Elastic Dislocation Theory Research Articles

On the Integrated Surface Uplift for Dip‐Slip Faults

AbstractInterferometric Synthetic Aperture Radar observations often provide maps of vertical displacement that can be integrated to estimate an uplift volume. Relating this measure to source processes requires a model of the deformation. Bignami et al. (2019) argue that the negative uplift volume associated with the 2016 Amatrice–Norcia, central Italy, earthquake sequence requires a coseismic volume collapse of the hanging wall. Using results for dip‐slip dislocations in an elastic half‐space we show that Vuplift=(P/4)(1−2ν)sin(2δ), in which P is the seismic potency, ν is the Poisson’s ratio, and δ is the fault dip, consistent with an earlier result of Ward (1986). For reasonable estimates of net potency for the 2016 Amatrice–Norcia sequence, this simple formula yields uplift volume estimates close to that observed. We conclude that the data are completely consistent with elastic dislocation theory and do not require a volume collapse at depth.

Atomistic simulations of the interactions between the 1/2 〈1 1 1〉 {1 1 0} edge dislocations and the intrinsic point defects in tungsten

Atomistic simulations were employed to investigate the stress field spatial distributions, strain energy of the 1/2 〈1 1 1〉 {1 1 0} edge dislocation, and the binding energies between the edge dislocation and the point defects in tungsten, based on two different embedded-atom method (EAM) potentials. The basic static properties are consistent with the elastic theory of dislocations for these two potentials. Comparatively speaking, the map of the binding energy between the edge dislocation and the monovacancy illustrates that the results based on the Marinica’s potential fits better with the elastic theory. In addition, we obtained the radii of absorption between the point defects and the edge dislocation in the slip plane (the maximum value is 19 Å for the monovacancy, while 34 Å for the self-interstitial atom (SIA)) at 0 K. By calculating the binding energy and the interaction radii, we found the intensity of the interaction between the SIA and the edge dislocation is stronger than that of the vacancy and the edge dislocation.

Surface volume and gravity changes due to significant earthquakes occurred in central Italy from 2009 to 2016

We have modelled the surface volume and gravity changes caused by four seismic events: three mainshocks (moment magnitude Mw 6.0, 5.9, 6.5) occurred during the last seismic period started on 2016, August 24 in central Italy, and the 2009, April 6 L’Aquila Earthquake (Mw 6.3). Our calculations start from the source parameters estimated by the inversion of the largest dataset of Interferometric Synthetic Aperture Radar (InSAR) and global positioning system observations ever managed in Italy after earthquake occurrences, based on the half-space elastic dislocation theory. The vertical displacements modelled after the 2016 events allow to infer a substantial unbalance between the subsided and uplifted volumes. In particular, we detected ~ 106 × 106 m3 of hangingwall subsidence against ~ 37 × 106 m3 of footwall uplift, that accounts for ~ 74% of the total volume mobilization. From the ratio between the footwall and total deformed volumes, we have computed an average fault dip of ~ 47°, in line with the values retrieved by seismological methods. The total gravity variations which affected the study area are of the order of ~ 1 μGal (1 μGal = 10−8 ms−2) in the far field, and ~ 170 μGal in the near field. The area affected within a gravity change of 1 μGal is ~ 140 km long and ~ 57 km wide, parallel to the Apennines mountain chain. The larger contribution is given by positive variations which account for the tensional style of deformation and larger subsided area. The significant gravity variations modelled from the coseismic deformations point out the need to update our knowledge about the absolute gravity field in Italy carrying out extensive measurements, and to align Italy to the recent international standards about national gravity and height networks (International Association of Geodesy, IAG Report, Commission 2—gravity field, http://www.iag-commission2.ch , 2015).

Effect of indium doping on motions of 〈a〉-prismatic edge dislocations in wurtzite gallium nitride

The influences of indium doping on dynamics of 〈a〉-prismatic edge dislocation along shuffle plane in wurtzite GaN have been investigated employing classical molecular dynamics (MD) simulations. The dependence of dislocation motion mode and dislocation velocity on indium doping concentration, temperature, and applied shear stress was clarified. Moreover, the simulation results were further analyzed using elastic theory of dislocation and thermal activation theory of dislocation motion, showing excellent agreement with the simulation. Our findings help gain deep insights into modifying dynamic behaviors of TDs through the alloying doping and offer generic tools to the study of other wurtzite materials of promising application prospects, such as AlGaN and ZnO.

