Roughness Amplitude Research Articles

A Fractal Prediction Method for Contact Stiffness of Helical Gear Considering Asperity Lateral Contact and Interaction

The normal contact stiffness (NCS) on rough surfaces has a significant impact on the dynamic characteristics of helical gear. Aiming at the problem of inaccurate calculation of the NCS model under the traditional Hertz theory of smooth surfaces, a fractal prediction model of helical gear contact stiffness considering asperity lateral contact and interaction between asperities is proposed in this paper. The variation formula of asperity and the correction coefficient of a tooth contact surface under asperity lateral contact and interaction are derived, and the influence of micro-elements on normal load and NCS is qualitatively analyzed. The results show that the NCS of considering the interaction and lateral contact of asperity is closer to the experimental results; the contact surface correction coefficient increases with the increase of curvature radius and load. The NCS of a tooth surface increases with the increase in fractal dimension D or the decrease in roughness amplitude G. The influence of asperity lateral contact and interaction decreases with the increase in D and the decrease in G. The NCS of the helical gear decreases under the lateral contact and interaction of the asperity, which is critical for exact estimation of the NCS of contact surfaces in gear.

Surface Roughness Effects on Magnetic Properties and Switching Mechanism in Iron Nanowires

Nanowires fabricated with experimental techniques are never perfect and possess structural imperfections. The effect of the resulting surface roughness on magnetic properties of iron nanowires has been simulated here with the use of numerical technique involving atomistic-resolved software Vampire. A two-regime or a power-law decrease in the coercive field has been found for the roughness amplitude up to 30% of the perfect radius of the wire. The roughness of the surface of the side face of cylindrical wire makes the ends of the cylinder inequivalent as far as the switching mechanism is concerned. As a result, the switching becomes dominated by a transverse domain wall arising at one specific end only. Both the coercive field and the switching mechanism are essential in designing magnetic devices, e.g., for memory storage.

Tactile Perception of Coated Smooth Surfaces.

Although surface coating is commonly utilized in many industries for improving the aesthetics and functionality of the end product, our tactile perception of coated surfaces has not been investigated in depth yet. In fact, there are only a few studies investigating the effect of coating material on our tactile perception of extremely smooth surfaces having roughness amplitudes in the order of a few nanometers. Moreover, the current literature needs more studies linking the physical measurements performed on these surfaces to our tactile perception in order to further understand the adhesive contact mechanism leading to our percept. In this study, we first perform 2AFC experiments with 8 participants to quantify their tactile discrimination ability of 5 smooth glass surfaces coated with 3 different materials. We then measure the coefficient of friction between human finger and those 5 surfaces via a custom-made tribometer and their surface energies via Sessile drop test performed with 4 different liquids. The results of our psychophysical experiments and the physical measurements show that coating material has a strong influence on our tactile perception and human finger is capable of detecting differences in surface chemistry due to, possibly, molecular interactions.

Employing spatial, hybrid and amplitude roughness parameters for unveiling the surface roughness features of mineral and organic admixtures

Scanning electron microscopy (SEM) permits to evaluate the surface morphology and surface roughness of pozzolans and admixtures. The field of mineral and organic admixtures has considerable interest in using SEM. However, several challenges are encountered which hamper the precision of quantitative roughness evaluation of mineral and organic admixtures using SEM and these challenges are usually bypassed in literature. In this research, surface roughness properties of pozzolans and admixtures were analysed from six perspectives: spatial parameters, hybrid parameters, amplitude parameters, surface roughness profiles, bearing ratio curves (BRCs) and amplitude density functions (ADFs). The generated roughness characteristics provided detailed information of roughness properties of the pozzolans and admixtures in a time efficient and cost effective way, which is usually very hard to achieve using experimental works. The comparisons of the obtained roughness data for the specimens showed considerable agreement with the roughness profiles and verified the interpretation of the established roughness profiles. Using the ADFs and BRCs for evaluating heights of the roughness profiles provided significant data encapsulated in the shapes of ADFs and BRCs. Moreover, the interpretation of the transformed logarithmic profiles seemed to have nearly retained similar meanings with the conventional profiles, although their scrutiny was observed to be complex. With brand new discussions on spatial, hybrid and amplitude parameters of mineral and organic admixtures, this research is a step forward in characterisation of roughness parameters of mineral and organic admixtures. This study expands the characterisation of pozzolans and admixtures, highlighting significant parameters to be considered in the application of mineral and organic admixtures.

