Estimation of Shallow S-Wave Velocity Structure in Damascus City,Syria, Using Microtremor Exploration

Array measurements of microtremors were carried out at thirty sites in Damascus city, Syria to estimate S-wave velocity structures of shallow soil formations for site effect analysis. The microtremor data were recorded by 6 vertical-component seismometers distributed along the circumferences of two circles as well as a 3-component seismometer deployed in the center. The phase velocities were estimated at each site from the vertical components of recorded microtremor data by using the Spatial Autocorrelation method. Then, Genetic Simulated Annealing Algorithm technique was applied for inversion of the phase velocities to estimate 1-D S-wave velocity structures beneath the sites. The inverted Vs profiles are not uniform in Damascus city and the results show that a shallow soft layer (∼200 m/s) appears in the eastern part of the city as well as the central part along Barada River. This layer controls the amplification distribution in the city with a high amplification mainly observed at the locations having this layer. The inversion results also show that the depth to the engineering bedrock (∼750 m/s) is very shallow along the foothills of Mt. Qasyoun in the north-west. Then the depth increases towards the east and the south. The maximum depth to the engineering bedrock (∼80 m) was observed in the southern part of Damascus. To validate the results of the inversions, the spectral ratios between the horizontal and vertical components (H/V) of the recorded microtremor data at the central seismometer were compared with the computed ellipticities of the fundamental-mode Rayleigh-waves based on the respective Vs structure. The results show a good agreement in a period range of 0.05 s to 0.5 s. In this period range, the dominant peaks of the H/V ratios are due to the overall effect of the velocity contrasts between the shallow layers representing the subsurface S-wave velocity structure. Moreover, the average S-wave velocity for the top 10 m of soils (V_S10) shows a better correlation with the averaged site amplification in a period range of 0.05 s to 0.5 s than V_S30 which indicates that V_S10 can be a better proxy for high-frequency site amplification in the case of Damascus city.     

Three‐dimensional VS profiling using microtremors in Kushiro,Japan

A practical method is presented for determining three‐dimensional S‐wave velocity (V_S) profile from microtremor measurements. Frequency–wave number (f–k) spectral analyses of microtremor array records are combined, for this purpose, with microtremor horizontal‐to‐vertical (H/V) spectral ratio techniques. To demonstrate the effectiveness of the proposed method, microtremor measurements using arrays of sensors were conducted at six sites in the city of Kushiro, Japan. The spectral analyses of the array records yield dispersion characteristics of Rayleigh waves and H/V spectra of surface waves, and joint inversion of these data results in V_S profiles down to bedrock at the sites. Conventional microtremor measurements were performed at 230 stations within Kushiro city, resulting in the H/V spectra within the city. Three‐dimensional V_S structure is then estimated from inversion of the H/V spectra with the V_S values determined from the microtremor array data. This reveals three‐dimensional V_S profile of Kushiro city, together with an unknown hidden valley that crosses the central part of the city. The estimated V_S profile is consistent with available velocity logs and results of subsequent borings, indicating the effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

Application of HVSR to estimating thickness of laterite weathering profiles in basalt

Lateritic weathering profiles (LWPs) are widespread in the tropics and comprise an important component of the Critical Zone (CZ). The Hawaiian Islands make an excellent natural laboratory for examining the tropical CZ, where the bedrock composition (basalt) is nearly uniform and rainfall varies greatly. This natural laboratory is employed to assess the utility of the HVSR (horizontal/vertical spectral ratio) method to characterize the shear-wave velocity (V_s) structure of LWPs, particularly the depth to the contact between saprolite and basalt bedrock. LWP thicknesses determined from HVSR provide good agreement with multi-channel analysis of surface waves (MASW) profiles, well logs and outcrop. LWP thicknesses may be estimated from the fundamental mode equation or through forward models. Prior knowledge about the subsurface from well, outcrop, and MASW profiles may greatly aid modeling in some cases. For the 3.2 to 1.8 Ma Koolau Volcano on Oahu, the downward rate of advance of the weathering front varies from 0.004 to 0.041 m/ka. For the 0.44 to 0.10 Ma Kohala Volcano (Big Island of Hawaii) rates vary from 0.013 to 0.047 m/ka. Simple H/V spectra develop in areas where the combined effects of time and elevated rainfall produce thick LWPs with a flat base and a general absence of core stones with an ideal layered geometry. Abundant buried core stones violate the assumption of simple layered geometries and scatter acoustic energy, leading to uninterpretable results. This is common where low rainfall and a young basaltic substrate leave abundant core stones as well as an undulating contact between saprolite and bedrock. Velocity inversions (high V_s intervals within low V_s saprolite) may also be present and originate from relatively intact bedrock horizons or mineralogical changes within saprolite. At Kohala, a gibbsite-rich horizon produces such a velocity inversion due to enhanced weathering and subsequent collapse of saprolite in a discrete horizon. © 2019 John Wiley & Sons, Ltd.     