The Key Role Played by Dislocation Core Radius and Energy in Hydrogen Interaction with Dislocations

It is generally believed that the H-induced reduction in dislocation energy plays a key role in modifying dislocation behaviors in the process of hydrogen embrittlement. Here, we examine the factors that lead to H reducing the line energies of the edge and screw dislocations in bcc Fe by atomistic simulations. Grand canonical Monte Carlo simulations are conducted to obtain the distribution of H around the dislocations. We find that H mainly aggregates at the dislocation cores and the H concentration in the elastic field of dislocations is extremely low. The direct consequences of such a distribution pattern of H are as follows. (i) In contrast with previous studies, H induces no change in the shear modulus of the dislocation systems. (ii) H increases the core radii and decreases the core energies of the dislocations, which are the only factors leading to the reduction of dislocation line energy by H. (iii) H brings little effect on the stress field of either the edge or screw dislocation, implying that H induces almost no stress-shielding effect on dislocations. A linear relation between the critical shear stress for homogeneous dislocation nucleation and logarithmic bulk H concentration is thus revealed, based on the atomistic result of the H-induced increase in the core radius and decrease in the core energy of the dislocations. The present results indicate that the dislocation-dislocation interaction in the presence of H, which is the key ingredient for the H-enhanced localized plasticity mechanism for hydrogen embrittlement, can be easily evaluated by the linear elastic theory of dislocations if the core radius and energy of dislocations are properly described.

Surface deformation and source modeling of Ayaz-Akhtarma mud volcano, Azerbaijan, as detected by ALOS/ALOS-2 InSAR

Azerbaijan, located on the western edge of the Caspian Sea in Central Asia, has one of the highest populations of mud volcanoes in the world. We used satellite-based synthetic aperture radar (SAR) images derived from two L-band SAR satellites, ALOS/PALSAR along an ascending track from 2006 to 2011, and its successor ALOS-2/PALSAR-2 along both ascending and descending tracks from 2014 to 2017. First, we applied interferometric SAR (InSAR) technique to detect surface displacements at the Ayaz-Akhtarma mud volcano in Azerbaijan. The 35 derived interferograms indicate that the deformation of the mud volcano is largely characterized by horizontal displacement. Besides the InSAR technique, we also used multiple-aperture interferometry (MAI) to derive the surface displacements parallel to the satellite flight direction to complement the InSAR data. Using the InSAR and MAI data, we obtained 3D displacements, which indicate that the horizontal displacement is dominant relative to subsidence and possible uplift. To explain the displacements, we performed source modeling, based on the assumption of elastic dislocation theory in a half space. The derived model consists of a convex surface on which normal-fault-type slips are semi-radially distributed, causing the significant horizontal displacements with minor subsidence. The convex source surface suggests that a steady overpressure system would be maintained by constantly intruding mud and gas.

Coseismic Stress and Strain Field Changes Investigation Through 3‐D Finite Element Modeling of DInSAR and GPS Measurements and Geological/Seismological Data: The L'Aquila (Italy) 2009 Earthquake Case Study

AbstractWe investigate the L'Aquila 2009 earthquake (AQE,Mw6.3, Italy) through a 3‐D Finite Element (FE) mechanical model based on the exploitation of ENVISAT DInSAR and GPS measurements and an independently generated fault model. The proposed approach mainly consists of (a) the generation of a 3‐D fault model of the active structures involved in the sequence and those neighboring to them, benefiting of a large geological and seismological data set; (b) the implementation of the generated 3‐D fault model in a FE environment, by exploiting the elastic dislocation theory and considering the curved fault geometry and the crustal heterogeneities information; and (c) the optimization of the seismogenic crustal blocks model parameters in order to reproduce the geodetic measurements. We show that our modeling approach allows us to well reproduce the coseismic surface displacements, including their significant asymmetric pattern, as shown by the very good fit between the modeled ground deformations and the geodetic measurements. Moreover, a comparative analysis between our FE model results and those obtained by considering a classical analytical (Okada) model, for both the surface displacements and the Coulomb stress changes, has been performed. Our model permits to investigate the coseismic stress and strain field changes relevant to the investigated volume and their relationships with the surrounding geological structures; moreover, it highlights the very good correlation with the seismicity spatial distribution. The retrieved stress field changes show different maxima: (a) at few kilometers depth, within the main event surface rupture zone; (b) at depths of 5–9 km in correspondence of main event hypocentral area, along the SW dipping Paganica Fault System (PFS); and (c) at depths of 12–14 km, in correspondence of the largest aftershock hypocentral area, along a steep segment of an underlying east dipping basal detachment. Moreover, the main event hypocenter is localized in a region of high‐gradient strain field changes, while a deeper volumetric dilatation lobe involves the largest aftershock zone. From these findings, we argue that the AQE hanging wall downward movement along the steep portion of PFS might have been modulated by the underlying basal detachment; on the other hand, the coseismic eastward motion of the PFS footwall might have triggered further slip on the OS, thus releasing the largest aftershock on an independent source. The retrieved stress and strain field changes, which support the active role of the OS, have been also validated through a comparative analysis with those obtained from independent geological, seismological, and GPS measurements.

