Surface Horizontal Displacement Research Articles

Empirical prediction of horizontal movements induced by tunnelling in fine-grained soils

Available evidence indicates that the focal depth of displacement vectors along the ground surface decreases with the transverse distance from the tunnel centre-line. Based on field and centrifuge observations, this paper presents a new empirical method in which the focal depth is a function of the transverse offset and, possibly, the tunnel volume loss. The comparison with experimental data from centrifuge experiments and case histories confirms the reliability of the proposed method, in terms of both surface horizontal displacements and strains. In particular, the predicted horizontal displacement profiles, both in terms of maximum value and extension, are in better agreement with the available experimental evidence than those obtained using the empirical and analytical methods currently adopted in design. Finally, an operational way to obtain the complete horizontal displacement field at the surface, near-surface, and at depths down to the tunnel crown is suggested and the importance of carrying out field monitoring for surface and subsurface horizontal displacements is highlighted.

Two-dimensional thermal and dynamical strain in landfast sea ice from InSAR: results from a new analytical inverse method and field observations

Abstract Observing continuous strain in sea ice at geophysical scales of tens of meters to kilometers requires displacement measurements made with millimeter-scale precision. Satellite-based interferometric synthetic aperture radar (InSAR) provides such precise measurements of relative surface displacement over broad spatial areas at regular intervals and, unlike point displacement measurements, it allows confident delineation of continuously deforming regions. However, InSAR only captures the 1-D component of surface displacement parallel to a radar's lines-of-sight. Additional analysis is required to translate between these 1-D observations and the horizontal or vertical displacements they arose from. Previous studies utilize an iterative inverse model to constrain estimates of horizontal surface displacement from InSAR. Here we build upon that work outlining a new analytical inverse modeling method for quantifying displacement and strain over continuous regions of sea ice and provide comparison between model results and independent displacement observations. We demonstrate the inverse method over both landfast and drifting ice along the Alaskan coastline. These intercomparisons highlight environments in which displacements inverted from interferograms may be used as an independent estimator of surface strain, as well as the potential for the outlined inverse methods to be used in conjunction with other observing methods.

Coupled surface-internal deformation monitoring in three-dimensional space for freezing-thawing soil

Soil frost deformation significantly influences engineering projects in cold regions. The anisotropic behavior of soil, involving surface and internal deformation in three dimensions (3D), introduces inaccuracies in evaluating freeze–thaw geological hazards. To explore the relationship between internal strain and surface displacement of soil in a 3D space during the freezing-thawing process, a platform for monitoring coupled surface-internal deformation in 3D were developed using binocular recognition technology and a novel 3D strain rosette. Subsequently, a freezing-thawing model test of soil in Dalian Offshore Airport filling is conducted using the platform. The results show that, the internal strain of soil is closely associated with the boundary conditions of the test unit. During freezing test, the vertical strain exhibits a more significant increase in comparison to the horizontal strain. Surface displacements in soil primarily occur during the initial freezing and thawing stages. The variation of surface horizontal displacement in each direction is minimal throughout the freezing-thawing process. A surface freezing boundary leads to an increment in internal strain, while the deep frozen stress relief causes the soil surface expand during thawing. This study provides a suggestion for the control of the cold source in cold region engineering.

Surface Green’s functions of a horizontally graded elastic half-plane

High-throughput mechanical testing based on functionally graded specimens is very promising for accelerating the development of new materials. However, due to the inhomogeneity-induced complexity, most existing analyses on functionally graded materials have recourse to numerical methods to predict their mechanical responses in reaction to external stimuli. This work investigates the surface Green’s functions for an inhomogeneous half-plane with horizontal exponential material gradient subject to both normal and tangential concentrated forces acting on the surface. The governing equations are first simplified by introducing appropriate potential functions, which facilitates the mathematical derivation of displacements via the Fourier transform technique. In the case of normal force, the vertical surface displacement is derived explicitly under the weak gradient assumption while the horizontal surface displacement is derived directly without the same assumption. In particular, the Meijer G-function and Fox H-function are introduced to express and simplify the vertical displacement. In the case of tangential force, the analytical expressions of surface displacements are also derived similarly. It is noted that the surface Green’s functions not only exhibit singularity and asymmetry properties as expected, but also can be reduced to the classical Boussinesq-Flamant solutions for a homogeneous half-plane. In addition, the analytical results are verified through comparison with the finite element analyses. The surface Green’s functions derived here could be a theoretical basis for developing high-throughput mechanical testing methods which use specimens made of functionally graded materials.