Soil characterization of Tınaztepe region (İzmir/Turkey) using surface wave methods and nakamura (HVSR) technique

To determine the shear wave velocity structure and predominant period features of T?naztepe in ?zmir, Turkey, where new building sites have been planned, active–passive surface wave methods and single-station microtremor measurements are used, as well as surface acquisition techniques, including the multichannel analysis of surface waves (MASW), refraction microtremor (ReMi), and the spatial autocorrelation method (SPAC), to pinpoint shallow and deep shear wave velocity. For engineering bedrock (V _s > 760 m/s) conditions at a depth of 30 m, an average seismic shear wave velocity in the upper 30 m of soil (AV_s30) is not only accepted as an important parameter for defining ground behavior during earthquakes, but a primary parameter in the geotechnical analysis for areas to be classified by V _s30 according to the National Earthquake Hazards Reduction Program (NEHRP). It is also determined that Z1.0, which represents a depth to V _s = 1000 m/s, is used for ground motion prediction and changed from 0 to 54 m. The sediment–engineering bedrock structure for T?naztepe that was obtained shows engineering bedrock no deeper than 30 m. When compared, the depth of engineering bedrock and dominant period map and geology are generally compatible.     

Earthquake Induced Site Effect in the Algiers–Boumerdes Region: Relation Between Spectral Ratios Higher Peaks and Observed Damage During the May 21st M w 6.8 Boumerdes Earthquake (Algeria)

The Algiers–Boumerdes regions were hit by an M _w 6.8 destructive earthquake on May 21, 2003. The accelerometric and seismometric networks successfully recorded the main shock and many aftershocks at some locations where the damage was most extensive. A microtremor measurement was performed in the same locations; some of them are localized on the Mitidja basin. In this paper, we propose to analyze earthquake-induced site effect derived from horizontal to vertical spectral ratio from ambient noise (noise horizontal to vertical—NHV), or from very weak, weak, moderate and strong ( peak ground acceleration—PGA >10 % g) seismic motions (EHV), and transfer function evaluation from soil velocity profile data at four sites. H/V spectral ratios are computed by using both Fourier and response spectra. Compared to the transfer function, the obtained results show that in the case of soft soils, NHV as well as EHV give a good estimation of the soil's fundamental frequency, whereas the NHV underestimate the H/V amplitude and the EHV amplitude increase with the seismic motion intensity. In the case of firm soils, whereas the NHV gives flat curves synonymous for a rock site or a bump, the EHV is more appropriate as seen by identifying clear peaks with non negligible amplitude. In the case of soft sites as well as in the case of firm sites, strong peaks at frequencies higher than the fundamental one are found from EHV curves. Those peaks would not be found when looking at NHV ratios alone, are evidenced by the computed transfer function as well as by an analytical formulation, and are in agreement with the observed distribution of damage during the M _w 6.8 2003 Boumerdes earthquake. Finally, the same analysis is performed by using response spectra rather than Fourier spectra and leads to the same conclusions. Moreover, the calculation of the response spectra is more easily compared with the smoothing operation of the Fourier spectra.     

Surface-to-base amplification evaluated from KiK-net vertical array strong motion records

Site amplification defined as the peak value of spectrum ratio was investigated using surface and base accelerations recorded in a number of KiK-net down-hole arrays in Japan during three major earthquakes. An important task was to determine the spectral amplifications relative to outcropping motions with the aid of the down-hole array records. Based on soil data available for individual arrays, theoretical amplifications were calculated and adjusted to coincide with the peak amplifications of the array records. A good and unique correlation was found between the peak amplifications thus obtained and S-wave velocity ratios, defined by S-wave velocity in base layer divided by average S-wave velocity , for different sites and different earthquakes. The value of was evaluated from fundamental mode frequency and the thickness of an equivalent surface layer in which peak amplification is exerted. The conventional parameter V_s30; averaged shear wave velocity in the top 30 m used in current design codes, did not correlate well with the obtained amplifications. It is suggested that may be determined not only from V_s-logging data but also from microtremor measurements.     

