Seismological Observations Research Articles

From fault creep to slow and fast earthquakes in carbonates

Abstract A major part of the seismicity striking the Mediterranean area and other regions worldwide is hosted in carbonate rocks. Recent examples are the destructive earthquakes of L’Aquila (Mw 6.1) in 2009 and Norcia (Mw 6.5) in 2016 in central Italy. Surprisingly, within this region, fast (≈3 km/s) and destructive seismic ruptures coexist with slow (≤10 m/s) and nondestructive rupture phenomena. Despite its relevance for seismic hazard studies, the transition from fault creep to slow and fast seismic rupture propagation is still poorly constrained by seismological and laboratory observations. Here, we reproduced in the laboratory the complete spectrum of natural faulting on samples of dolostones representative of the seismogenic layer in the region. The transitions from fault creep to slow ruptures and from slow to fast ruptures were obtained by increasing both confining pressure (P) and temperature (T) up to conditions encountered at 3–5 km depth (i.e., P = 100 MPa and T = 100 °C), which corresponds to the hypocentral location of slow earthquake swarms and the onset of seismicity in central Italy. The transition from slow to fast rupture is explained by an increase in the ambient temperature, which enhances the elastic loading stiffness of the fault, i.e., the slip velocities during nucleation, allowing flash weakening and, in turn, the propagation of fast ruptures radiating intense high-frequency seismic waves.

A stochastic rupture earthquake code based on the fiber bundle model (TREMOL v0.1): application to Mexican subduction earthquakes

Abstract. In general terms, earthquakes are the result of brittle failure within the heterogeneous crust of the Earth. However, the rupture process of a heterogeneous material is a complex physical problem that is difficult to model deterministically due to numerous parameters and physical conditions, which are largely unknown. Considering the variability within the parameterization, it is necessary to analyze earthquakes by means of different approaches. Computational physics may offer alternative ways to study brittle rock failure by generating synthetic seismic data based on physical and statistical models and through the use of only few free parameters. The fiber bundle model (FBM) is a stochastic discrete model of material failure, which is able to describe complex rupture processes in heterogeneous materials. In this article, we present a computer code called the stochasTic Rupture Earthquake MOdeL, TREMOL. This code is based on the principle of the FBM to investigate the rupture process of asperities on the earthquake rupture surface. In order to validate TREMOL, we carried out a parametric study to identify the best parameter configuration while minimizing computational efforts. As test cases, we applied the final configuration to 10 Mexican subduction zone earthquakes in order to compare the synthetic results by TREMOL with seismological observations. According to our results, TREMOL is able to model the rupture of an asperity that is essentially defined by two basic dimensions: (1) the size of the fault plane and (2) the size of the maximum asperity within the fault plane. Based on these data and few additional parameters, TREMOL is able to generate numerous earthquakes as well as a maximum magnitude for different scenarios within a reasonable error range. The simulated earthquake magnitudes are of the same order as the real earthquakes. Thus, TREMOL can be used to analyze the behavior of a single asperity or a group of asperities since TREMOL considers the maximum magnitude occurring on a fault plane as a function of the size of the asperity. TREMOL is a simple and flexible model that allows its users to investigate the role of the initial stress configuration and the dimensions and material properties of seismic asperities. Although various assumptions and simplifications are included in the model, we show that TREMOL can be a powerful tool to deliver promising new insights into earthquake rupture processes.

Observations of guided waves from the Pamir seismic zone provide additional evidence for the existence of subducted continental lower crust

As part of the TIPAGE (TIen shan – PAmir GEodynamic program) project, passive seismological observations were made along an approximately N-S profile crossing the Pamir seismic zone for about one year. From these observations guided waves were recognized. These guided waves occur as a single, continuous, secondary, compressional (P) wave phase behind the first P-wave arrivals. An equivalent phase in the shear (S) wavefield is hardly recognizable. Modelling of the phase shows that an approximately 10 km thick low velocity zone (LVZ) between the Moho and about 160 km depth reproduces the guided waves as a single, continuous phase much better than a 15–20 km thick LVZ. Modelling of the arrival times of the guided waves reveals that a model with a P-wave velocity of 6.3 km/s above about 100 km depth, and a velocity of 7.6 km/s between this depth and the deep cluster of earthquakes at about 150 km depth provides the best fit to the observed travel-time data. One plausible way to explain the low velocity of 6.3 km/s is to invoke the presence of melts in the LVZ. Then, taking a velocity of 6.9 km/s for the lower crust being subducted, about 10–13% melt is required to obtain a velocity of about 6.3 km/s in the LVZ between the Moho and about 100 km depth. This would be in keeping with the estimated burial depths from xenoliths of Gondwana terrane affinity brought to the surface in the southeastern Pamir around 11 million yr. ago. The present-day LVZ is interpreted to comprise continental lower crust. Although guided waves are known to exist associated with subducted oceanic crust or fault zones, this is the first time to the knowledge of the authors that guided waves have been observed resulting from a LVZ associated with subducted continental lower crust.