Slow slip event displacement on 2018 offshore Boso Peninsula detected by Sentinel-1 InSAR time-series analysis with numerical weather model assistance

SUMMARY The south-eastern offshore of the Boso Peninsula in Japan periodically experiences short-term slow slip events (SSEs) every few years. On 2018 June, an SSE occurred with the maximum surface horizontal displacement reaching up to 4.7 cm by according to the operational global navigation satellite system (GNSS) network. This study performed a time-series analysis of interferometric synthetic aperture radar (InSAR) with Sentinel-1 SAR images to investigate detailed spatial pattern of surface displacements caused by the SSE. With the assistance of an atmospheric delay correction with a regional numerical weather model output, the InSAR time-series analysis successfully captured displacement signals in three paths, whose maximum amplitudes in line-of-sight directions were 1.46, 1.86 and −0.80 cm. A checkerboard test revealed that the resolution of the slip inversion was higher when InSAR was used than that using GNSS, especially in and around the inland. The slip inversion with the actual displacement data derived from the InSAR time-series analysis was performed with the L-curve optimization, showing that the estimated slip area was concentrated offshore south-eastward from the Boso Peninsula with the maximum slip of 5 cm and the estimated moment magnitude of 6.4. As similar to previous SSEs in the Boso Peninsula, a seismic swarm simultaneously occurred in the downdip area adjacent to the estimated slip with the SSE occurrence, suggesting a different friction characteristics between them. This study demonstrates usefulnesses of the InSAR observation for capturing detailed spatial characteristics of small-displacement events like SSEs and of the hybrid use of the externally derived delay correction with the time-series analysis to improve the displacement detection accuracy.

Study on the Cause Analysis and Trend Prediction of Typical Landslide Disasters in Pukou District

This paper takes the typical soil-rock binary structure landslide on the east side of the middle section of Yanshan Avenue in Pukou District as the research object. Through field investigation, geological surveying and mapping, Lidar scanning, drilling, rainfall and deformation monitoring data analysis and other means, the basic characteristics of the landslide and the factors affecting the stability of the landslide are analyzed. It is found that the expansibility of kaolin and the floating support force of temporary confined water are one of the factors affecting the stability of the slope. Through real-time monitoring to explore the relationship between rainfall and surface horizontal displacement and vertical displacement, it is found that the surface deformation is greatly affected by the season. When the rainfall is large, the impact of temporary confined water has a large time lag. The faster the speed to reach the saturated state, the shorter the lag time, and vice versa. On this basis, the relationship model between landslide and rainfall is established, and the development trend of landslide is predicted.

Photogrammetric Monitoring of Rock Glacier Motion Using High-Resolution Cross-Platform Datasets: Formation Age Estimation and Modern Thinning Rates

The availability of remote sensing imagery at high spatiotemporal resolutions presents the opportunity to monitor the surface motion of rock glaciers, a key constraint for characterizing the dynamics of their evolution. In this paper, we investigate four North American rock glaciers by automatically measuring their horizontal surface displacement using photogrammetric data acquired with crewed and uncrewed aircraft along with orbital spacecraft over monitoring periods of up to eight years. We estimate vertical surface changes on these rock glaciers with photogrammetrically generated digital elevation models (DEM) and digitized topographic maps. Uncertainty analysis shows that the imagery with the highest resolution and most precise positioning have the best performance when used with the automated change detection algorithm. This investigation produces gridded velocity fields over the entire surface area of each study site, from which we estimate the age of rock glacier formation using along-flow velocity integration. Though the age estimates vary, the ice within the modern extent of these landforms began flowing between 3000 and 7000 years before present, postdating the last glacial maximum. Surface elevation change maps indicate present-day thinning at the lower latitude/higher elevation sites in Wyoming, while the higher latitude/lower elevation sites in Alaska exhibit relatively stable surface elevations.