Roughness effect on the correction factor of surface velocity for rill flows

Flow velocity is one of the most important hydrodynamic variables for both channelized (rill and gullies) and interrill erosive phenomena. The dye tracer technique to measure surface flow velocity V_s is based on the measurement of the travel time of a tracer needed to cover a known distance. The measured V_s must be corrected to obtain the mean flow velocity V using a factor α_v = V/V_s which is generally empirically deduced. The V_s measurement can be influenced by the method applied to time the travel of the dye-tracer and α_v can vary in different flow conditions. Experiments were performed by a fixed bed small flume simulating a rill channel for two roughness conditions (sieved soil, gravel). The comparison between a chronometer-based (CB) and video-based (VB) technique to measure V_s was carried out. For each slope-discharge combination, 20 measurements of V_s, characterized by a sample mean V_m, were carried out. For both techniques, the frequency distributions of V_s/V_m resulted independent of slope and discharge. For a given technique, all measurements resulted normally distributed, with a mean equal to one, and featured by a low variability. Therefore, V_m was considered representative of surface flow velocity. Regardless of roughness, the V_m values obtained by the two techniques were very close and characterized by a good measurement precision. The developed analysis on α_v highlighted that it is not correlated with Reynolds number for turbulent flow regime. Moreover, α_v is correlated neither with the Froude number nor with channel slope. However, the analysis of the empirical frequency distributions of the correction factor demonstrated a slope effect. For each technique (CB, VB)-roughness (soil, gravel) combination, a constant correction factor was statistically representative even if resulted in less accurate V estimations compared to those yielded by the slope-specific correction factor.     

Seismic hazard evaluation in Anjar city area of western India: Microtremor array measurement

In western India during the Bhuj earthquake (Mw 7.6) on January 26, 2001, the Anjar City at ~30 km southwest of Bhuj experienced three types of damage scenario: severely damaged, less damaged and non-damaged. Similar damage patterns were also observed for the 1819 (Mw 7.8) and the 1956 (Mw 6.0) earthquakes. Microtremor array measurements were conducted in and around the Anjar city to examine the strength of soil structures and damage pattern. Significant differences are observed in frequencies and amplitudes in horizontal-to-vertical spectral ratio (HVSR) using microtremor measurements. The severely- damaged site shows two peak amplitudes: 2.8 at 1.2 Hz; and 4.0 at 8.0 Hz. The less-damaged site also shows two amplitudes: 2.5 and 2.1 at 1.4 Hz; and 2.0 Hz, respectively. The non-damaged site, on the other hand, shows that the HVSR curves become almost flatter. Similar results for three types of damage scenario based on analyses of earthquake records are also observed for the study area. The microtremor array measurements has revealed shear wave velocity V_s≥400 m/s at 18 m depth in the non-damaged, at 40 m in the less-damaged and at 60 m depth in the severely-damaged sites. The site amplitudes and the V_s values show a good correlation with the soil characteristics and damage pattern, suggesting that strength of soil layers at varying depths is a dictating factor for the estimate of the earthquake risk evaluation of the area under study.     

Estimation of sedimentary layer shear wave velocity using micro-tremor H/V ratio measurements for Bangalore city

For assessing earthquake hazard of metro cities, knowledge of soil amplification, thickness and properties of sedimentary layer are essential. In order to map the soil thickness using microtremor survey method, in Bangalore city, it is required to calibrate the relation between fundamental resonance frequency of the soil layer and its thickness for the region. For this purpose microtremor survey was carried out at 34 locations in the city where borehole log was available. The resonance frequency of the soil is evaluated from the microtremor recordings using the H/V ratio technique. A nonlinear regression relation between the thickness of sedimentary layer h (m), from the borehole logs, and the resonance frequency f_r (Hz), was derived as h=(58.3±8.8)f_r^{−(0.95)±0.1}. Using the model of shear wave velocity increasing with depth at these locations, the derived average shear wave velocity and the corresponding soil thickness were used, to get an empirical relation between V_S (m/s) and depth z(m), as V_s=(174±28)(1+z)^0.16±0.07. This relation also compares reasonably with the fit obtained between simulated V_S and depth from borehole logs for Bangalore city. The calibrated relations can be used at locations in Bangalore city where borehole logs are not available, for finding the thicknesses and shear wave velocities of the local soil layers at the survey locations.     

