasing stepover geometries and friction values. All models result in skewed distributions for which a randomly selected site has a higher probability of sampling a slip rate that exceeds the mean. For most configurations, individual point measurements are unlikely (p < 0.5) to yield a slip rate within +/- 1 mm/yr of the mean. The probability can be notably improved (15%-300%) by summing slip rates of overlapping segments. Second, we use 3D mechanical models of a well-studied releasing stepover along the San Jacinto fault to investigate the impact of specific fault geometries on slip-rate distribution and the implications for existing slip-rate estimates. The model-calculated dextral-slip rates are consistent with the abundant geologic slip-rate data available for this system. Although summing the slip rates at geologic sites across the stepover may produce a nonrepresentative slip rate, the summed slip rates from the model are compatible with the representative slip rate. Thus, the complete along-trace slip-rate distribution produced from the geologically consistent models provides a way to select sites for determining slip rates or interpreting isolated geologic slip-rate data. The site-specific models also illustrate how to assess the uncertainty of slip-rate data due to the spatial variability of slip rates in geometrically complex fault systems.