Effective Stacking Fault Energy in Face-Centered Cubic Metals

As a typical configuration in plastic deformations, dislocation arrays possess a large variation of the separation of the partial dislocation pairs in face-centered cubic (fcc) metals. This can be manifested conveniently by an effective stacking fault energy (SFE). The effective SFE of dislocation arrays is described within the elastic theory of dislocations and verified by atomistic simulations. The atomistic modeling results reveal that the general formulae of the effective SFE can give a reasonably satisfactory prediction for all dislocation types, especially for edge dislocation arrays. Furthermore, the predicted variation of the effective SFE is consistent with several previous experiments, in which the measured SFE is not definite, changing with dislocation density. Our approach could provide better understandings of cross-slip and the competition between slip and twinning during plastic deformations in fcc metals.

Coseismic Coulomb failure stress changes caused by the 2017 M7.0 Jiuzhaigou earthquake, and its relationship with the 2008 Wenchuan earthquake

On August 8, 2017, a M 7.0 earthquake occurred in Jiuzhaigou County, Sichuan Province, China, resulting in significant casualties and property damage. Therefore, it is critical to identify the areas of potential aftershocks before reconstruction and re-settling people to avoid future disasters. Based on the elastic dislocation theory and a multi-layered lithospheric model, we calculate the Coulomb failure stress changes caused by the Wenchuan and Jiuzhaigou earthquakes, discuss the relationship between the M w7.9 Wenchuan and M 7.0 Jiuzhaigou earthquakes, and analyze the influence of the aftershock distribution and stress changes on the major faults in this region caused by the Jiuzhaigou earthquake. The co- and post-seismic stress changes caused by the Wenchuan earthquake significantly increased the stress accumulation at the hypocenter of the Jiuzhaigou earthquake. Therefore, the occurrence of the Jiuzhaigou earthquake was probably stimulated by the Wenchuan earthquake. The aftershock distribution is well explained by the co-seismic stress changes of the Jiuzhaigou earthquake. The stress accumulation and corresponding seismic hazard on the Maqu-Heye segment of the East Kunlun fault and the northern extremity of the Huya fault has been further increased by the Jiuzhaigou earthquake.

Magnitude, moment, and measurement: The seismic mechanism controversy and its resolution

This paper examines the history of two related problems concerning earthquakes, and the way in which a theoretical advance was involved in their resolution. The first problem is the development of a physical, as opposed to empirical, scale for measuring the size of earthquakes. The second problem is that of understanding what happens at the source of an earthquake. There was a controversy about what the proper model for the seismic source mechanism is, which was finally resolved through advances in the theory of elastic dislocations. These two problems are linked, because the development of a physically-based magnitude scale requires an understanding of what goes on at the seismic source. I will show how the theoretical advances allowed seismologists to re-frame the questions they were trying to answer, so that the data they gathered could be brought to bear on the problem of seismic sources in new ways.

Coseismic changes of gravitational potential energy induced by global earthquakes based on spherical‐Earth elastic dislocation theory

AbstractWe compute the coseismic gravitational potential energy Eg change using the spherical‐Earth elastic dislocation theory and either the fault model treated as a point source or the finite fault model. The rate of the accumulative Eg loss produced by historical earthquakes from 1976 to 2016 (about 42,000 events) using the Global Centroid Moment Tensor Solution catalogue is estimated to be on the order of −2.1 × 1020 J/a, or −6.7 TW (1 TW = 1012 W), amounting to 15% in the total terrestrial heat flow. The energy loss is dominated by the thrust faulting, especially the megathrust earthquakes such as the 2004 Sumatra earthquake (Mw 9.0) and the 2011 Tohoku‐Oki earthquake (Mw 9.1). It is notable that the very deep focus events, the 1994 Bolivia earthquake (Mw 8.2) and the 2013 Okhotsk earthquake (Mw 8.3), produced significant overall coseismic Eg gain according to our calculation. The accumulative coseismic Eg is mainly lost in the mantle of the Earth and also lost in the core of the Earth but with a relatively smaller magnitude. By contrast, the crust of the Earth gains gravitational potential energy cumulatively because of the coseismic deformations. We further investigate the tectonic signature in the coseismic crustal Eg changes in some complex tectonic zone, such as Taiwan region and the northeastern margin of the Tibetan Plateau. We found that the coseismic Eg change is consistent with the regional tectonic character.