Modeling and Machine Learning of Vibration Amplitude and Surface Roughness after Waterjet Cutting.

This study focused on analyzing vibrations during waterjet cutting with variable technological parameters (speed, vfi; and pressure, pi), using a three-axis accelerometer from SEQUOIA for three different materials: aluminum alloy, titanium alloy, and steel. Difficult-to-machine materials often require specialized tools and machinery for machining; however, waterjet cutting offers an alternative. Vibrations during this process can affect the quality of cutting edges and surfaces. Surface roughness was measured by contact methods after waterjet cutting. A machine learning (ML) model was developed using the obtained maximum acceleration values and surface roughness parameters (Ra, Rz, and RSm). In this study, five different models were adopted. Due to the characteristics of the data, five regression methods were selected: Random Forest Regressor, Linear Regression, Gradient Boosting Regressor, LGBM Regressor, and XGBRF Regressor. The maximum vibration amplitude reached the lowest acceleration value for aluminum alloy (not exceeding 5 m/s2), indicating its susceptibility to cutting while maintaining a high surface quality. However, significantly higher acceleration amplitudes (up to 60 m/s2) were registered for steel and titanium alloy in all process zones. The predicted roughness parameters were determined from the developed models using second-degree regression equations. The prediction of vibration parameters and surface quality estimators after waterjet cutting can be a useful tool that for allows for the selection of the optimal abrasive waterjet machining (AWJM) technological parameters.

Development of ultra-low cycle fatigue life prediction model for structural steel considering the effects of surface roughness, loading frequency, and loading amplitude

Abrasive blast cleaning is often done for steel structures before applying various protective coatings, which produces rough surfaces with changes in fatigue properties. This problem has been addressed in the low- and high-cycle fatigue regimes; however, the effect of surface roughness in combination with different loading parameters on the ultra-low cycle fatigue (ULCF) life has not been reported thus far. To this aim, a total of 59 ULCF tests on designed specimens of SM400 steel with five levels of surface roughness were performed under various loading frequencies and displacement amplitudes. The analysis of experimental results indicates a substantial reduction in fatigue life with an increase in the surface roughness and loading amplitude and a decrease in the loading frequency. Additionally, the strength degradation, dissipation energy, and load–displacement curves are discussed in detail. With the use of experimental data, a new life prediction model characterizing the combined effects of surface roughness, loading frequency, and loading amplitude on the ULCF life is proposed. Moreover, the proposed model is validated by predicting the fatigue life under variable and constant loading amplitude patterns. Comparison between experimental and theoretical results shows that the proposed model accurately estimates the ULCF life within an error band of ±15%, with a reasonable selection of model parameters.

Comparative study of surface roughness models in the hydro-thermal characterization of flow over rough walls

Surface roughness is responsible for the localized turbulence, which disrupts the viscous sublayer, affecting pressure drop and heat transfer. Thus, the numerical modeling of the effect of roughness on the fluid flow and heat transfer is quite essential. In this work, a numerical model is developed in OpenFOAM to incorporate the effect of surface roughness by modifying the wall function. Its accuracy is validated with available semi-empirical correlations and experimental results. The efficacy of available models for evaluating equivalent sand–grain roughness height (ks) based on surface statistics is investigated. A correlation for the dimensionless near-wall cell center distance (y+) is developed as the function of the Reynolds number and the equivalent sand–grain roughness height. The developed numerical model is validated with the semi-empirical relation and experimental results from the literature with average deviations of 7%. It is found that the equivalent sand–grain roughness height, evaluated using expressions reported by Flack et al. [ “Skin friction measurements of systematically-varied roughness: Probing the role of roughness amplitude and skewness,” Flow Turbul. Combust. 104, 317–329 (2020)], shows the lowest average deviation of 3.48% with the experimental data among all the considered formulas of ks. The proposed correlation of y+ well predicts the minimum dimensionless near-wall distance that gives near-wall spacing independent result with a mean absolute deviation of 2.1% compared to that obtained from the numerical results. The correlation of y+ developed based on the fluid flow analysis is further used to predict the Stanton number, which reasonably agrees with the experimental results.

