Steady‐State Homogeneous Approximations of Vertical Velocity from EC Profiles

Electrical conductivity (EC) logs were obtained by both open‐borehole logging and passive multilevel sampling (MLS) in an observation borehole penetrating the Coastal Aquifer in Tel Aviv, Israel. Homogeneous vertical velocities for a 70‐m thick subaquifer were approximated from each profile using a steady‐state advection‐diffusion model. The open‐borehole log led to an overestimation of the steady‐state upward advective flux of deep brines (vertical velocity of 0.95 cm/yr as compared to 0.07 cm/yr for the MLS profile). The combination of depth‐dependent data and the suggested simple modeling approach comprises a method for assessing the vertical location of salinity sources and the nature of salt transport from them (i.e., advective vs. diffusive). However, in this case, the easily obtained open‐borehole logs should not be used for collecting depth‐dependent data.     

Pattern and mechanism of volcanic activity at the Santiaguito Volcanic Dome,Guatemala

Santiaguito volcano has shown a continuous slow extrusion of dacite lava since 1922. In the 50 years of activity there have been four periods of abnormally high extrusion rates, interspersed by periods of little magma production. The type of activity shown by the volcano has been varied and crudely cyclic. Dome extrusion periods are accompanied by pyroclastic activity and followed by lava flows. There are now 16 time stratigraphic units delineated on the dome. Activity since 1967 has been especially closely observed. Dome extrusion at the west end of the complex has been accompanied by pyroclastic cruptions and plug dome extrusion at the east end. The eurrent extrusion rate has remained essentially constant since 1967 at about 5×10⁶ m³/yr, far below Santiaguito’s 1922–71 average of 14×10⁶ m³/yr. The active vent at the east end of the volcano (Caliente vent) has been the principal vent of the volcano since the creation of the explosion crater in 1902. After its initial period of dome extrusion (1922–25), the Caliente vent has chiefly produced pyroclastic eruptions as well as at least 95% of the dome’s lumarolic activity, while lateral vents have continued to give rise to lavas. Lava flows at Santiaguito have effective viscosity values of about 10⁶ poises, while dome lavas are significantly more viscous. The differences in viscosity are in part related to volatile content of the lava when it reaches the surface. During dome extrusion, lavas lose their volatiles through pyroclastic activity before they reach the surface. Lava flows at Santiaguito occur when lava reaches the surface with higher volatile content. Obstruction of either the central (pyroclastic) vent or the lateral (dome extrusion) vent or both vents has an important influence on succeeding activity. In June 1972, at the time of this writing, the outbreak of new lava flows at both the Caliente and lateral El Brujo vents has just occurred, resulting from obstruction of pyroclastic activity by a large plug dome at the Caliente vent.     

Submesoscale vortex structures at the entrance of the Gulf of Lions in the Northwestern Mediterranean Sea

The meanders of a baroclinic coastal current in the Northwestern Mediterranean Sea have already been reported in the literature. These meanders can be surrounded by vortices. Such vortices have been observed in the western part of the Gulf of Lions but the location and the mechanism of their formation are poorly documented. In this paper, we use the current measurements of a one-year experiment, which was conducted in the eastern part of the Gulf of Lions to detect and characterize the vortex activity. A vortex detection algorithm based on few velocity data was developed. Current measurements were available at the sea surface (HF radars) and in the water column from 50 to 140 m depth (four current meter moorings). SST images and hydrologic data were also used. Results focus on observations that are coherent 50 m and at the surface. Vortices are anticyclonic, of submesoscale size and present maximal velocities of 30–50 cm/s. The drift speed of the vortices is comparable to but less than the velocity of the Northern Current. These observations enable to estimate the minimum vortex occurrence in this area. The presence of vortex structures is strongly correlated with a specific sequence of wind patterns.     

