Rate and state variable friction laws: Estimation of model parameters for slip velocity dependence at coseismic slip rates

The frictional behavior of rocks in the laboratory is reasonably well described by rate- and state-variable friction laws, which reproduce a rich variety of natural phenomena when used in models of earthquakes. Despite the widespread adoption of the rate and state formalism in earthquake mechanics, the physical mechanisms that occur at microscopic contacting asperities on the sliding surface, which give rise to the observed rate and state effects, are still poorly understood. In an attempt to identify these underlying mechanisms, a series of nanoindentation experiments on quartz, an abundant mineral in the earth’s crust, was conducted. These experiments demonstrate the utility of using continuous stiffness measurements as a means of obtaining reliable indentation creep data on hard materials like quartz at room temperature. The projected area of indentation in quartz increases linearly with the logarithm of the time of indentation, in agreement with the increase in real area of contact with log time inferred from slide-hold-slide friction experiments on quartz rocks. However, the increase in fractional area with time in the indentation tests was larger than that inferred from friction experiments by a factor of 1.7. Differences between the rates of fractional area increase in the two tests may indicate that the increase in contact area during the hold portion of slide-hold-slide tests was modulated by slip that occurs during reloading after the hold, as was observed for other materials. The nanoindentation results suggest that the increase in frictional strength (i.e., the increase of state in the rate- and state-variable friction laws) during slide-hold-slide friction experiments was caused by creep of the highly stressed asperity contacts.

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Mixed state variable friction laws: Some implications for experiments and a stability analysis

Geophysical Research Letters ◽

10.1029/gl015i011p01243 ◽

1988 ◽

Vol 15 (11) ◽

pp. 1243-1246 ◽

Cited By ~ 11

Author(s):

Franklin G. Horowitz

Keyword(s):

Stability Analysis ◽

Mixed State ◽

Friction Laws ◽

State Variable ◽

Variable Friction

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A flexible framework for sequential estimation of model parameters in computational hemodynamics

Advanced Modeling and Simulation in Engineering Sciences ◽

10.1186/s40323-020-00186-x ◽

2020 ◽

Vol 7 (1) ◽

Author(s):

Christopher J. Arthurs ◽

Nan Xiao ◽

Philippe Moireau ◽

Tobias Schaeffter ◽

C. Alberto Figueroa

Keyword(s):

Unscented Kalman Filter ◽

Three Dimensional ◽

Synthetic Data ◽

Sequential Estimation ◽

Wall Material ◽

Patient Specific ◽

Model Parameters ◽

Computational Framework ◽

Lumped Parameter ◽

Estimation Of Model Parameters

AbstractA major challenge in constructing three dimensional patient specific hemodynamic models is the calibration of model parameters to match patient data on flow, pressure, wall motion, etc. acquired in the clinic. Current workflows are manual and time-consuming. This work presents a flexible computational framework for model parameter estimation in cardiovascular flows that relies on the following fundamental contributions. (i) A Reduced-Order Unscented Kalman Filter (ROUKF) model for data assimilation for wall material and simple lumped parameter network (LPN) boundary condition model parameters. (ii) A constrained least squares augmentation (ROUKF-CLS) for more complex LPNs. (iii) A “Netlist” implementation, supporting easy filtering of parameters in such complex LPNs. The ROUKF algorithm is demonstrated using non-invasive patient-specific data on anatomy, flow and pressure from a healthy volunteer. The ROUKF-CLS algorithm is demonstrated using synthetic data on a coronary LPN. The methods described in this paper have been implemented as part of the CRIMSON hemodynamics software package.

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Mixture of Inverse Weibull and Lognormal Distributions: Properties, Estimation, and Illustration

Mathematical Problems in Engineering ◽

10.1155/2015/526786 ◽

2015 ◽

Vol 2015 ◽

pp. 1-8 ◽

Cited By ~ 2

Author(s):

K. S. Sultan ◽

A. S. Al-Moisheer

Keyword(s):

Information Matrix ◽

Real Data ◽

Likelihood Method ◽

Model Parameters ◽

Component Mixture ◽

Data Set ◽

Hazard Functions ◽

Lognormal Distributions ◽

Proposed Model ◽

Estimation Of Model Parameters

We discuss the two-component mixture of the inverse Weibull and lognormal distributions (MIWLND) as a lifetime model. First, we discuss the properties of the proposed model including the reliability and hazard functions. Next, we discuss the estimation of model parameters by using the maximum likelihood method (MLEs). We also derive expressions for the elements of the Fisher information matrix. Next, we demonstrate the usefulness of the proposed model by fitting it to a real data set. Finally, we draw some concluding remarks.

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Complex Slip Distribution of the 2021 Mw 7.4 Maduo, China, Earthquake: An Event Occurring on the Slowly Slipping Fault

Seismological Research Letters ◽

10.1785/0220210226 ◽

2021 ◽

Author(s):

Rumeng Guo ◽

Hongfeng Yang ◽

Yu Li ◽

Yong Zheng ◽

Lupeng Zhang

Keyword(s):

Slip Rate ◽

Slip Distribution ◽

Seismic Gap ◽

Seismogenic Fault ◽

Coseismic Slip ◽

Slip Rates ◽

Kunlun Mountain ◽

Coulomb Failure ◽

Main Fault ◽

Large Earthquakes

Abstract The 21 May 2021 Maduo earthquake occurred on the Kunlun Mountain Pass–Jiangcuo fault (KMPJF), a seismogenic fault with no documented large earthquakes. To probe its kinematics, we first estimate the slip rates of the KMPJF and Tuosuo Lake segment (TLS, ∼75 km north of the KMPJF) of the East Kunlun fault (EKLF) based on the secular Global Positioning System (GPS) data using the Markov chain Monte Carlo method. Our model reveals that the slip rates of the KMPJF and TLS are 1.7 ± 0.8 and 7.1 ± 0.3 mm/yr, respectively. Then, we invert high-resolution GPS and Interferometric Synthetic Aperture Radar observations to decipher the fault geometry and detailed coseismic slip distribution associated with the Maduo earthquake. The geometry of the KMPFJ significantly varies along strike, composed of five fault subsegments. The most slip is accommodated by two steeply dipping fault segments, with the patch of large sinistral slip concentrated in the shallow depth on a simple straight structure. The released seismic moment is ∼1.5×1020 N·m, equivalent to an Mw 7.39 event, with a peak slip of ∼9.3 m. Combining the average coseismic slip and slip rate of the main fault, an earthquake recurrence period of ∼1250−400+1120 yr is estimated. The Maduo earthquake reminds us to reevaluate the potential of seismic gaps where slip rates are low. Based on our calculated Coulomb failure stress, the Maduo earthquake imposes positive stress on the Maqin–Maqu segment of the EKLF, a long-recognized seismic gap, implying that it may accelerate the occurrence of the next major event in this region.

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