Spatial correlation of shear-wave velocity in the San Francisco Bay Area sediments

Ground motions recorded within sedimentary basins are variable over short distances. One important cause of the variability is that local soil properties are variable at all scales. Regional hazard maps developed for predicting site effects are generally derived from maps of surficial geology; however, recent studies have shown that mapped geologic units do not correlate well with the average shear-wave velocity of the upper 30 m, V_s(30). We model the horizontal variability of near-surface soil shear-wave velocity in the San Francisco Bay Area to estimate values in unsampled locations in order to account for site effects in a continuous manner. Previous geostatistical studies of soil properties have shown horizontal correlations at the scale of meters to tens of meters while the vertical correlations are on the order of centimeters. In this paper we analyze shear-wave velocity data over regional distances and find that surface shear-wave velocity is correlated at horizontal distances up to 4 km based on data from seismic cone penetration tests and the spectral analysis of surface waves. We propose a method to map site effects by using geostatistical methods based on the shear-wave velocity correlation structure within a sedimentary basin. If used in conjunction with densely spaced shear-wave velocity profiles in regions of high seismic risk, geostatistical methods can produce reliable continuous maps of site effects.     

Measuring wave propagation characteristics in artificial sand-clay mixtures

Ultrasonic compressional (V _p ) and shear (V _s ) velocities have been measured on artificial sand-clay mixtures. The measurements were carried out in a drained triaxial load cell using a pulse transition method. The measuring device was equiped with a waveform storage facility. The investigated mixtures consisted mainly of kaolinite and quartz sand. Some mixtures also contained Na-montmorillonite, illites or quartz-flour. The acoustic behaviour was observed during a pressure increase up to 72 MPa vertical and 36 MPa horizontal pressure. At a given pressure,V _p andV _s in pure sand turned out to be similar to those in pure kaolinite. As predicted by the sand-clay model of Marion (1990), a velocity maximum corresponds to a minimum in total porosity. This porosity minimum marks the transition from a clayey sand to a sandy clay. It is not only reflected in bothV _p andV _s , but also in the quality of the received pulse. The effective tension of the received signal during 20µs after the first arrival, was used as an indication for P-wave pulse attenuation. This apparent attenuation decreases with increasing clay content and increases with increasing porosity. It is shown that clay mineralogy does not measurably affect wave velocities in clayey sands.     

Controls on sonic velocity in carbonates

Compressional and shear-wave velocities (V _p andV _s) of 210 minicores of carbonates from different areas and ages were measured under variable confining and pore-fluid pressures. The lithologies of the samples range from unconsolidated carbonate mud to completely lithified limestones. The velocity measurements enable us to relate velocity variations in carbonates to factors such as mineralogy, porosity, pore types and density and to quantify the velocity effects of compaction and other diagenetic alterations.Pure carbonate rocks show, unlike siliciclastic or shaly sediments, little direct correlation between acoustic properties (V _p andV _s) with age or burial depth of the sediments so that velocity inversions with increasing depth are common. Rather, sonic velocity in carbonates is controlled by the combined effect of depositional lithology and several post-depositional processes, such as cementation or dissolution, which results in fabrics specific to carbonates. These diagenetic fabrics can be directly correlated to the sonic velocity of the rocks.At 8 MPa effective pressureV _p ranges from 1700 to 6500 m/s, andV _s ranges from 800 to 3400 m/s. This range is mainly caused by variations in the amount and type of porosity and not by variations in mineralogy. In general, the measured velocities show a positive correlation with density and an inverse correlation with porosity, but departures from the general trends of correlation can be as high as 2500 m/s. These deviations can be explained by the occurrence of different pore types that form during specific diagenetic phases. Our data set further suggests that commonly used correlations like Gardner's Law (V _p-density) or the time-average-equation (V _p-porosity) should be significantly modified towards higher velocities before being applied to carbonates.The velocity measurements of unconsolidated carbonate mud at different stages of experimental compaction show that the velocity increase due to compaction is lower than the observed velocity increase at decreasing porosities in natural rocks. This discrepancy shows that diagenetic changes that accompany compaction influence velocity more than solely compaction at increasing overburden pressure.The susceptibility of carbonates to diagenetic changes, that occur far more quickly than compaction, causes a special velocity distribution in carbonates and complicates velocity estimations. By assigning characteristic velocity patterns to the observed diagenetic processes, we are able to link sonic velocity to the diagenetic stage of the rock.     