Strong variation in weathering of layered rock maintains hillslope‐scale strength under high precipitation

The evolution of volcanic landscapes and their landslide potential are both dependent upon the weathering of layered volcanic rock sequences. We characterize critical zone structure using shallow seismic V_p and V_s profiles and vertical exposures of rock across a basaltic climosequence on Kohala peninsula, Hawai’i, and exploit the dramatic gradient in mean annual precipitation (MAP) across the peninsula as a proxy for weathering intensity. Seismic velocity increases rapidly with depth and the velocity–depth gradient is uniform across three sites with 500–600 mm/yr MAP, where the transition to unaltered bedrock occurs at a depth of 4 to 10 m. In contrast, velocity increases with depth less rapidly at wetter sites, but this gradient remains constant across increasing MAP from 1000 to 3000 mm/yr and the transition to unaltered bedrock is near the maximum depth of investigation (15–25 m). In detail, the profiles of seismic velocity and of weathering at wet sites are nowhere monotonic functions of depth. The uniform average velocity gradient and the greater depths of low velocities may be explained by the averaging of velocities over intercalated highly weathered sites with less weathered layers at sites where MAP > 1000 mm/yr. Hence, the main effect of climate is not the progressive deepening of a near‐surface altered layer, but rather the rapid weathering of high permeability zones within rock subjected to precipitation greater than ~1000 mm/yr. Although weathering suggests mechanical weakening, the nearly horizontal orientation of alternating weathered and unweathered horizons with respect to topography also plays a role in the slope stability of these heterogeneous rock masses. We speculate that where steep, rapidly evolving hillslopes exist, the sub‐horizontal orientation of weak/strong horizons allows such sites to remain nearly as strong as their less weathered counterparts at drier sites, as is exemplified by the 50°–60° slopes maintained in the amphitheater canyons on the northwest flank of the island. Copyright © 2017 John Wiley & Sons, Ltd.     

Experiments on internal strain in lava dome cross sections

Simple experiments have been conducted to study the strain evolution in lava dome cross sections. A viscous fluid is injected vertically from a reservoir into a feeding conduit. Silicone putty is used as analogue magma. Two-dimensional experiments allow the assessment of the internal strain within the dome. Particle paths are symmetrical on either side of a central line passing through the feeding conduit and display parabolic trajectories. The highest strain zone is located above the extrusion zone. In cross sections, stretch trajectories show a remarkable concentric pattern, wrapping around the extrusion zone of the analogue magma. To the lateral margins, a triple junction of stretch trajectories defines an isotropic point in the strain field. In the main central part of the dome, an intermediate zone of reversed sense of shearing is caused by a change in the sign of the velocity gradient with respect to that in the upper and lower zones. Knowledge of this evolving strain pattern can provide a better understanding of the evolution of natural domes. Also, it can help to unravel the kinematic history of ancient domes partly removed by erosion.     

背景噪声面波与布格重力异常联合反演:山西断陷带三维地壳结构

讨论了利用面波与布格重力异常联合反演三维地壳速度结构的新方法,并利用该方法联合反演获得山西断陷带地壳S波速度结构.通过建立速度与密度之间的经验关系,利用非线性迭代反演方法获得最终速度模型.结果显示,联合反演获得的速度模型可以同时提高对面波及重力数据的观测拟合程度,而面波单独反演得到的速度模型则无法很好的拟合重力观测数据.相比较,联合反演速度模型中的大同火山区中下地壳的低速异常幅值小于面波单独反演模型中低速异常体的幅值.联合反演速度模型结果揭示,吕梁山地区在中下地壳存在低速异常,并且和北部的大同火山区低速异常相连接,说明可能导致新生代以来大同火山区岩浆活动的上地幔构造活动(上地幔局部上涌,地幔柱)可能对山西断陷带的形成和构造活动起到了一定的控制作用,并且导致了吕梁山地区中下地壳的低速异常.     

High spatial resolution mapping of surface velocities and depths for shallow overland flow

Point measurements of flow rate, depth or velocity are not sufficient to validate overland flow models, particularly when the interaction of the water with the soil surface creates a complex flow geometry. In this study, we present the coupling of two techniques obtaining spatial data of flow depths and surface velocity measurements for water depths as low as 1 mm. Overland flow experiments were performed in the laboratory at various flow rates and slopes on two surfaces. The first surface was 120 cm by 120 cm showing three undulations of sinusoidal shape with an amplitude of 1 cm and a wavelength of 20 cm, while the second was a 60 cm by 60 cm moulded reproduction of a seedbed with aggregates up to 2 cm in size. Large scale particle image velocimetry (LSPIV) was used for velocity measurements with a sub‐centimetre spatial resolution. An instantaneous‐profile laser scanner was used to map flow depths with a sub‐millimetre spatial resolution. A sensitivity analysis of the image processing of the LSPIV showed good robustness of the method. Comparison with measurements performed with hot film anemometer and salt velocity gauge showed that LSPIV surface velocities were representative of the flow. Water depths measured with the laser scanner were also in good agreement with single‐point measurements performed with a dial indicator. Spatially‐distributed flow rates could be computed by combining both presented techniques with a mean relative error less than 20%. Copyright © 2012 John Wiley & Sons, Ltd.     