Study on Surface Deformation and Movement Caused by Deep Continuous Mining of Steeply Inclined Ore Bodies

In order to study the surface movement and deformation law of deep continuous mining of steeply inclined orebodies in high-stress areas, the surface movement and deformation law of deep continuous mining by caving method in the Shizishan mining area was studied based on the field fissures investigation, GPS monitoring, and large-scale geotechnical engineering numerical simulation software FLAC3D 5.0. The results show that with deep continuous mining of the orebody, surface fissures, and monitoring displacement are rapidly increasing. After the stoping of different sublevel orebodies, there will be an obvious settlement center on the surface, and the horizontal surface displacement also shows a trend of gradual increase. The results indicate that surface subsidence at the mine site is in an active development phase. The research results are of great significance to the prevention and control of surface rock movement disasters in mining areas.

Multi-Source SAR-Based Surface Deformation Monitoring and Groundwater Relationship Analysis in the Yellow River Delta, China

Land motions are significantly widespread in the Yellow River delta (YRD). There is, however, a lack of understanding of the delta-wide comprehensive deformation mode and its dynamic mechanism, especially triggered by groundwater extraction. This paper adopts an integrated analysis of multidisciplinary data of image geodesy, geophysics, geology and hydrogeology to provide insights into Earth surface displacement patterns and dynamics in the YRD. Delta-scale land motions were measured for the first time using L-band ALOS images processed using multi-temporal InSAR, illustrating multiple obvious surface sinking regions and a maximum annual subsidence velocity of up to 130 mm. Then, the InSAR-constrained distributed point source model with optimal kernel parameters, a smoothness factor of 10 and a model grid size of 300 m was established and confirmed to be rational, reliable and accurate for modeling analysis over the YRD. Remarkable horizontal surface displacements, moving towards and converging on a sinking center, were recovered by means of modeling and measured using InSAR, with a maximum rate of up to 60 mm per year, which can trigger significant disasters, such as ground fissures and building damage. In addition, the annual total water storage variation at the delta scale, the most meaningful outcome, can be calculated and reaches a total of approximately 12,010 × 103 m3 in Guangrao city, efficiently filling the gap of GRACE and in situ investigations for delta-wide aquifer monitoring. Finally, a comparative analysis of time series InSAR measurements, modeling outcomes, and fault and groundwater data was conducted, and the strong agreement demonstrates that faults control aquifer distribution and hence the spatial distribution of groundwater-withdrawal-related regional land subsidence. Moreover, the obvious asymmetric displacements, demonstrating a northeasterly displacement trend, further reveal that faults control aquifer distribution and Earth surface deformation. These findings are useful for understanding the land motion patterns and dynamics, helping to sustainably manage groundwater and control disasters in the YRD and elsewhere worldwide.

Landslide surface horizontal displacement monitoring based on image recognition technology and computer vision