Velocity‐Density Systematics of Fe‐5wt%Si: Constraints on Si Content in the Earth's Inner Core

AbstractThe elasticity of hcp‐Fe‐5wt%Si has been investigated by synchrotron X‐ray diffraction up to 110 GPa and 2,100 K and by picosecond acoustics measurements at ambient temperature up to 115 GPa. The established Pressure‐Volume‐Temperature equation of state shows that the density of the Earth's inner core can be matched by an Fe‐Si alloy with 5wt% Si for all reasonable core temperatures, but that its compressional and shear velocities remain too high with respect to seismological observations. On the other hand, Fe‐Si alloys whose velocities are expected to get close to seismological observations are too dense at relevant temperatures. Thus, based on these combined velocity‐density measurements, silicon is not likely to be the sole light element in the inner core.

Reassessment of the 1907 Sumatra “Tsunami Earthquake” Based on Macroseismic, Seismological, and Tsunami Observations, and Modeling

On 4 January 1907, an earthquake occurred off the west coast of Sumatra, Indonesia, with an instrumental surface-wave magnitude (MS) in the range of 7.5–8.0 at periods of ~ 40 s. The tsunami it generated was destructive on the islands of Nias and Simeulue, where it killed hundreds and gave rise to the legend of the S’mong. This tsunami was also observed in other parts of the Indian Ocean basin. Relative to its instrumented magnitude, the size of the tsunami was anomalous, qualifying the event as a “tsunami earthquake”. However, unusually for a tsunami earthquake, the shaking on Nias was severe (7 EMS). We revisit the 1907 earthquake with a multidisciplinary approach by extracting evidence describing shaking effects or the tsunami from written documents and by acquiring new seismograms. Combining these, we discriminate two large earthquakes within an hour of each other with clear differences in seismological character. The first we interpret to be a tsunami earthquake with characteristic low levels of shaking, an estimated average seismic moment (M0) of 2.5 × 1028 dyn cm (MW ≈ 8.2) in the frequency band 6–8 mHz, and an epicentral location close to the front of the Sunda Megathrust. The seismograms we analyzed also document a regular growth of moment with period, approaching MW ≈ 8.4 at the longest resolvable period (~ 170 s). For the second earthquake that caused damage on Nias, we estimate MS ≈ 7 based on seismograms and phase data. We also identify two MS ≈ 6 aftershocks within 24 h of the mainshock. Additionally, we present a dataset of 88 locations within the Indian Ocean basin where the tsunami was observed. Using a subset of these, we forward modeled the tsunami to propose a seismic rupture model extending along the Sunda Megathrust for about 220 km (~ 94.7°E to ~ 97°E) with a maximum modeled slip of ~ 21 m. Our new rupture model provides an acceptable fit to our new dataset of tsunami runup and inundation values from 88 local and far-field locations in the Indian Ocean basin. We also urge caution against an over-reliance on the S’mong legend for tsunami evacuation as its premise, that a tsunami will only follow an earthquake with very severe ground motions, is rendered ineffective for tsunami earthquakes.

Optimizing a soil gas monitoring network layout across faults based on a seismogenic model