Gravity contributions to the understanding of salt tectonics from the Jebel Cheid area (dome zone, Northern Tunisia)

Detailed gravity measurements integrated with geological data were computed to constrain the mechanisms that were active during the emplacement of the Triassic evaporite-bearing folds of Jebel Cheid from the salt-dome zone in the Atlassic region. The gravity analysis consists in mapping the contrasting gravity responses: complete Bouguer anomaly, residual anomaly and derivative maps; the main results display a positive amplitude gravity anomaly as the response of Triassic evaporite bodies and important NE–SW-trending features at the boundaries between the Triassic outcrops and their enveloping strata. In contrast with gravity calculations of a salt dome structure usually resulting in negative gravity anomaly models, the Jebel Cheid clearly expresses a positive gravity anomaly; furthermore, this result is supported by synthetic gravity interpretation.     

Subsidence analysis on the Sardinian margin and the central Tyrrhenian Basin: Thermal modelling and heat flow control; deep structure implications

The subsidence of the Tyrrhenian Basin is analysed based on numerous MCS reflection data and related seismic velocities, and calibrated using subsidence curves versus time at ODP Leg 107 sites 654 and 652 on the Sardinian margin. Two main phases of rifting are clearly defined for the margin-basin evolution: the first, beginning at 7 Ma, split the Sardinian-Calabrian margins, the second, beginning at 5 Ma formed the Central oceanic subbasins.Thermal models, based on thinned crust geometry from reflection-refraction data, are used which consider both vertical and horizontal conduction over time along a NW-SE transect across the entire Tyrrhenian Basin from Sardinia to Calabria. In general, there is a close agrrement between the predicted and the observed surface heat flow and the rate of subsidence over time. However, within the oceanic domain an initial subsidence must be chosen about 1000 m greater than observed on typical spreading centers, i.e., at about 3500 m as postulated in numerous back-arc basins.Thermal models, constrained by subsidence analysis and gravity observations, imply a large difference for the Moho depth beneath the Sardinian margin as determined after refraction seismic experiments. The upper mantle, hot but with high density, would be situated much higher than is postulated by seismic data and probably includes 7.3–7.4 km/s velocity layers previously interpreted as deep crustal layers.     

基于阈值约束的协克里金法联合反演重力与重力梯度数据

常规协克里金方法反演重力或重力梯度数据具有抗噪性好、加入先验信息容易等优点,其反演的地下密度分布能够识别异常体中心位置,还原异常体基本形态,但反演图像光滑,分辨率低,这是由于常规方法估计的密度协方差矩阵全局发散、平稳.为了通过协克里金方法获得聚焦的密度分布需要改善密度协方差矩阵的性质.首先,本文推导了理论密度协方差公式,其性质表明,当理论模型聚焦分布时,其密度协方差矩阵是非平稳且聚焦分布的.为了打破常规协方差矩阵全局平稳、发散的特征,本文设置密度阈值处理协方差矩阵,通过不断更新协方差矩阵来迭代实现协克里金反演,最终得到相对聚焦的反演结果.用本文方法处理重力与重力梯度数据恢复两种密度模型,均得到了与正演模型匹配的反演结果;再将方法运用于文顿盐丘的实际测量重力与重力梯度数据,反演结果与已知的地质情况匹配较好.     

利用长周期面波研究华北地区地壳与上地幔结构的横向非均匀性

本文以太行山为界将华北地区分为东西两部分,东部为河淮块体,西部为鄂尔多斯块体.利用最小二乘法,从混合路径基阶瑞利面波群速度频散提取两块体的纯路径频散,并反演其地壳、上地幔的层状结构.所得结表果明,两块体的面波频散和地壳、上地幔结构存在明显差异.东部的河淮块体地壳较薄,地壳内平均速度比西部的鄂尔多斯块体壳内平均速度约低0.13km/s,壳内20km深度左右出现低速层;而西部的块体壳内速度成层递增,未见低速层出现.两块体上地幔顶部速度均偏低,地幔低速层的埋藏深度基本相同.但西部块体地幔低速层厚,且比东部块体地幔低速层的速度约低0.3km/s.     