Can the splitting joint reproduce the characteristics of the natural joint in the lab? —A comparison study based on the roughness analysis and shear test

Splitting joints have been widely used to study the morphology characteristic and shear behavior of rock joints in the laboratory. There are some differences between the splitting joint and natural joint both in morphology characteristic and shear behavior. To quantitatively compare the differences, the present study used several splitting joints and natural joints to carry out the roughness analysis and direct shear test. Six profiles were extracted from each joint surface with a 30° interval to calculate the 2D roughness parameters (i.e., amplitude roughness parameter, average asperity inclination, root-mean-square of profile slope, and joint roughness coefficient). These parameters of the natural joints have a wide range and have obvious fluctuation. On the contrary, these parameters of the splitting red sandstone joints converge on a small range with tiny fluctuation, even calculated from different joint surfaces. The directional parameter (θ⁎max(C + 1)) was adopted to calculate the 3D roughness with a 5° interval. The directional parameter of the natural joints in range of 0° ∼ 360° forms a peanut, a prolate ellipse, or a gourd shape, presenting significant anisotropy. For the splitting joints, it forms a circle or a roughly circular shape, presenting insignificant anisotropy. The asperity heights of natural joints mainly present an irregular distribution, and they present an approximately normal distribution in few joints. For the splitting joints, the asperity heights generally obey a normal distribution. It indicates that there are huge differences between natural joint and splitting joint in morphology characteristic. To study the shear behavior, two types of joint were reconstructed for repeated test. The mechanical performance and failure characteristic of the splitting joint under different shear directions are similar. On the contrary, those of the natural joints under different shear directions are different, presenting obvious anisotropy. Based on the comparative analysis of the natural joints and the sandstone splitting joints in the present study, there is substantial difference between two types of joints both in morphology characteristic and shear behavior. The splitting joints cannot reproduce the characteristics of the natural joints well.

Formation of new erosion-deposition patterns after farmland conversion: The major role of topography

The “Grain for Green” project has a profound impact on the allochthonous process of erosion sediment stripping and transportation, which in turn interferes with the distribution of erosion patterns. Therefore, understanding the changes in erosion patterns after farmland conversion and the factors controlling the new patterns of erosion distribution are essential for understanding the mechanism of slope erosion. Accordingly, this study investigated the formation of new erosion patterns and their control factors after farmland conversion by field sampling combined with nuclear tracing (137Cs) techniques, considering the “Grain for Green” project on the Loess Plateau as the study focus. We found that the implementation of the “Grain for Green” project can significantly reduce soil erosion intensity and create a new erosion-sediment source-sink pattern on the slope. The conversion of farmland to grassland can effectively store soil organic carbon as well as more environmentally sensitive active organic carbon, and the sorting effect on sediment particles is more obvious. Meanwhile, using stepwise regression, we found that the key limiting factor affecting the erosion intensity of farmland is the topography; the response of topographic factors to erosion is much higher than the physicochemical properties of the soil itself. By quantified the direct and interactive contributions to erosion intensity, we find that the direct contributions of silt and relief amplitude were 0.48 and 0.46 in farmland, while slope (0.16), Roughness (0.20) and Relief amplitude (0.33) in grassland, respectively. The interactive contributions were 0.06 and 0.30 in farmland and grassland. The conversion of farmland to grassland results in an increase in the factors that resist erosion and the factors interact more closely with each other to limit the occurrence of soil erosion. Our study provides scientific support for a deeper understanding of the slope erosion mechanism.

A contribution to debate on surface roughness of clay brick powder generated using varying milling treatments

Recently, the correlation between surface roughness and fineness of materials including pozzolans has been subjected to too much debate in literature. Exploiting the surface roughness of pozzolans has been proven to be significant for cement-based composites. Although research works have been conducted to assess the effects of milling treatments on surface roughness of pozzolans, limited dedicated studies have explored the use of multi-scale characterisation methods for analysing this complex parameter. In this research, an economic and novel technique was employed to characterise the surface roughness of clay brick powder (CBP) subjected to varying milling treatments of various sample masses. The main aim of this research was to investigate the correlations between fineness levels of CBP and surface roughness parameters. Characterisation of CBP generated from ball milling was performed using scanning electron microscopy (SEM) and Gwyddion. There was significant effort employed during the search for significant trends between roughness parameters and grinding clay bricks using different specimen masses, sadly without success. The results of amplitude roughness parameters, fast Fourier transformations, autocorrelation functions and power spectral density functions demonstrated no significant trends for CBP specimens generated under varying specimen masses. Although CBP specimen with highest fineness level seemed to illustrate the lowest roughness characteristics in some cases (i.e. root mean square roughness of 159.182 nm and mean roughness of 115.444 nm), CBP specimen with lowest fineness level did not illustrate the highest surface roughness properties. Through the analyses, it seemed that CBP specimens subjected to different fineness levels could not illustrate significant differences in surface roughness properties and this observation is contrary to some findings in literature. It is believed that the algorithms used for surface roughness characterisation in this research facilitate the understanding of surface roughness properties of CBP specimens subjected to different fineness levels.