Modelling shear waves in OBS data from the Vøring basin (Northern Norway) by 2-D ray-tracing

Three component recordings from an array of five ocean bottom seismographs in the northwestern part of the Vøring basin have been used to obtain a 2-D shear-wave (S-wave) velocity-depth model. The shear waves are identified by means of travel-time differences compared to the compressional (P) waves, and by analyzing their particle motions. The model has been obtained by kinematic (travel-time) ray-tracing modelling of the OBS horizontal components.The shear-wave modelling indicates that mode conversions occur at several high velocity interfaces (sills) in the 4–10 km depth range, previously defined by a compressional-wave velocity-depth model using the same data set.An averageV _p /V _s ratio of 2.1 is inferred for the layers above the uppermost sill, indicative of both poorly consolidated sediments and a low sand/shale ratio. A significant decrease in theV _p /V _s ratio (1.7) below the first sill may in part be atributed to well consolidated sediments, and to a change in lithology to more sandy sediments. This layer is interpreted to lie within the lower Cretaceous sequence. At 5–10 km depthV _p /V _s ratios of 1.85 indicate a lower sand/shale ratio consistent with the expected lithologies. The averageV _p /V _s ratio inferred for the crust is 1.75, which is consistent with values obtained north of Vøring, in the Lofoten area. An eastward thinning of the crystalline basement is supported by the shear-wave modelling.     

Tomographic imaging of seismic velocity structure in and around the Onikobe volcanic area, northeastern Japan: implications for fluid distribution

We estimated three-dimensional P- (V_p) and S-wave velocity (V_s) and V_p/V_s structures in and around the Onikobe volcanic area, northeastern Japan, by local travel time tomography. We used travel time data from source and receiver pairs located within and outside the study area, which plays an important role in obtaining the optimum ray coverage and in elucidating the deeper structure more accurately. Detailed information on deeper structures is essential for imaging the complete volcanic system from the magmatic source zone through areas of shallow hydrothermal circulation. More than 50 000 travel time data for the P-waves and 35 000 for the S-waves were used to image the velocity structure. Our results show the following dominant features: (1) two conduits in the upper crust with low V_p and low V_s indicative of H₂O-rich fluid pathways: one lying beneath Naruko volcano, the other beneath the focal area of the 1962 Northern Miyagi earthquake (M6.5); (2) an underlying broad region in the lower crust with low V_p, low V_s and high V_p/V_s, suggestive of a zone of partial melt, from which the fluids in (1) are derived; and (3) low V_p/V_s areas near the surface of the Sanzugawa and Onikobe calderas, suggesting a diffuse vapor-saturated cap.     

Receiver function study in northern Sumatra and the Malaysian peninsula

In this receiver function study, we investigate the structure of the crust beneath six seismic broadband stations close to the Sunda Arc formed by subduction of the Indo-Australian under the Sunda plate. We apply three different methods to analyse receiver functions at single stations. A recently developed algorithm determines absolute shear-wave velocities from observed frequency-dependent apparent incidence angles of P waves. Using waveform inversion of receiver functions and a modified Zhu and Kanamori algorithm, properties of discontinuities such as depth, velocity contrast, and sharpness are determined. The combination of the methods leads to robust results. The approach is validated by synthetic tests. Stations located on Malaysia show high-shear-wave velocities (V _S) near the surface in the range of 3.4–3.6 km s^− 1 attributed to crystalline rocks and 3.6–4.0 km s^− 1 in the lower crust. Upper and lower crust are clearly separated, the Moho is found at normal depths of 30–34 km where it forms a sharp discontinuity at station KUM or a gradient at stations IPM and KOM. For stations close to the subduction zone (BSI, GSI and PSI) complexity within the crust is high. Near the surface low V _S of 2.6–2.9 km s^− 1 indicate sediment layers. High V _S of 4.2 km s^− 1 are found at depth greater than 6 and 2 km at BSI and PSI, respectively. There, the Moho is located at 37 and 40 km depth. At station GSI, situated closest to the trench, the subducting slab is imaged as a north-east dipping structure separated from the sediment layer by a 10 km wide gradient in V _S between 10 and 20 km depth. Within the subducting slab V _S ≈ 4.7 km s^− 1. At station BSI, the subducting slab is found at depth between 90 and 110 km dipping 20° ± 8° in approximately N 60° E. A velocity increase in similar depth is indicated at station PSI, however no evidence for a dipping layer is found.     