利用长周期面波研究华北地区地壳与上地幔结构的横向非均匀性

本文以太行山为界将华北地区分为东西两部分,东部为河淮块体,西部为鄂尔多斯块体.利用最小二乘法,从混合路径基阶瑞利面波群速度频散提取两块体的纯路径频散,并反演其地壳、上地幔的层状结构.所得结表果明,两块体的面波频散和地壳、上地幔结构存在明显差异.东部的河淮块体地壳较薄,地壳内平均速度比西部的鄂尔多斯块体壳内平均速度约低0.13km/s,壳内20km深度左右出现低速层;而西部的块体壳内速度成层递增,未见低速层出现.两块体上地幔顶部速度均偏低,地幔低速层的埋藏深度基本相同.但西部块体地幔低速层厚,且比东部块体地幔低速层的速度约低0.3km/s.     

Endogenous growth of a Miocene submarine dacite cryptodome, Rebun Island, Hokkaido, Japan

Momo-iwa, Rebun Island, Hokkaido, Japan, is a dacite cryptodome 200–300 m across and 190 m high. The dome is inferred to have intruded wet, poorly consolidated sediment in a shallow marine environment. The internal structure of the dome is concentric, with a massive core, banded rim, and narrow brecciated border, all of which are composed of compositionally uniform feldspar-phyric dacite. Boundaries between each of the zones are distinct but gradational. The massive core consists of homogeneous coherent (unfractured) dacite and is characterized by radial columnar joints 60–200 cm across. The banded rim encircles the massive core and is 40 m wide. It is characterized by large-scale flow banding parallel to the dome surface. The flow banding comprises alternating partly crystalline and more glassy bands 80–150 cm thick. The outermost brecciated border is up to 80 cm thick, and consists of in situ breccia and blocky peperite. The in situ breccia comprises polyhedral dacite clasts 5–20 cm across and a cogenetic granular matrix. The blocky peperite consists of polyhedral dacite clasts 0.5–2 cm across separated by the host sediment (mudstone). The internal structures of the dome suggest endogenous growth involving a continuous magma supply during a single intrusive phase and simple expansion from the interior. Although much larger, the internal structures of Momo-iwa closely resemble those of lobes in subaqueous felsic lobe-hyaloclastite lavas.     

基于重力异常反演的三维地震波速度结构分析方法研究

利用重力异常反演测试三维地震波速度结构,存在解不唯一、可靠性不高的问题。将面波反演充分融合到重力异常反演方程中,降低传统反演方法的非唯一性,并提升可靠性。以川滇地区为例,采用融合后的重力异常反演方法分析三维地震波速度结构。通过速度和密度的关系转换,得到对应的重力异常数据。由于面波频射数据主要对地震波横波速度敏感,因此将重力异常数据和初始横波速度相连,依据地震波速度和岩石密度之间的关系,获取重力异常反演方程,用于分析速度结构。选取21.6°~34.2°N、97.1°~105.9°E范围内的川滇地区活动块体作为实验数据,经过实验分析发现：使用该方法迭代反演川滇地区地壳上地幔顶部横波速度,重力异常数据和面波频射数据的残差值分别是6.24 mGal和0.027 km/s,实际拟合效果较好;分析该地区不同深度切面横波速度发现,在24 km深度处,上地壳中含有相对低速层,在44 km深度处,中下地壳中存在低速层;且该方法分析川滇地区三维地震波速度结构解的分辨率较高。     

Phreatic eruption clouds: the activity of la Soufrière de Guadeloupe,F.W.I., August — October, 1976