The deformation and displacement of landslides has always been the priority of landslide monitoring and early warning. With the development of image processing technology in recent years, the analysis of landslide surface deformation through image data has become a popular method and different methods of image analysis are rapidly increasing. However, the current method of analyzing landslide deformation and displacement using a single image processing method tends to analyze the displacement of the local deformation area of the landslide, which lacks overall monitoring of the slope and is difficult to use for pre-disaster monitoring of landslide hazards, easily leading to missed detection of landslide potential hazard points. Therefore, this paper combines image recognition technology and computer vision (IR-CV) to propose a method for monitoring and identifying the deformation displacement of landslide surfaces, which has been validated by indoor landslide model tests and unmanned aerial vehicle field simulation displacement recognition tests. In the model tests, the IR-CV method successfully identified the displacements generated during the deformation and damage of the landslide model while using the model deformation time series image data recorded by the camera to analyze the overall deformation of the surface of the landslide model. Further, in this paper, a field simulation displacement identification test was conducted using an unmanned aerial vehicle (UAV), and the orthophoto data obtained by the UAV verified that the IR-CV method can be used for overall deformation displacement identification of landslides in the field. The results of indoor model tests and field UAV simulation tests show that the monitoring method of IR-CV can effectively identify the deformation and displacement of landslide surfaces, which has good application prospects in pre-disaster monitoring and displacement identification of landslides, thus providing a cost-effective and feasible solution for monitoring the deformation and displacement of landslide surfaces.

Quantifying Two-Dimensional Surface Displacements Using High-Resolution Cosmo-SkyMed, TerraSAR-X and Medium-Resolution Sentinel-1 SAR Interferometry: Case Study for the Tengiz Oilfield.

The present study was aimed at comparing vertical and horizontal surface displacements derived from the Cosmo-SkyMED, TerraSAR-X and Sentinel-1 satellite missions for the detection of oil extraction-induced subsidence in the Tengiz oilfield during 2018–2021. The vertical and horizontal surface displacements were derived using the 2D decomposition of line-of-sight measurements from three satellite missions. Since the TerraSAR-X mission was only available from an ascending track, it was successfully decomposed by combining it with the Cosmo-SkyMED descending track. Vertical displacement velocities derived from 2D Decomposition showed a good agreement in similar ground motion patterns and an average regression coefficient of 0.98. The maximum average vertical subsidence obtained from the three satellite missions was observed to be −57 mm/year. Higher variations and deviations were observed for horizontal displacement velocities in terms of similar ground motion patterns and an average regression coefficient of 0.80. Fifteen wells and three facilities were observed to be located within the subsidence range between −55.6 mm/year and −42 mm/year. The spatial analyses in the present studies allowed us to suspect that the subsidence processes occurring in the Tengiz oilfield are controlled not solely by oil production activities since it was clearly observed from the detected horizontal movements. The natural tectonic factors related to two seismic faults crossing the oilfield, and terrain characteristics forming water flow towards the detected subsidence hotspot, should also be considered as ground deformation accelerating factors. The novelty of the present research for Kazakhstan’s Tengiz oilfield is based on the cross-validation of vertical and horizontal surface displacement measurements derived from three radar satellite missions, 2D Decomposition of Cosmo-SkyMED descending and TerraSAR-X ascending line-of-sight measurements and spatial analysis of man-made and natural factors triggering subsidence processes.

Correlation Dimension in Sumatra Island Based on Active Fault, Earthquake Data, and Estimated Horizontal Crustal Strain to Evaluate Seismic Hazard Functions (SHF)

This study intends to evaluate the possible correlation between the correlation dimension (DC) and the seismic moment rate for different late Quaternary active fault data, shallow crustal earthquakes, and GPS on the island of Sumatra Probabilistic Seismic Hazard Analysis (PSHA). The seismicity smoothing was applied to estimate the DC of active faults (DF) and earthquake data (DE) and then to correlate that with the b-value, which will be used to identify seismic hazard functions (SHF) along with the Sumatra Fault Zone (SFZ). The seismicity based on GPS data was calculated by the seismic moment rate that is estimated based on pre-seismic horizontal surface displacement data. The correlation between DF, DE, and the b-value was analyzed, and a reasonable correlation between the two seismotectonic parameters, DF-b, and DE-b, respectively, could be found. The relatively high DC coincides with the high seismic moment rate model derived from the pre-seismic GPS data. Furthermore, the SHF curve of total probability of exceedance versus the mean of each observation point’s peak ground acceleration (PGA) shows that the relatively high correlation dimension coincides with the high SHF. The results of this study might be very beneficial for seismic mitigation in the future.

