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S.H. Hickman

Publications and source records attributed to S.H. Hickman.

9 recordsLinked to original sources
USGS2007

Integrating laboratory creep compaction data with numerical fault models: A Bayesian framework

[1] We developed a robust Bayesian inversion scheme to plan and analyze laboratory creep compaction experiments. We chose a simple creep law that features the main parameters of interest when trying to identify rate-controlling mechanisms from experimental data. By integrating the chosen creep law or an approximation thereof, one can use all the data, either simultaneously or in overlapping subsets, thus making more complete use of the experiment data and propagating statistical variations in the data through to the final rate constants. Despite the nonlinearity of the problem, with this technique one can retrieve accurate estimates of both the stress exponent and the activation energy, even when the porosity time series data are noisy. Whereas adding observation points and/or experiments reduces the uncertainty on all parameters, enlarging the range of temperature or effective stress significantly reduces the covariance between stress exponent and activation energy. We apply this methodology to hydrothermal creep compaction data on quartz to obtain a quantitative, semiempirical law for fault zone compaction in the interseismic period. Incorporating this law into a simple direct rupture model, we find marginal distributions of the time to failure that are robust with respect to errors in the initial fault zone porosity.

Journal of Geophysical Research B: Solid Earth↗
USGS2004

Stress-induced, time-dependent fracture closure at hydrothermal conditions

Time-dependent closure of fractures in quartz was measured in situ at 22–530°C temperature and 0.1-150 MPa water pressure. Unlike previous crack healing and rock permeability studies, in this study, fracture aperture is monitored directly and continuously using a windowed pressure vessel, a long-working-distance microscope, and reflected-light interferometry. Thus the fracture volume and geometry can be measured as a function of time, temperature, and water pressure. Relatively uniform closure occurs rapidly at temperatures and pressures where quartz becomes significantly soluble in water. During closure the aperture is reduced by as much as 80% in a few hours. We infer that this closure results from the dissolution of small particles or asperities that prop the fracture open. The driving force for closure via dissolution of the prop is the sum of three chemical potential terms: (1) the dissolution potential, proportional to the logarithm of the degree of undersaturation of the solution; (2) the coarsening potential, proportional to the radius of curvature of the prop; and (3) the pressure solution potential, proportional to the effective normal stress at the contact between propping particles and the fracture wall. Our observations suggest that closure is controlled by a pressure solution-like process. The aperture of dilatant fractures and microcracks in the Earth that are similar to those in our experiments, such as ones generated from thermal stressing or brittle failure during earthquake rupture and slip, will decrease rapidly with time, especially if the macroscopic stress is nonhydrostatic.

Journal of Geophysical Research B: Solid Earth↗
USGS2003

On the expected relationships among apparent stress, static stress drop, effective shear fracture energy, and efficiency

We consider expected relationships between apparent stress τ a and static stress drop Δτ s using a standard energy balance and find τ a = Δτ s (0.5 - ξ), where ξ is stress overshoot. A simple implementation of this balance is to assume overshoot is constant; then apparent stress should vary linearly with stress drop, consistent with spectral theories (Brune, 1970) and dynamic crack models (Madariaga, 1976). Normalizing this expression by the static stress drop defines an efficiency η sw = τ s a/Δτ s as follows from Savage and Wood (1971). We use this measure of efficiency to analyze data from one of a number of observational studies that find apparent stress to increase with seismic moment, namely earthquakes recorded in the Cajon Pass borehole by Abercrombie (1995). Increases in apparent stress with event size could reflect an increase in seismic efficiency; however, η sw for the Cajon earthquakes shows no such increase and is approximately constant over the entire moment range. Thus, apparent stress and stress drop co-vary, as expected from the energy balance at constant overshoot. The median value of η sw for the Cajon earthquakes is four times lower than η sw for laboratory events. Thus, these Cajon-recorded earthquakes have relatively low and approximately constant efficiency. As the energy balance requires η sw = 0.5 - ξ, overshoot can be estimated directly from the Savage-Wood efficiency; overshoot is positive for Cajon Pass earthquakes. Variations in apparent stress with seismic moment for these earthquakes result primarily from systematic variations in static stress drop with seismic moment and do not require a relative decrease in sliding resistance with increasing event size (dynamic weakening). Based on the comparison of field and lab determinations of the Savage-Wood efficiency, we suggest the criterion η sw > 0.3 as a test for dynamic weakening in excess of that seen in the lab.

Bulletin of the Seismological Society of America↗
USGS2001

Earthquake stress drop and laboratory-inferred interseismic strength recovery

We determine the scaling relationships between earthquake stress drop and recurrence interval t r that are implied by laboratory-measured fault strength. We assume that repeating earthquakes can be simulated by stick-slip sliding using a spring and slider block model. Simulations with static/kinetic strength, time-dependent strength, and rate- and state-variable-dependent strength indicate that the relationship between loading velocity and recurrence interval can be adequately described by the power law V L ∝ t r n where n≈−1. Deviations from n=−1 arise from second order effects on strength, with n>−1 corresponding to apparent time-dependent strengthening and n<−1 corresponding to weakening. Simulations with rate and state-variable equations show that dynamic shear stress drop Δτ d scales with recurrence as d Δτ d / d ln t r ≤σ e ( b-a ), where σ e is the effective normal stress, μ=τ/σ e , and ( a-b )= d μ ss / d ln V is the steady-state slip rate dependence of strength. In addition, accounting for seismic energy radiation, we suggest that the static shear stress drop Δτ s scales as d Δτ s / d ln t r ≤σ e (1 +ζ)( b-a ), where ζ is the fractional overshoot. The variation of Δτ s with ln t r for earthquake stress drops is somewhat larger than implied by room temperature laboratory values of ζ and b-a . However, the uncertainty associated with the seismic data is large and the discrepancy between the seismic observations and the rate of strengthening predicted by room temperature experiments is less than an order of magnitude.

Journal of Geophysical Research B: Solid Earth↗
USGS2000

Pore fluid pressure, apparent friction, and Coulomb failure

Many recent studies of stress-triggered seismicity rely on a fault failure model with a single free parameter, the apparent coefficient of friction, presumed to be a material constant with possible values 0 ≤ μ′ ≤ 1. These studies may present a misleading view of fault strength and the role of pore fluid pressure in earthquake failure. The parameter μ′ is intended to incorporate the effects of both friction and pore pressure, but is a material constant only if changes in pore fluid pressure induced by changes in stress are proportional to the normal stress change across the potential failure plane. Although specific models of fault zones permit such a relation, neither is it known that fault zones within the Earth behave this way, nor is this behavior expected in all cases. In contrast, for an isotropic homogeneous poroelastic model the pore pressure changes are proportional to changes in mean stress, μ′ is not a material constant, and −∞ ≤ μ′ ≤ +∞. Analysis of the change in Coulomb failure stress for tectonically loaded reverse and strike-slip faults shows considerable differences between these two pore pressure models, suggesting that such models might be distinguished from one another using observations of triggered seismicity (e.g., aftershocks). We conclude that using the constant apparent friction model exclusively in studies of Coulomb failure stress is unwise and could lead to significant errors in estimated stress change and seismic hazard.

Journal of Geophysical Research B: Solid Earth↗