From August to October, 1976, La Soufrière de Guadeloupe was observed, and recorded with an automated sequence camera and numerous handheld cameras. During the period of observation, the nature of volcanic activity ranged from mild steam emission to moderately energetic phreatic eruptions. Background fumarolic activity (steam emission) was characterized by the emission of generally tephra-free steam clouds 50 to 150 m above the summit. The clouds rose buoyantly above the vent and were blown downwind at prevailing wind velocities. Phreatic eruptions were well-documented on September 22, October 2, and October 4. In the latter two eruptions, small bursts of tephra-laden steam erupted at intervals of 30 to 45 min, and rose from 350 to 500 m above the summit. In the largest observed eruption, that of October 2, the steam and tephra cloud rose to a maximum height of 600 to 650 m in 20 min. A white vapor cloud and a medium gray, tephra-laden cloud were erupted simultaneously from the summit vent and both were surrounded by a vapor collar: the clouds were thoroughly mixed within 1 km downwind of the summit. The concurrent growth of clouds from separate vents (summit and flank) implies a common source. Simultaneous eruption of tephra-free and tephra-laden clouds from the same vent is puzzling and implies: (i) lateral changes in the degree of alteration of dome rocks along the elongate vent, hence erodability of the dome lavas, or (ii) differences in the gas velocities. These «mixed» clouds moved westward, downwind and downslope as a density current, along the watersheds of the R. Noire and R. des Pères with an approximate velocity of 10 to 25 m/sec. Upon reaching the sea the clouds continued to move forward, but at a decreased velocity, and spread laterally, having left behind the restrictions of valley walls. A thin gray veneer of moist tephra, ranging from several cm thick near the dome to less than 1 mm thick several km downwind, was deposited along a narrow corridor southwest of the summit. Tephra from the phreatic eruptions consisted mostly of hydrothermally altered lithic, mineral, and glass fragments derived from dome lavas; no fresh (juvenile) pyroclasts were present in the tephra. Absence of juvenile tephra at La Soufrière supports the view that activity was due to groundwater circulating in a vapor-dominated geothermal system, probably driven by a shallow heat source. At La Soufrière, most vapor-dominated systems are located in elevated areas of groundwater recharge where groundwater movement is downward and outward. The sporadic phreatic eruptions may be related to the rate of recharge of meteoric waters within the dome, the decrease in pore pressure during fortnightly tidal minimums or both. Whatever the triggering mechanism, vapor-dominated fluids eroded vent walls during phreatic eruptions and carried out fine-grained, hydrothermally altered, pre-existing dome material as tephra.     

大陆深俯冲带的地壳速度结构——东大别造山带深地震宽角反射/折射研究

在安徽大别山(东大别)进行的深地震宽角反射/折射探测获得6条二维地壳速度结构剖面. 结果显示，东大别造山带地壳为一高速穹隆构造，在其核部中、下地壳变质岩出露于地表，波速高达5.0km/s；在其翼部，上、中地壳发育速度约6.1km/s的壳内低速层(体). 莫霍面的起伏变化较大，中心部位深达41km左右，周边地区则抬升到32～34km. 在晓天—磨子潭断裂一线下方莫霍面垂向错断，断距约4km. 东大别造山带具有大陆深俯冲-碰撞造山带地壳结构的典型式样. 莫霍面错断与扬子陆块深俯冲有关，错断处表征扬子与华北陆块碰撞缝合的深部位置. 高速穹隆构造可能是两陆块碰撞挤压的产物，穹隆翼部上、中地壳发育的低速滑脱带(面)可能在碰撞期之后的地壳伸展、超高压变质岩从中地壳抬升出露于地表过程中起到重要作用.     

Post-eruptive volcanic dome evolution as revealed by deformation and microgravity observations at Usu volcano (Hokkaido, Japan)

Usu volcano (Hokkaido, Japan) is a dacitic volcano, known for its high production rate of lava domes and crypto-domes. It is thus a good target to study processes of volcanic dome evolution (upheaval and/or relaxation). We carried out repeated GPS and microgravity surveys on the three most recent domes of Mt. Usu (1910: Meiji Shinzan; 1943–1945: Showa-Shinzan and 1977–1982: Usu-Shinzan). The repeat period was 1 to 2 months and extended from October 1996 to June 1997. We also compare new data with results from former studies. More than 20 years after the start of Usu-Shinzan dome growth, there is still subsidence at a maximum rate of about 7 to 8 cm/year. The reasons for this subsidence are discussed. Repeated gravity surveys revealed an increase of gravity on the domes (about 60±10 microgal/year for Usu-Shinzan, about 15 microgal at Showa-Shinzan and 10 to 20 microgal for Meiji-shinzan); this gravity increase exceeds that expected due to subsidence. We discuss and interpret the excess gravity change in terms of a density increase in the edifice, caused by a combination of processes (contraction of the edifice, water level change, devesiculisation, cooling and magma intrusion). Quantification of these processes at Usu volcano may help to understand the processes of evolution at domes on other volcanoes such as Merapi (Indonesia), Unzen (Japan) or Montserrat (West Indies).     