Stacking fault tetrahedron induced plasticity in copper single crystal

Stacking fault tetrahedron (SFT) is the most common type of vacancy clustered defects in fcc metals and alloys, and can play an important role in the mechanical properties of metallic materials. In this study, molecular dynamics (MD) simulations were carried out to investigate the incipience of plasticity and the underlying atomic mechanisms in copper single crystals with SFT. Different deformation mechanisms of SFT were reported due to the crystal orientations and loading directions (compression and tension). The results showed that the incipient plasticity in crystals with SFT resulted from the heterogeneous dislocation nucleation from SFT, so the stress required for plastic deformation was less than that needed for perfect single crystals. Three crystal orientations ([1 0 0], [1 1 0] and [1 1 1]) were specified in this study because they can represent most of the typical deformation mechanisms of SFT. MD simulations revealed that the structural transformation of SFT was frequent under the applied loading; a metastable SFT structure and the collapse of SFT were usually observed. The structural transformation resulted in a different reduction of yield stress in compression and tension, and also caused a decreased or reversed compression/tension asymmetry. Compressive stress can result in the unfaulting of Frank loop in some crystal orientations. According to the elastic theory of dislocation, the process of unfaulting was closely related to the size of the dislocation loop and the stacking fault energy.

Coseismic Gravity and Displacement Signatures Induced by the 2013 Okhotsk Mw8.3 Earthquake.

In this study, Gravity Recovery and Climate Experiment (GRACE) RL05 data from January 2003 to October 2014 were used to extract the coseismic gravity changes induced by the 24 May 2013 Okhotsk Mw8.3 deep-focus earthquake using the difference and least square fitting methods. The gravity changes obtained from GRACE data agreed well with those from dislocation theory in both magnitude and spatial pattern. Positive and negative gravity changes appeared on both sides of the epicenter. The positive signature appeared on the western side, and the peak value was approximately 0.4 microgal (1 microgal = 10−8 m/s2), whereas on the eastern side, the gravity signature was negative, and the peak value was approximately −1.1 microgal. It demonstrates that deep-focus earthquakes Mw ≤ 8.5 are detectable by GRACE observations. Moreover, the coseismic displacements of 20 Global Positioning System (GPS) stations on the Earth’s surface were simulated using an elastic dislocation theory in a spherical earth model, and the results are consistent with the GPS results, especially the near-field results. We also estimated the gravity contributions from the coseismic vertical displacements and density changes, analyzed the proportion of these two gravity change factors (based on an elastic dislocation theory in a spherical earth model) in this deep-focus earthquake. The gravity effect from vertical displacement is four times larger than that caused by density redistribution.

Robust atomistic calculation of dislocation line tension

The line tension of a dislocation is an important and fundamental property ubiquitous to continuum scale models of metal plasticity. However, the precise value of in a given material has proven difficult to assess, with literature values encompassing a wide range. Here results from a multiscale simulation and robust analysis of the dislocation line tension, for dislocation bow-out between pinning points, are presented for two widely-used interatomic potentials for Al. A central part of the analysis involves an effective Peierls stress applicable to curved dislocation structures that markedly differs from that of perfectly straight dislocations but is required to describe the bow-out both in loading and unloading. The line tensions for the two interatomic potentials are similar and provide robust numerical values for Al. Most importantly, the atomic results show notable differences with singular anisotropic elastic dislocation theory in that (i) the coefficient of the scaling with dislocation length L differs and (ii) the ratio of screw to edge line tension is smaller than predicted by anisotropic elasticity. These differences are attributed to local dislocation core interactions that remain beyond the scope of elasticity theory. The many differing literature values for are attributed to various approximations and inaccuracies in previous approaches. The results here indicate that continuum line dislocation models, based on elasticity theory and various core-cut-off assumptions, may be fundamentally unable to reproduce full atomistic results, thus hampering the detailed predictive ability of such continuum models.