Three-Dimensional Surface Displacements of the 8 January 2022 Mw6.7 Menyuan Earthquake, China from Sentinel-1 and ALOS-2 SAR Observations

The 8 January 2022 Mw6.7 Menyuan earthquake was generated in the transition zone between the western Lenglongling fault and the eastern Tuolaishan fault, both being part of the Qilian–Haiyuan fault system with an important role in the adjustment of the regional tectonic regime. In this study, four pairs of SAR (synthetic aperture radar) data from Sentinel-1 and ALOS-2 (Advanced Land Observation Satellite-2) satellites were used to derive the surface displacement observations along the satellite line-of-sight (LOS) and azimuth directions using the differential interferometric SAR (InSAR, DInSAR), pixel offset-tracking (POT), multiple aperture InSAR (MAI), and burst overlap InSAR (BOI) methods. An SM-VCE method (i.e., a method for measuring three-dimensional (3D) surface displacements with InSAR based on a strain model and variance component estimation) was employed to combine these derived SAR displacement observations to calculate the 3D co-seismic displacements. Results indicate that the 2022 Menyuan earthquake was dominated by left-lateral slip, and the maximum horizontal and vertical displacements were 1.9 m and 0.6 m, respectively. The relative horizontal surface displacement across the fault was as large as 2–3 m, and the fault-parallel displacement magnitude was larger on the southern side of the fault compared with the northern side. Furthermore, three co-seismic strain invariants were also investigated, revealing that the near-fault area suffered severe deformation, and two obviously expanding and compressed zones were identified. We provide displacements/strains derived in this study in the prevailing geotiff format, which will be useful for the broad community studying this earthquake; in addition, the SM-VCE code used in this study is open to the public so that readers can better understand the method.

Persistent Scatterer Interferometry for Pettimudi (India) Landslide Monitoring using Sentinel-1A Images

The continuous monitoring of land surface movement over time is of paramount importance for assessing landslide triggering factors and mitigating landslide hazards. This research focuses on measuring horizontal and vertical surface displacement due to a devastating landslide event in the west-facing slope of the Rajamala Hills, induced by intense rainfall. The landslide occurred in Pettimudi, a tea-plantation village of the Idukki district in Kerala, India, on August 6–7, 2020. The persistent-scatterer synthetic aperture radar interferometry (PSInSAR ) technique, along with the Stanford Method for Persistent Scatterers (StaMPS), was applied to investigate the land surface movement over time. A stack of 20 Sentinel-1A single-look complex images (19 interferograms) acquired in descending passes was used for PSInSAR processing. The line-of-sight (LOS ) displacement in long time series, and hence the average LOS velocity, was measured at each measurement-point location. The mean LOS velocity was decomposed into horizontal east–west (EW ) and vertical up–down velocity components. The results show that the mean LOS, EW, and up–down velocities in the study area, respectively, range from –18.76 to +11.88, –10.95 to +6.93, and –15.05 to +9.53 mm/y, and the LOS displacement ranges from –19.60 to +19.59 mm. The displacement values clearly indicate the instability of the terrain. The time-series LOS displacement trends derived from the applied PSInSAR technique are very useful for providing valuable inputs for disaster management and the development of disaster early-warning systems for the benefit of local residents.

Diffuse Deformation and Surface Faulting Distribution from Submetric Image Correlation along the 2019 Ridgecrest, California, Ruptures