We undertake a sturdy body seismogenic model study along the northern margin of the West Qinling fault zone, China, to address some existing problems of neglecting scientific layout based on certain prediction theory and observation facts surrounding underground fluid monitoring networks across faults. A combination of high-density underground fluid measurements and vertical crustal deformation and seismological observations were used to elucidate the interplay between fluid dynamics, crustal deformation, and seismic activity and to comprehensively analyze the fault segment characteristics along the fault zone. We found correspondence between these parameters along the northern margin of the West Qinling fault zone. All parameters showed higher values in the Wu Shan (WS) segment than in the western Xia He–Huang Xiang Gou–Zhang Xian (XH-HXG-ZX) segment and eastern Tian Shui (TS) area. The 222Rn concentration reached 5.0942 at BZC, and the Hg concentration reached 3.4398 at LJG in WS. Similarly, the vertical crustal deformation and seismic activity in this area were both stronger than those in the western XH–HXG–ZX and TS area. Based on the sturdy body seismogenic model, we found that the ZX and TS segments exhibited weaker activity than the surrounding areas and may be in a deep locked state under the corresponding regional stress. Compared with existing monitoring network for background value detection and comprehensive research results, we propose a technical underground flow monitoring network prototype that includes two grade I and five grade II survey sites along the northern margin of the West Qinling fault zone based on the sturdy body seismogenic model. This prototype will provide a more reliable basis for earthquake prediction, tracking and mitigation, and disaster risk reduction. The presented scheme can be used as a guideline for deploying fault soil gas monitoring networks in China.

Seismicity and mineral destabilizations in the subducting mantle up to 6 GPa, 200 km depth

In the subducting oceanic lithosphere, a significant part of the seismicity is triggered in the mantle, especially along the upper and lower Wadati-Benioff planes. Several studies have investigated the potential involvement of dehydration reactions in the triggering mechanism of mantle earthquakes. Recent experimental results reveal that, under subduction conditions, mechanical instabilities nucleate in strong stable mineral aggregates during the destabilization of minor amounts of antigorite, i.e. the high-temperature serpentine, through a stress transfer, without any fluid overpressure. Here I confront these laboratory results to seismological observations. On one hand, most of the natural hydrous magnesium silicates seem to be known, with experimentally deduced stability limits up to 7 GPa, at least, available as relatively accurate estimates. On the other hand, recent achievements in thermal structure of subduction zones combined with precise hypocentre relocation give access to pressure and temperature conditions at earthquakes hypocentres. A series of P-T diagrams summarizes the stability limit of minerals that may be part of natural peridotites or serpentinites with variable compositions at pressures from 0.5 to 6 GPa and temperatures from 200 to 950 °C, and compares it with seismicity. Both hydrous and anhydrous phases are considered. A myriad of minor metamorphic reactions could participate in a transformation-driven stress transfer, even if the stability limits of serpentine minerals seem to correlate with most of the observed seismicity.

Multiple Observations of the Prompt Elastogravity Signals Heralding Direct Seismic Waves

AbstractThe recent first observations of the prompt elastogravity signals (PEGS) induced by the 2011 Mw = 9.1 Tohoku megathrust earthquake generated interest in how these signals might best be observed, especially for lower‐magnitude events. Simulations of these signals preceding the direct P wave, for different depths and focal mechanisms, first reveal that shallow strike‐slip earthquakes offer a better detection potential than subduction megathrust earthquakes. Consistently, clear PEGS are observed at several broadband seismometers during the 2012 Mw = 8.6 Wharton Basin earthquake. Due to their short source durations, large deep earthquakes are then shown to have an even larger detection potential, confirmed by the successful seismological observations for the 2018 Mw = 8.2 Fiji and 1994 Mw = 8.2 Bolivia earthquakes. Detection is even improved when an earthquake is recorded by a number of good‐quality stations, allowing for stacking techniques. Thanks to the deployment of the USArray network across Alaska, the recent 2018 Mw = 7.9 off‐Alaska earthquake (strike slip) is thus observed with an excellent signal‐to‐noise ratio. Array stacking is also shown to reveal the PEGS induced by the large 2010 Mw = 8.8 Maule megathrust earthquake, for which individual observations are impeded by the long‐lasting radiation generated by a distant large earthquake. As a whole, we show new observations and successful modeling of the PEGS for five earthquakes in the 7.9–8.8 magnitude range. These findings demonstrate that, even without considering promising future instruments, the PEGS detection is not restricted to exceptional events, confirming their potential for magnitude and focal mechanism determination within the few minutes following a large earthquake.