Triangular dislocation: an analytical, artefact-free solution

S U M M A R Y Displacements and stress-field changes associated with earthquakes, volcanoes, landslides and human activity are often simulated using numerical models in an attempt to understand the underlying processes and their governing physics. The application of elastic dislocation theory to these problems, however, may be biased because of numerical instabilities in the calculations. Here, we present a new method that is free of artefact singularities and numerical instabilities in analytical solutions for triangular dislocations (TDs) in both full-space and half-space. We apply the method to both the displacement and the stress fields. The entire 3-D Euclidean space R3 is divided into two complementary subspaces, in the sense that in each one, a particular analytical formulation fulfils the requirements for the ideal, artefact-free solution for a TD. The primary advantage of the presented method is that the development of our solutions involves neither numerical approximations nor series expansion methods. As a result, the final outputs are independent of the scale of the input parameters, including the size and position of the dislocation as well as its corresponding slip vector components. Our solutions are therefore well suited for application at various scales in geoscience, physics and engineering. We validate the solutions through comparison to other well-known analytical methods and provide the MATLAB codes.

Strain mapping in nanocrystalline grains simulated by phase field crystal model

In recent years, the phase field crystal (PFC) model has been confirmed as a good candidate to describe grain boundary (GB) structures and their nearby atomic arrangement. To further understand the mechanical behaviours of nanocrystalline materials, strain fields near GBs need to be quantitatively characterized. Using the strain mapping technique of geometric phase approach (GPA), we have conducted strain mapping across the GBs in nanocrystalline grains simulated by the PFC model. The results demonstrate that the application of GPA in strain mapping of low and high angles GBs as well as polycrystalline grains simulated by the PFC model is very successful. The results also show that the strain field around the dislocation in a very low angle GB is quantitatively consistent with the anisotropic elastic theory of dislocations. Moreover, the difference between low angle GBs and high angle GBs is revealed by the strain analysis in terms of the strain contour shape and the structural GB width.

Fault Response Modelling – Application of Elastic Dislocation theory in earthquake research and industry

Fault Response Modelling – Application of Elastic Dislocation theory in earthquake research and industry

Coseismic Strains on Plate Boundary Observatory Borehole Strainmeters in Southern California

Abstract Strainmeters can record offsets coincident with earthquakes, but how much these represent strain changes from elastic rebound, and how much they are contaminated by local effects, remains an open question. To study this, we use a probabilistic detection method to estimate coseismic offsets on nine borehole strainmeters (BSMs) operated by the Plate Boundary Observatory (PBO) in southern California, from 34 earthquakes with a wide range of magnitudes and distances. In general, the offsets estimated for the BSM data differ substantially from the static strain predicted by elastic dislocation theory, which is well supported by other techniques, though 10% of the observed offsets agree well with theory. For one earthquake, the BSM offsets significantly disagree with collocated long‐base laser strainmeter data. Comparisons with collocated seismic data provide strong evidence that the absolute errors between the observed and predicted strains scale with the level of seismic energy density but also that relative errors (normalized by the model size) do not. We conclude that apparent strain offsets are induced by seismic waves, occurring presumably because of irreversible deformation, whether in the rock or cementing materials close to the BSMs, or in the instruments themselves. Coseismic offsets seen in PBOBSM data should therefore be viewed with caution before being used as a measure of large‐scale coseismic deformation. Online Material: Tables of offset estimates and predictions, error estimates, strike sensitivities, and figures of observed versus predicted offsets.

Inclination of a threading dislocation in an epilayer of 4H-SiC

Threading dislocations (TDs) are inclined from the [0001] c-axis in 4H-SiC epilayers which are produced by the step-controlled technique. The reason for this inclination is discussed in the framework of isotropic elastic theory of dislocation. The elastic strain energy of a TD in an epilayer is calculated as a function of its orientation, and the minimum energy orientation is used to predict the inclination angle. The results of the calculations are as follows. For a cut-off angle (α) of 4°, a threading edge dislocation (TED) and a threading pure screw dislocation (TpSD) are inclined from the c-axis by 12 and 2°, respectively: Threading near screw dislocations (TnSDs) and threading mixed dislocations (TMDs) are inclined by angles ranging from 8 to 15° from the c-axis, depending on their actual Burgers vectors. Similarly for α of 8°, a TED and a TpSD are inclined from the c-axis by 21 and 4°, respectively: TnSDs and TMDs are inclined from the c-axis by angles ranging from 7 to 17°. These predictions are in good agreement with experiment.

Earthquake-origin expansion of the Earth inferred from a spherical-Earth elastic dislocation theory

Earthquake-origin expansion of the Earth inferred from a spherical-Earth elastic dislocation theory