ABSTRACT The 2019 Mw 6.4 and 7.1 Ridgecrest, California, earthquake sequence (July 2019) ruptured consecutively a system of high-angle strike-slip cross faults (northeast- and northwest-trending) within 34 hr. The complex rupture mechanism was illuminated by seismological and geodetic data, bringing forward the issue of the interdependency of the two fault systems both at depth and at the surface, and of its effect on the final surface displacement pattern. Here, we use high-resolution (WorldView and Pleiades) optical satellite image correlation to measure the near-fault horizontal and vertical surface displacement fields at 0.5 m ground resolution for the two earthquakes. We point out significant differences with previous geodetic- and geologic-based measurements, and document the essential role of distributed faulting and diffuse deformation in producing the observed surface displacement patterns. We derive strain fields from the horizontal displacement maps, and highlight the predominant role of rotation and shear strain in the surface rupture process. We discuss the segmentation of the rupture based on the fault geometry and along-strike slip variations. We also image several northeast-trending faults with similar orientation to the deeply embedded shear fabric identified in aftershock studies, and show that these cross faults are present all along the rupture, including at a scale <100 m. Finally, we compare our results to kinematic slip inversions, and show that the surface diffuse deformation is primarily associated with areas of shallow slip deficit; however, this diffuse deformation cannot be explained using elastic modeling. We conclude that inelastic processes play an important role in contributing to the total surface deformation associated with the 2019 Ridgecrest sequence.

Mechanical Response of Shallow Crust to Groundwater Storage Variations: Inferences From Deformation and Seismic Observations in the Eastern Southern Alps, Italy

AbstractChanges in continental water storage generate vertical surface deformation, induce crustal stress perturbations, and modulate seismicity rates. However, the degree to which regional changes in terrestrial water content influence crustal stresses and the occurrence of earthquakes remains an open problem. We show how changes in groundwater storage, computed for a ∼1,000 km2 basin, focus deformation in a narrow zone, causing large horizontal, nonseasonal displacements. We present results from a karstic mountain range located at the edge of the Adria‐Eurasia plate boundary system in Northern Italy, where shortening is accommodated across an active fold‐and‐thrust belt. The presence of geological structures with high permeabilities and of deeply rooted hydrologically active fractures focus groundwater fluxes and pressure changes, generating transient surface horizontal displacements up to 5 mm and perturbations of crustal stress up to 25 kPa at seismogenic depths. The background seismicity rates appear correlated, without evident temporal delay, with groundwater storage changes in the hydrological basin. With no evidence of pore pressure propagation from the hydrologically active fractures, seismicity modulation is likely affected by direct stress changes on faults planes.

KINEMATIC MODEL OF THE SLOW-MOVING KOSTANJEK LANDSLIDE IN ZAGREB, CROATIA

The interpretation of landslide kinematics provides important information for those responsible for the management of landslide risk. This paper presents an interpretation of the kinematics of the slow-moving Kostanjek landslide, located in the urbanized area of the city of Zagreb, Croatia. The sliding material (very weak to weak marls, often covered with clayey topsoil) exhibits plastic, rather than rigid behavior. Due to this reason, and low landslide velocities, landslide features, such as main scarps or lateral flanks, are barely noticeable or do not exist in most of the landslide area. The data used for the kinematic interpretation were obtained from 15 GNSS sensors, for the period of 2013-2019. The monitoring data revealed a different spatial and temporal distribution of landslide velocities, resulting as a consequence of geomorphological conditions and forces that govern the landslide movements. Temporally, eight periods of faster movements and seven periods of slower movements were determined. Spatially, velocities measured in the central part of the landslide were higher than on its boundaries. The interpretation of the surface (horizontal and vertical) displacements and the direction of movement reveal a new insight into the engineering geological model and provide important information for the management of the Kostanjek landslide risk.

Coseismic Slip Distribution of the 24 January 2020 Mw 6.7 Doganyol Earthquake and in Relation to the Foreshock and Aftershock Activities