What is measured when measuring a thermoelectric coefficient?

A thermal gradient generates an electric field in any solid hosting mobile electrons. In presence of a finite magnetic field (or Berry curvature) this electric field has a transverse component. These are known as Seebeck and Nernst coefficients. As Callen argued, back in 1948, the Seebeck effect quantifies the entropy carried by a flow of charged particles in absence of thermal gradient. Similarly, the Nernst conductivity, α xy , quantifies the entropy carried by a flow of magnetic flux in absence of thermal gradient. The present paper summarizes a picture in which the rough amplitude of the thermoelectric response is given by fundamental units and material-dependent length scales. Therefore, knowledge of material-dependent length scales allows predicting the amplitude of the signal measured by experiments. Specifically, the Nernst conductivity scales with the square of the mean-free-path in metals. Its anomalous component in magnets scales with the square of the fictitious magnetic length. Ephemeral Cooper pairs in the normal state of a superconductor generate a signal, which scales with the square of the superconducting coherence length and smoothly evolves to the signal produced by mobile vortices below the critical temperature.

Effect of Photoinitiator Concentration and Film Thickness on the Properties of UV-Curable Self-Matting Coating for Wood-Based Panels

Matte coatings have found wide-ranging applications across diverse industries. In this study, self-matting films with surface wrinkles were produced by exposing UV-curable polyurethane acrylate (UV-WPUA) resin to 172 nm Xe2* excimer and medium-pressure mercury lamps. The gloss values, micromorphologies, water contact angles (WCAs), roughness values, and friction behaviors of UV-WPUA films with different photoinitiator (PI) concentrations and thickness were investigated for the first time. The results indicate that the gloss values of the films at the same thickness enhance with the increase of PI concentration, while the amplitude of wrinkles, roughness, and WCAs decrease; however, the friction coefficient shows insignificant variations. While the PI concentration is unchanged, an increase in film thickness results in a decrease in gloss value and an increase in roughness and friction coefficient. Nevertheless, the WCA is relatively constant. The PI concentration of 0.5 wt% (lowest gloss value of cured film) was utilized to prepare the UV-WPUA wood coating. The cured coating film exhibited low gloss (4.9 GU at 60° and 5.2 GU at 85°) and outstanding mechanical properties, including 3H pencil hardness, grade 0 adhesion, excellent wear resistance, and tensile property. These findings can be utilized to guide the development of self-matting wood coatings and the production of wood-based panels used in industrial finishing.

A coupled approach to predict cone-cracks in spherical indentation tests with smooth or rough indenters

Indentation tests are largely exploited in experiments to characterize the mechanical and fracture properties of the materials from the resulting crack patterns. This work proposes an efficient theoretical and computational framework, whose implementation is detailed for 2D axisymmetric and for 3D geometries, to simulate indentation-induced cracking phenomena caused by non-conforming contacts with indenter profiles of an arbitrary shape. The formulation hinges on the coupling of the MPJR (eMbedded Profile for Joint Roughness) interface finite elements which embed the indenter profile to efficiently solve the contact problem between non-planar bodies, and the phase-field model for brittle fracture to simulate crack evolution and nonlocal damage in the substrate. The novel framework is applied to predict cone-crack formation in the case of indentation tests with smooth spherical indenters, with validation against experimental data. Then, the methodology is employed for the very first time in the literature to assess the effect of surface roughness superimposed on the shape of the smooth spherical indenter. In terms of physical insights, numerical predictions quantify the dependencies of the critical load for crack nucleation and the crack radius on the amplitude of roughness in comparison with the behavior of smooth indenters. Again, the consistency with available experimental trends is noticed.