SPECTRAL FEATURES OF THE MICROSEMIC FIELD OF THE URBANIZED TERRITORY

Currently, seismic monitoring is considered as a geophysical technique for recording and determining earthquake parameters. This determines the distribution of such type of monitoring in seismic areas. At the same time, seismic signals carry important information about various natural phenomena and the human impact on the environment. Registration of microseismic vibrations allows to determine the resonant features of the soil strata, which can enhance the vibrations during earthquakes, as well as during the operation of various mechanisms, causing structural damage and such a phenomenon as vibrational liquefaction of clay soils. The paper analyzes the data of long-term observations of microseismic noise in an urbanized area by the network of seismological observations Vladikavkaz and mobile stations. Daily variations of the microseismic field are shown and a map of the predominant frequencies of microseismic vibrations due to the influence of ground conditions is compiled.

Relationship Between Depth of Seismicity and Heat Flow: The Case of the Gargano Area (Italy)

We consider a thermo-rheological model made of a viscoelastic half-space with Maxwell rheology and temperature-dependent viscosity. The half-space is made of layers with different values of density, thermal conductivity, activation energy and heat productivity. The model relates the surface heat flow to the depth of the brittle-ductile transition and the thickness of the seismogenic layer. The model is applied to the Gargano area (Italy) which is subject to a frequent low-magnitude seismic activity, although it lies out of the Apennine axis, which is the main Italian seismogenic area. The seismic activity in the Gargano area and surroundings occurs at depths that are systematically different in the north-eastern zone with respect to the south-western zone. In correspondence with the change in depth of earthquake foci, we observe a change in the value of surface heat flow. Starting from these observations and from the knowledge of the lithospheric structure, we propose two different geotherms for the two zones. Assuming a constant strain rate, the shear stress is computed as a function of depth and the thickness of the seismogenic layer in the two zones is inferred. The comparison of the results of the thermo-rheological model with the seismological observation is good.

Power spectra of random heterogeneities in the solid earth

Abstract. Recent seismological observations focusing on the collapse of an impulsive wavelet revealed the existence of small-scale random heterogeneities in the earth medium. The radiative transfer theory (RTT) is often used for the study of the propagation and scattering of wavelet intensities, the mean square amplitude envelopes through random media. For the statistical characterization of the power spectral density function (PSDF) of the random fractional fluctuation of velocity inhomogeneities in a 3-D space, we use an isotropic von Kármán-type function characterized by three parameters: the root mean square (RMS) fractional velocity fluctuation, the characteristic length, and the order of the modified Bessel function of the second kind, which leads to the power-law decay of the PSDF at wavenumbers higher than the corner. We compile reported statistical parameters of the lithosphere and the mantle based on various types of measurements for a wide range of wavenumbers: photo-scan data of rock samples; acoustic well-log data; and envelope analyses of cross-hole experiment seismograms, regional seismograms, and teleseismic waves based on the RTT. Reported exponents of wavenumber are distributed between −3 and −4, where many of them are close to −3. Reported RMS fractional fluctuations are on the order of 0.01–0.1 in the crust and the upper mantle. Reported characteristic lengths distribute very widely; however, each one seems to be restricted by the dimension of the measurement system or the sample length. In order to grasp the spectral characteristics, eliminating strong heterogeneity data and the lower mantle data, we have plotted all the reported PSDFs of the crust and the upper mantle against wavenumber for a wide range (10−3–108 km−1). We find that the spectral envelope of those PSDFs is well approximated by the inverse cube of wavenumber. It suggests that the earth-medium randomness has a broad spectrum. In theory, we need to re-examine the applicable range of the Born approximation in the RTT when the wavenumber of a wavelet is much higher than the corner. In observation, we will have to carefully measure the PSDF on both sides of the corner. We may consider the obtained power-law decay spectral envelope as a reference for studying the regional differences. It is interesting to study what kinds of geophysical processes created the observed power-law spectral envelope at different scales and in different geological environments in the solid earth medium.