AbstractOn 24 January 2020 (UTC), a destructive Mw 6.7 earthquake struck the east Anatolian fault of eastern Turkey after a series of foreshocks, causing many casualties and significant property damage. In this study, the rupture process of this earthquake is investigated with teleseismic broadband body-wave and surface-wave records. Results indicate that this earthquake is a left-lateral strike-slip event, and the rupture extends mainly to south. The main slip patch spreads ∼30 km along strike in the shallow above 14 km with a peak slip of ∼1.2 m, and the total seismic moment is 1.69×1019 N·m. The east–west component of horizontal surface displacement predicted with our slip model ranges from ∼0.4 to −0.3 m. The predicted displacements are consistent with the observed ones obtained from satellite images. We relocate 459 foreshocks and early aftershocks to explore the relationship between foreshock and aftershock sequences and coseismic slip. It is noted that there is an anticorrelation relationship between the distributions of early aftershocks and the coseismic slip. The strain energy in the large slip patch may have been sufficiently released by the mainshock; therefore, fewer early aftershocks occurred in that patch. Although we note a similar pattern between the relocated foreshock and coseismic slip, and a migration of foreshock, our dataset may not well resolve the correlation and migration due to the incomplete relocation foreshock catalog. Based on the slip model, we calculate the coulomb stress changes on the surrounding faults caused by the mainshock. The results reveal that the mainshock promoted stress accumulation on the northern and southern ends of the Elazig–Matalya segment and may reactivate the locked fault segment, leading to a high seismic risk in these regions. Although this earthquake does not significantly increase the coulomb stress change, the seismic risk of the Matalya–Kahraman Maras–Antakya segment should draw attention.

Reliability assessment of the performance of granular column in the nonuniform liquefiable ground to mitigate the liquefaction-induced ground deformation

ABSTRACT Granular columns have been widely used to mitigate the liquefaction-induced ground deformation. The increment in lateral stress due to densification, shear reinforcement, and drainage capacity of granular columns are believed to increase the liquefaction resistance of the ground. However, several case histories and recent research development exhibited the limitations of the effectiveness of granular columns under strong earthquakes. Besides, the mechanism of shear reinforcement governed by granular columns is poorly understood. Moreover, the spatial nonuniformity of the ground should be considered for a reliable engineering assessment of the performance of granular columns. A series of three-dimensional nonlinear stochastic analyses are carried out using the OpenSees framework with PDMY02 elasto-plastic soil constitutive model to map the reliability of the performance of equally-spaced granular columns. Soil variability is implemented with stochastic realizations of overburden and energy-corrected, equivalent clean sand, (N1)60cs values using spatially correlated Gaussian random field. The reliability of the performance of granular column is assessed based on the stochastic distributions of average surface settlement and horizontal ground displacement associated with the degree of confidence. The implications of cumulative absolute velocity, Arias Intensity and peak acceleration of different ground motions on the efficacy of the granular column are also discussed.

Reply to the comment by Alexander G. Sorokin, Anatoly V. Klyuchevskii on “Hovsgol earthquake 5 December 2014, MW = 4.9: seismic and acoustic effects” by Anna A. Dobrynina, Vladimir A. Sankov, Larisa R. Tcydypova, Victor I. German, Vladimir V. Chechelnitsky, Ulzibat Munkhuu

We again give thanks to A. Sorokin and A. Klyuchevskii and the Editorial Board of the Journal for the opportunity to discuss our results that have been published in the “Journal of Seismology” (Dobrynina, A.A., Sankov, V.A., Tcydypova, L.R., German, V.I., Chechelnitsky V.V., Ulzibat M. Hovsgol Earthquake 5 December 2014, Mw = 4.9: seismic and acoustic effects // J Seismology. 2018. V. 22, Is. 2. P. 377–389. https://doi.org/10.1007/s10950-017-9711-z ). In our article, on the basis of the arrival time of the infrasound signal at the Tory site, the seismic waveform analysis and evaluations of the horizontal and vertical surface displacement, we suggested that the registered acoustic signal of the Hovsgol earthquake on 5 December 2014, Mw = 4.9 was generated by the interaction of seismic waves with the regional topography. In contrast, A. Sorokin and A. Klyuchevskii believe that the infrasound signal was associated with flexural waves from ice on the surface of the lake above the source of the earthquake. However, there are many crucial points in their comments that we find to be scientifically flawed and poorly reasoned. In this reply, we give a detailed response to their comments.