Bayesian inference and Markov chain Monte Carlo based estimation of a geoscience model parameter

The critical slip distance in rate and state model for fault friction in the study of potential earthquakes can vary wildly from micrometers to few meters depending on the length scale of the critically stressed fault. This makes it incredibly important to construct an inversion framework that provides good estimates of the critical slip distance purely based on the observed acceleration at the seismogram. The framework is based on Bayesian inference and Markov chain Monte Carlo. The synthetic data is generated by adding noise to the acceleration output of spring-slider-damper idealization of the rate and state model as the forward model.

Bayesian inference and Markov chain Monte Carlo based estimation of critical slip distance parameter in rate and state model for fault friction

We present an algorithmic framework to solve an inverse problem using Bayesian inference and Markov chain Monte Carlo sampling. The input of the inverse problem is the acceleration of the slipping seismogenic fault and the output is the probability distribution of the critical slip distance parameter of the rate and state model for fault friction.

A framework to quantify uncertainty in critical slip distance in rate and state friction model for earthquakes

We arrive at estimates of critical slip distance in the rate and state model for friction evolution using synthetic earthquake data via the Bayesian inference. The conventional solution to the inverse problem is the deterministic parameter values, which may not represent the true value, and quantifying uncertainty in the model parameters increases confidence in the estimation. In this work, the uncertainty in the critical slip distance is estimated by the posterior distribution obtained through the Bayesian inversion.

Sensitivity of the Seismic Moment Released During Fluid Injection to Fault Hydromechanical Properties and Background Stress

Fluid pressure perturbations in subsurface rocks affect the fault stability and can induce both seismicity and aseismic slip. Nonetheless, observations show that the partitioning between aseismic and seismic fault slip during fluid injection may strongly vary among reservoirs. The processes and the main fault properties controlling this partitioning are poorly constrained. Here we examine, through 3D hydromechanical modeling, the influence of fault physical properties on the seismic and aseismic response of a permeable fault governed by a slip-weakening friction law. We perform a series of high-rate, short-duration injection simulations to evaluate the influence of five fault parameters, namely the initial permeability, the dilation angle, the friction drop, the critical slip distance, and the initial proximity of stress to failure. For sake of comparison between tests, all the simulations are stopped for a fixed rupture distance relative to the injection point. We find that while the fault hydraulic behavior is mainly affected by the change in initial permeability and the dilation angle, the mechanical and seismic response of the fault strongly depends on the friction drop and the initial proximity of stress to failure. Additionally, both parameters, and to a lesser extent the initial fault permeability and the critical slip distance, impact the spatiotemporal evolution of seismic events and the partitioning between seismic and aseismic moment. Moreover, this study shows that a modification of such parameters does not lead to a usual seismic moment-injected fluid volume relationship, and provides insights into why the fault hydromechanical properties and background stress should be carefully taken into account to better anticipate the seismic moment from the injected fluid volume.

Predicting spondylolisthesis correction with prone traction radiographs

Aims To determine the effectiveness of prone traction radiographs in predicting postoperative slip distance, slip angle, changes in disc height, and lordosis after surgery for degenerative spondylolisthesis of the lumbar spine. Methods A total of 63 consecutive patients with a degenerative spondylolisthesis and preoperative prone traction radiographs obtained since 2010 were studied. Slip distance, slip angle, disc height, segmental lordosis, and global lordosis (L1 to S1) were measured on preoperative lateral standing radiographs, flexion-extension lateral radiographs, prone traction lateral radiographs, and postoperative lateral standing radiographs. Patients were divided into two groups: posterolateral fusion or posterolateral fusion with interbody fusion. Results The mean changes in segmental lordosis and global lordosis were 7.1° (SD 6.7°) and 2.9° (SD 9.9°) respectively for the interbody fusion group, and 0.8° (SD 5.1°) and -0.4° (SD 10.1°) respectively for the posterolateral fusion-only group. Segmental lordosis (ρ = 0.794, p < 0.001) corrected by interbody fusion correlated best with prone traction radiographs. Global lumbar lordosis (ρ = 0.788, p < 0.001) correlated best with the interbody fusion group and preoperative lateral standing radiographs. The least difference in slip distance (-0.3 mm (SD 1.7 mm), p < 0.001), slip angle (0.9° (SD 5.2°), p < 0.001), and disc height (0.02 mm (SD 2.4 mm), p < 0.001) was seen between prone traction and postoperative radiographs. Regression analyses suggested that prone traction parameters best predicted correction of slip distance (Corrected Akaike’s Information Criterion (AICc) = 37.336) and disc height (AICc = 58.096), while correction of slip angle (AICc = 26.453) was best predicted by extension radiographs. Receiver operating characteristic (ROC) cut-off showed, with 68.3% sensitivity and 64.5% specificity, that to achieve a 3.0° increase in segmental lordotic angle, patients with a prone traction disc height of 8.5 mm needed an interbody fusion. Conclusion Prone traction radiographs best predict the slip distance and disc height correction achieved by interbody fusion for lumbar degenerative spondylolisthesis. To achieve this maximum correction, interbody fusion should be undertaken if a disc height of more than 8.5 mm is attained on preoperative prone traction radiographs. Level of Evidence: Level II Prognostic Study Cite this article: Bone Joint J 2020;102-B(8):1062–1071.