Neogene Epeirogeny of Iberia

AbstractThe origin of Iberia's topography is examined by combining gravity, magmatic, topographic, and seismological observations with geomorphic considerations. We have four principal results. First, the highest coherence between free‐air gravity and topography is at wavelengths 250 km where admittance indicates that elastic thickness of Iberia's plate is 20 ± 3 km. These results imply that flexural and subplate support of Iberian topography could be expressed at wavelengths of O(100) km. Second, P‐to‐S receiver functions and simple isostatic calculations indicate that while crustal thickness variations and flexural loading (e.g., as a result of plate shortening) partially explain the elevation of Pyrenean, Betics, Cantabrian, Spanish Central System, and Iberian Chain topography, they fail to explain the elevation of large parts of Iberia. Third, a new full waveform shear wave tomographic model and velocity to temperature conversions suggest that the asthenosphere beneath Iberia is anomalously slow and has excess temperatures of up to 162 ± 14 °C. Simple isostatic calculations indicate asthenospheric support of topography of up to 1 km. Neogene‐Recent (∼23–0 Ma) extrusive magmatism (e.g., Calatrava, Catalan) sit atop many of the slow shear wave velocity anomalies. Finally, biostratigraphic data, combined with inversion of 3,217 river profiles, show that most of Iberia's topography grew during the last ∼30 Ma at rates of up to 0.3 mm/year. Best‐fitting theoretical rivers have a low residual root‐mean‐square misfit (=0.96) and calculated uplift is consistent with an independent inventory of stratigraphic and biostratigraphic observations. We suggest that Neogene‐Recent growth of most of central Iberia's topography was a result of asthenospheric support.

Seismic Potential Around the Northeastern Edge of the Longmenshan Fault Zone as Inferred from Seismological Observations

We assessed the seismic potential around the northeastern edge of the Longmenshan fault zone (LFZ) by analyzing the aftershocks of the 2008 Mw 7.9 Wenchuan earthquake, focusing on the right-lateral strike-slip Qingchuan fault (QCF). The data used in the present study were collected from a dense network of broadband seismographs, installed after the Mw 7.9 mainshock by the China Earthquake Administration. We analyzed 440 aftershocks that occurred around the northeastern part of the aftershock area between December 2008 and June 2009, the local magnitudes (ML) of which ranged from 2.0 to 5.2. We determined 127 well-constrained focal mechanism solutions for these aftershocks down to ML 2.5 by using P-wave polarity data in conjunction with body-wave amplitudes. An analysis of the stress tensor inversion revealed that, upon approaching the QCF from the LFZ, the stress field changes from a reverse faulting regime to a mixed regime containing strike-slip components and the orientation of the maximum compressional stress changes from a NW–SE to a WNW–ESE direction. This stress field favors a right-lateral strike-slip movement along the fault. The slip tendency analysis revealed that the QCF is regarded as being favorably oriented to the present-day stress field. The coseismic Coulomb stress changes induced by the mainshock increased along the preferred fault plane in the northeastern half of the QCF, which is further loaded by viscoelastic relaxation. This evidence suggests that the potential for a future earthquake in the QCF is high.

Geological factors of gassing of the east inclined longwall # 3 of m3 bed at O.F. Zasiadko mine

The paper deals with the fact that gassing of the East inclined longwall (EIL) # 3 of the m3 bed at the «O.F. Zasiadko mine» are caused by a combination of mining-geological conditions. The main geological factor is the presence of a synclinal fold, characterized by increased fracturing. The map construction of local structures, the use of gravity data and seismological observations allow to effectively isolate gas-saturated zones and, therefore, correct degassing projects and parameters of ways to prepare workings.

Plate Coupling Mechanism of the Central Andes Subduction: Insight from Gravity Model

Abstract The Central Andes experienced major earthquake (Mw =8.2) in April 2014 in a region where the giant 1877 earthquake (Mw=8.8) occurred. The 2014 Iquique earthquake did not break the entire seismic gap zones as previously predicted. Geodetic and seismological observations indicate a highly coupled plate interface. To assess the locking mechanism of plate interfaces beneath Central Andes, a 2.5-D gravity model of the crust and upper mantle structure of the central segment of the subduction zone was developed based on terrestrial and satellite gravity data from the LAGEOS, GRACE and GOCE satellite missions. The densities and major structures of the gravity model are constrained by velocity models from receiver function and seismic tomography. The gravity model defined details of crustal and slab structure necessary to understand the cause of megathrust asperity generation. The densities of the upper and lower crust in the fore-arc (2970 – 3000 kg m−3) are much higher than the average density of continental crust. The high density bodies are interpreted as plutonic or ophiolitic structures emplaced onto continental crust. The plutonic or ophiolitic structures may be exerting pressure on the Nazca slab and lock the plate interfaces beneath the Central Andes subduction zone. Thus, normal pressure exerted by high density fore-arc structures and buoyancy force may control plate coupling in the Central Andes. However, this interpretation does not exclude other possible factors controlling plate coupling in the Central Andes. Seafloor roughness and variations in pore-fluid pressure in sediments along subduction channel can affect plate coupling and asperity generation.