Interpretation of S-wave data from Tai’an-Xinzhou DSS profile and its relationship with Xingtai earthquakes

On the basis of S wave information from Tai’an-Xinzhou DSS profile and with reference to the results from P-wave interpretation, the 2-D structures, including S-wave velocity V _s, ratio γ between V _p and V _s; and Poisson’ s ratio σ, are calculated; the structural configuration of the profile is presented and the relevant inferences are drawn from the above results. Upwarping mantle districts (V _s≈4.30 km/s) and sloping mantle districts (V _s≈4.50 km/s) of the profile with velocity difference about −4% at the top of upper mantle are divided according to the differences of V _s, γ and σ in different media and structures, also with reference to the information of their neighbouring regions; the existence of Niujiaqiao-Dongwang high-angle ultra-crustal fault zone is reaffirmed; the properties of low and high velocity blocks (zones) including the crust-mantle transitionalzone and the boudary indicators of North China rift valley are discussed. A comprehensive study is conducted on the relation of the interpretation results with earthquakes. It is concluded that the mantle upwarps, thermal material upwells through the high-angle fault, the primary hypocenter was located at the crust-mantle juncture 30.0∼33.0 km deep, and additional stress excited the M _S=6.8 and M _S=7.2 earthquakes at specific locations around 9.0 km below Niujiaqiao-Dongwang, the earthquakes took place around the high-angle ultra-crustal fault and centered in the brittle media and rock strata with low γ and low σ values. This subject is part of the 85-907-02 key project during the “8th Five-Year Plan” from the State Science and Technology Commission.     

CrustalP-wave velocity and velocity-ratio study in northeast India by a microearthquake survey

The upper crustal (20 km)P-wave velocity beneath the Shillong Plateau and Nowgong area has been studied by the time-distance plot method. TheP-arrival data of the shallow (20 km) microearthquakes from three temporary networks are used, and the average velocity is found to be 5.55 km/s. The velocity ratio (V _p /V _s ) for the upper crust (0–20 km) as well as for the lower crust (21–40 km) are determined by the Wadati-plot method and station-by-station method. The average value obtained by the two methods is compatible; theV _p /V _s ranges between 1.74 to 1.76. A generalized seismic velocity model of the area is suggested by this study, which has been very useful for microearthquake location.     

Determination of S-wave velocity structure using microtremors and spac method applied in Thessaloniki (Greece)

Array measurements of microtremors at 16 sites in the city of Thessaloniki were performed to estimate the V_s velocity of soil formations for site effect analysis. The spatial autocorrelation method was used to determine phase velocity dispersion curves in the frequency range from 0.8–1.5 to 6–7 Hz. A Rayleigh wave inversion technique (stochastic method) was subsequently applied to determine the Vs profiles at all the examined sites. The determination of V_s profiles reached a depth of 320 m. Comparisons with V_s values from cross-hole tests at the same sites proved the reliability of the SPAC method. The accuracy of the V_s profiles, the ability to reach large penetration depths in densely populated urban areas and its low cost compared to conventional geophysical prospecting, make Mictrotremor Exploration Method very attractive and useful for microzonation and site effects studies. An example of its application for the site characterization in Thessaloniki is presented herein.     

A numerical model of the wave boundary layer

A numerical model of deep, uniform, oscillatory, rough-turbulent boundary-layer flow is described. The model is based upon the governing horizontal momentum equation and a closure scheme involving the turbulent-energy equation and various turbulence-scaling laws. Finite difference solutions of these equations are obtained for a range of values of the ‘relative roughness’ (A₀/k_s), whereA₀ is the excursion amplitude of the water particles in the free-stream flow andk_s is the ‘equivalent bed roughness’. Typical vertical profiles of horizontal velocity, turbulence energy and eddy viscosity, and time-series of the bed shear stress are presented. The model results are then used to determine the wave drag coefficient, boundary-layer thickness and phase lead of the bed shear stress over the free-stream velocity, each as a function ofA₀/k_s. These results are shown to be in generally good agreement with previous experimental and theoretical results. Finally, the model is used to test for the existence of a universal velocity distribution for uniform oscillatory (sinusoidal) rough-turbulent flow. The ‘law of the wall’ and the ‘defect law’ proposed by Jonsson (1980, Ocean Engineering, 7, 109–152) are well supported by the model, and the existence of a logarithmic ‘velocity overlap layer’ in which both of these laws are valid is demonstrated forA_o/k_s30.