Analysis and Experimental Verification of the Sealing Performance of PEM Fuel Cell Based on Fractal Theory

Aiming to accurately predict the leakage rate of the sealing interface, this work proposes a two-dimensional finite element model of a proton exchange membrane fuel cell, which includes the microscopic surface morphology and the asperity contact process of the components. First of all, we constructed the surface morphology of the seal by the two-dimensional W-M (Weierstrass–Mandelbrot) fractal function and explored the influence of fractal dimension (D) and scale parameter (G) on the surface profile. Furthermore, the finite element method and Poiseuille fluid theory were adopted to obtain the deformation variables of the asperity under different clamping pressures and leakage rates. Moreover, we quantitatively analyzed the impact of surface roughness on the clamping pressure and leakage rate. It was found that both the surface amplitude and surface roughness are positively correlated with G and negatively correlated with D. Surface morphology is proportional to D but has no relationship with G. Additionally, the deformation asperity decreases exponentially with growing clamping pressure, and the leakage rate is consistent with the experimental values at a clamping pressure of 0.54 MPa. With the same leakage rate, when the seal surface roughness value is less than 1 μm, a doubled roughness value leads to an increase of 31% in the clamping pressure. In contrast, when the surface roughness of the seal is greater than 1 μm, a doubled roughness value induces an increase of 50% in the corresponding clamping pressure.

On the contact between elasto-plastic media with self-affine fractal roughness

Modeling the elasto-plastic contact between rough interfaces may require high computational effort as real surfaces present broad roughness spectra. In this work, we propose an efficient multi-asperity model where each asperity follows Jackson and Green’s equations and both coupling and coalescence of contact spots are considered. In agreement with previous studies, the contact area A is found to rise linearly with the applied load. Moreover, under the assumption of yield stress independent of the asperity size, no differences are found with respect to the elastic contact solution for nanometric root mean square (rms) roughness amplitudes hrms. On the contrary, for micrometric hrms, the slope of the area-load relation is observed to increase when reducing the yield strength σY. We have also investigated the effect of increasing the rms roughness gradient of the surface hrms′ by adding fine-scale wavelengths to the roughness spectrum. Due to plastic deformations, the contact area A is found to be independent of the high-frequency cut-off of the roughness spectrum as it converges when increasing the number of roughness scales.

Transport of a passive scalar in wide channels with surface topography: An asymptotic theory

We generalize classical dispersion theory for a passive scalar to derive an asymptotic long-time convection–diffusion equation for a solute suspended in a wide, structured channel and subject to a steady low-Reynolds-number shear flow. Our asymptotic theory relies on a domain perturbation approach for small roughness amplitudes of the channel and holds for general surface shapes expandable as a Fourier series. We determine an anisotropic dispersion tensor, which depends on the characteristic wavelengths and amplitude of the surface structure. For surfaces whose corrugations are tilted with respect to the applied flow direction, we find that dispersion along the principal direction (i.e. the principal eigenvector of the dispersion tensor) is at an angle to the main flow direction and becomes enhanced relative to classical Taylor dispersion. In contrast, dispersion perpendicular to it can decrease compared to the short-time diffusivity of the particles. Furthermore, for an arbitrary surface shape represented in terms of a Fourier decomposition, we find that each Fourier mode contributes at leading order a linearly-independent correction to the classical Taylor dispersion diffusion tensor.

Optimization of dead metal zone to reduce cutting forces in micro milling of Inconel 718 using RSM

This study focuses on the mechanism of DMZ (dead metal zone) creation, as well as the impact of cutting edge geometries (sharp, chamfered, double chamfered, and blunt edges), cutting speed, and coefficient of friction on DMZ formation while milling Inconel 718 material (FEM). A non-contact type sensor called a laser doppler vibrometer (LDV) is used to monitor the vibration of rotating surfaces. In current research work, the LDV is used to measure the mill cutter vibration in micro-milling of Inconel 718 in terms of acoustic optic emission signals. A FFT (fast fourier transformer) is used for signals processing in to frequency domain. Design of experiments as per Taguchi, experiments were performed on the alloy at three levels of spindle speeds, depth of cuts, feed rates. Experimental results on the amplitude o vibration of tool along X and Y directions, surface roughness were measured and analysed using response surface methodology. Analysis obtained from the variance was used to recognize the significant parameters which effect the vibration of tool and roughness of surface. RSM was implemented and optimized process parameters for the minimum vibration amplitude and surface roughness.