Distribution of seisms foci during the mining of 19th eastern longwall and Eastern inclined longwall #3

The paper presents the results performed at the O.F. Zasiadko mine seismological observations on the registration and location of seisms that occur during the mining of the m3 bed. According to the constructed magnitude-frequency relationship for the worked out longwalls, it was concluded that the longwalls worked out in different mining-geological conditions differ in the relative energy of seisms, in their number, recording time and spatial location of foci.

Effects of Fe and Al incorporations on the bridgmanite–postperovskite coexistence domain

The postperovskite phase transition of Fe and Al-bearing MgSiO3 bridgmanite, the most aboundant mineral in the Earth's lower mantle, is believed to be a key to understanding seismological observations in the D″ layer, e.g., the discontinuous changes in seismic wave velocities. Experimentally reported phase transition boundaries of Fe and Al-bearing bridgmanite are currently largely controversial and generally suggest wide two-phase coexistence domains. Theoretical simulations ignoring temperature effects cannot evaluate correctly two-phase coexistence domains under high-temperature. We show high-pressure and high-temperature phase transition boundaries for various compositions with geophysically relevant impurities of Fe2+SiO3, Fe3+Fe3+O3, Fe3+Al3+O3, and Al3+Al3+O3 derived from the ab initio finite-temperature free energies calculated combining the internally consistent LSDA+U method and a lattice dynamics approach. We found that at ∼2500K, incorporations accompanied by Fe3+ expand the two-phase coexistence domains distinctly, implying that D″ seismic discontinuities likely arise from the phase transition of Fe2+-bearing bridgmanite.

Anelasticity from seismic to tidal timescales: Theory and observations

We examine strain energy dissipation of Earth's normal modes and body tides in order to compare these observations with predictions from an experimental model of intrinsic dissipation. For this comparison we employ a recently developed self-consistent treatment of modes and tides, that includes the separation of dynamical processes (self-gravity and inertia) from intrinsic attenuation. We select a set of normal modes and tides with similar depth sampling centered on the lower mantle, without contributions from the core. This dataset ranges from 7 min to 18.6 yr, or about 6 decades in frequency. The results show that the attenuation of the higher-frequency modes defines a broad plateau in dissipation (inferred experimentally to occur at the transition from elastic to anelastic behavior) whereas the attenuation of lower-frequency tides falls on a frequency-dependent absorption band. This reconciles published, seemingly contradictory models of dissipation for modes versus tides: the absorption band for modes terminates at periods where tidal models infer its onset. Microphysically, the experimental data can be explained by elastically accommodated grain boundary sliding, producing a broad plateau at short periods, transitioning to diffusionally assisted grain boundary sliding at longer periods, corresponding to an absorption band. Extrapolation of the fit to the experimental data with parameters adopted for the lower mantle can reconcile the seismological and geodetic observations.

Rapid ground deformation corresponding to a mining-induced seismic event followed by a massive collapse

On 17 April 2015, the Wujek/Śląsk underground coal mine in Poland was struck by a strong induced tremor of magnitude M4.0. The event was followed by a massive rock burst and a collapse of tunnels in the vicinity of the hypocentre. The earthquake was widely felt in the densely populated surrounding area. In this paper, we describe a possible connection between seismological parameters, such as the seismic source location and the focal mechanism, and the ground deformation just above the collapsed tunnels a very short time after the event occurred. We have shown that joint seismological and satellite observation can be very valuable and important tools not only to improve the knowledge concerning mining rock bursts and tunnel collapses, but also to find their influences on the ground effects observed on the surface.

An Analytic Study of Frictional Effect on Slip Pulses of Earthquakes

Seismological observations show the existence of slip pulses with T R /T D >1; while the CS shows a crack-like rupture for VW friction when u is not too large. For SW friction, T R and T R /T D decrease when the slip pulse propagates in advance along the fault and when w o and g increase. T R and T R /T D also depend on v R (rupture velocity) and increasing L (fault length). For the PS, T p /T D is a good indication to show the existence of pulse-like oscillations at a site, because T p (t he predominant period of oscillations at a site) is slightly longer than T R . Results show the existence of a pulse-like oscillation at a site for the two types of friction. A pulse-like oscillation is generated when D >1.6 for SW friction and when u >0.6 for VW friction. T p /T D decreases with increasing D . For the two types of friction, T o /T D decreases when v R and L increase.