Friction

This chapter introduces friction as it manifests itself in everyday life. The chapter begins with Amontons’ law (1699) that friction is proportional to the loading force between contacting surfaces (the proportionality constant is called the coefficient of friction). The two primary mechanisms for unlubricated friction are adhesive friction and plowing friction, with the predominant mechanism generally being adhesive friction. Adhesive friction is proportional to the real area of contact; for rough surfaces, this contact area is proportional to the loading force, providing a physical underpinning for Amontons’ law. Processes like the nanoscale flow of atoms and molecules around contact points results in the force needed to induce sliding (static friction) being higher than the force needed to maintain sliding (kinetic friction). Friction decreasing with increasing velocity leads stick-slip motion of the sliding surfaces, where the slip distance can be as short as the distance between atoms.

Mechanisms and Influence of Casing Shear Deformation near the Casing Shoe, Based on MFC Surveys during Multistage Fracturing in Shale Gas Wells in Canada

Casing shear deformation has become a serious problem in the development of shale gas fields, which is believed to be related to fault slipping caused by multistage fracturing, and the evaluation of the reduction of a casing’s inner diameter is key. Although many fault slipping models have been published, most of them have not taken the fluid-solid-heat coupling effect into account, and none of the models could be used to calculate the reduction of a casing’s inner diameter. In this paper, a new 3D finite element model was developed to simulate the progress of fault slipping, taking the fluid-solid-heat coupling effect during fracturing into account. For the purpose of increasing calculation accuracy, the elastoplastic constitutive relations of materials were considered, and the solid-shell elements technique was used. The reduction of the casing’s inner diameter along the axis was calculated and the calculation results were compared with the measurement results of multi-finger caliper (MFC) surveys. A sensitivity analysis was conducted, and the influences of slip distance, casing internal pressure, thickness of production and intermediate casing, and the mechanical parameters of cement sheath on the reduction of a casing’s inner diameter in the deformed segment were analyzed. The numerical analysis results showed that decreasing the slip distance, maintaining high pressure, decreasing the Poisson ratio of cement sheath, and increasing casing thickness were beneficial to protect the integrity of the casing. The numerical simulation results were verified by comparison to the shape of MFC measurement results, and had an accuracy up to 90.17%. Results from this study are expected to provide a better understanding of casing shear deformation, and a prediction method of a casing’s inner diameter after fault slipping in multistage fracturing wells.

Casing Shear Deformation Based on Micro Seismic Data

Casing shear deformation, which is caused by fault slipping, is the main morphology of casing deformation occurred during multistage fracturing. In order to determine the relationship between fault slipping and casing shear deformation, the micro seismic data collected from engineering field which can reflect the reality of the formations was analyzed. A new numerical model was developed, and the influential factors on casing shear deformation were studied, including the fault slip distance of lower and upper interface, fault dip angle, the thickness of cement sheath and casing. The results of research shows that: (1) Fault is easily activated by fracturing, which was the main reason of casing shear deformation; (2) The greater the fault dip angel, the slip distance, the greater the casing shear deformation; (3) Increasing the wall thickness of casing or cement sheath is beneficial to decrease the degree of the shear deformation; (4) Two ways can be used to avoid and control the casing shear deformation, one is keeping the designed horizontal segment of well trajectory keep away from fracture-developed area, or be parallel to natural fracture, the other is using stage cementing technology. Research results can provide important reference for design and control of casing integrity during multistage fracturing in shale gas wells.