High-fidelity computational study of roughness effects on high pressure turbine performance and heat transfer

While blade surface roughness arising from in-service wear and/or the manufacturing process greatly affects aero-thermal performance, the detailed underlying physical mechanisms remain far from fully understood. In this study, a series of highly-resolved Large-Eddy Simulations of compressible flow past a high-pressure turbine vane with systematically varied levels of blade surface roughness have been performed, along with a smooth-blade simulation at matched flow conditions for comparison. Three non-dimensional roughness amplitudes have been investigated, namely, ks/c={1.0,2.0,3.0}×10−3, where ks is an equivalent value of Nikuradse’s sandgrain roughness for an irregular, multi-scale near-Gaussian height distribution, and c is the axial blade chord. All simulations have been performed at an axial chord Reynolds number of 0.59 ×106 and a Mach number of 0.9, based on the exit conditions of the reference smooth vane, and with synthetic inflow turbulence to mimic unsteady, three-dimensional disturbances from an upstream combustion chamber. The present investigation highlights the profound impact that blade surface roughness can have upon boundary-layer transition mechanisms, wall shear stress and blade surface heat flux, as well as the levels of turbulence kinetic energy and total pressure losses incurred in the wake. While blade surface roughness leads to major aero-thermal differences between the suction-side of the smooth and rough vanes, the pressure-side surface remains relatively unaffected — even for the largest roughness amplitude investigated here.

The transition from Elasto-Hydrodynamic to Mixed Regimes in Lubricated Friction of Soft Solid Surfaces.

Lubricated contacts in soft materials are common in various engineering and natural settings, such as tires, haptic applications, contact lenses, and the fabrication of soft electronic devices. Two major regimes are elasto-hydrodynamic lubrication (EHL), in which solid surfaces are fully separated by a fluid film, and mixed lubrication (ML), in which there is partial solid-to-solid contact. The transition between these regimes governs the minimum sliding friction achievable and is thus very important. Generally, the transition from EHL to ML regimes is believed to occur when the thickness of the lubricant layer is comparable with the amplitude of surface roughness. Here, it is reported that in lubricated sliding experiments on smooth, soft, poly(dimethylsiloxane) substrates, the transition can occur when the thickness of the liquid layer is much larger than the height of the asperities. Direct visualization of the "contact" region shows that the transition corresponds to the formation of wave-like surface wrinkles at the leading contact edge and associated instabilities at the trailing contact edge, which are believed to trigger the transition to the mixed regime. These results change the understanding of what governs the important EHL-ML transition in the lubricated sliding of soft solids.

Frictional power dissipation in a seismic ancient fault

The frictional power per unit area Q˙ (product of frictional traction τ and slip rate u˙ in MW m−2) dissipated during earthquakes triggers fault dynamic weakening mechanisms that control rupture nucleation, propagation and arrest. Although of great relevance in earthquake mechanics, Q˙ cannot, with rare exceptions, be determined by geophysical methods. Here we exploit theoretical, experimental and geological constraints to estimate Q˙ dissipated on a fault patch exhumed from 7-9 km depth. According to theoretical models, in polymineralic, silicate rocks the amplitude (< 1 mm) of the grain-scale roughness of the boundary between frictional melt (pseudotachylyte) and host rock decreases with increasing Q˙. The dependence of grain-scale roughness with Q˙ is due to differential melt front migration in the host rock minerals. This dependence is confirmed by friction experiments reproducing seismic slip where pseudotachylytes were produced by shearing tonalite at Q˙ ranging from 5 to 25 MW m−2. In natural pseudotachylytes across tonalites, the grain-scale roughness broadly decreases from extensional to compressional fault domains where lower and higher Q˙ are expected, respectively. Analysis of the natural dataset calibrated by experiments yields Q˙ values in the range of 4-60 MW m−2 (16 MW m−2 average value). These values, estimated in small fault patches, are at the lower end of broad estimates of Q˙ (3-300 MW m−2) obtained from frictional tractions (30-300 MPa) and fault slip rates (0.1-1 m/s) assumed as typical of upper crustal earthquakes.