Pyroclastic flows from the 1991 eruption of Unzen volcano,Japan

Pyroclastic flows from Unzen were generated by gravitational collapse of the growing lava dome. As soon as the parental lobe failed at the edge of the dome, spontaneous shattering of lava occurred and induced a gravity flow of blocks and finer debris. The flows had a overhanging, tongue-like head and cone- or rollershaped vortices expanding outward and upward. Most of the flows traveled from 1 to 3 km, but some flows reached more than 4 km, burning houses and killing people in the evacuated zone of Kita-kamikoba on the eastern foot of the volcano. The velocities of the flows ranged from 15 to 25 m/s on the gentle middle flank. Observations of the flows and their deposits suggest that they consisted of a dense basal avalanche and an overlying turbulent ash cloud. The basal avalanche swept down a topographic low and formed to tongue-like lobe having well-defined levees; it is presumed to have moved as a non-Newtonian fluid. The measured velocities and runout distances of the flows can be matched to a Bingham model for the basal avalanche by the addition of turbulent resistance. The rheologic model parameters for the 29 May flow are as follows: the density is 1300 kg/m³, the yield strength is 850 Pa, the viscosity is 90 Pa s, and the thickness of the avalanche is 2 m. The ash cloud is interpreted as a turbulent mixing layer above the basal avalanche. The buoyant portions of the cloud produced ash-fall deposits, whereas the dense portions moved as a surge separated from the parental avalanche. The ash-cloud surges formed a wide devastated zone covered by very thin debris. The initial velocities of the 3 June surges, when they detached from avalanches, are determined by the runout distance and the angle of the energy-line slope. A comparison between the estimated velocities of the 3 June avalanches and the surges indicates that the surges that extended steep slopes along the avalanche path, detached directly from the turbulent heads of the avalanches. The over-running surge that reached Kita-Kamikoba had an estimated velocity higher than that of the avalanche; this farther-travelled surge is presumed to have been generated by collapse of a rising ash-cloud plume.     

蒙古及周边地区重力异常和地壳不均匀体分布

基于全球EGM2008自由空气重力异常模型,本文计算了蒙古及周边地区的布格重力异常和AiryHeiskanen均衡重力异常.在此基础上,本文采用Crust 1.0地壳模型为参考,通过重力正演方法,对蒙古及周边地区不同深度地壳密度结构模型的重力异常进行了计算,并对得到的正演布格重力异常与实际重力异常进行了对比和分析.研究结果表明:蒙古西部杭爱山地区与阿尔泰山地区的构造变形差异性明显,现今均衡重力异常中杭爱山周边没有明显的均衡异常高值区,而阿尔泰山地区西南方向存在均衡重力异常高值分布,分析与新构造运动密切相关;Crust 1.0模型给出的壳幔横向密度不均匀体分布对于计算Moho面起伏引起的重力异常作用明显;Crust 1.0给出的地壳内界面变形可以反映深大活动断裂的深部构造变形.研究结果对于认识蒙古东西部构造特征差异,以及现今西部活动断裂的地球物理场特征具有参考意义,也可以为进一步应用Crust 1.0模型为参考开展三维密度结构反演提供一定帮助.     

Ray tomography based on azimuthal anomalies

A method of estimating the lateral velocity variations in the 2D case using the data on deviations of wave paths from straight lines (or great circle paths in the spherical case) is proposed. The method is designed for interpretation of azimuthal anomalies of surface waves which contain information on lateral variations of phase velocities supplementary to that obtained from travel-time data in traditional surface wave tomography. In the particular 2D case, when the starting velocity is constant (c ₀) and velocity perturbations δc(x,y) are sufficiently smooth, a relationship between azimuthal anomaly δα and velocity perturbations δc(x,y) can be obtained by approximate integration of the ray tracing system, which leads to the following functional: $$\delta \alpha = \int_0^L {\frac{{s(\nabla m,n_0 )}}{L}} ds,$$ wherem(x,y)=δc(x,y)/c ₀,L is the length of the ray,n ₀ is a unit vector perpendicular to the ray in the starting model, integration being performed from the source to the receiver. This formula is valid for both plane and spherical cases. Numerical testing proves that for a velocity perturbation which does not exceed 10%, this approximation is fairly good. Lateral variations of surface wave velocities satisfy these assumptions. Therefore this functional may be used in surface wave tomography. For the determination ofm(x,y) from a set ofδα _k corresponding to different wave paths, the solution is represented as a series in basis functions, which are constructed using the criterion of smoothness of the solution proposed byTarantola andNersessian (1984) for time-delay tomography problems. Numerical testing demonstrates the efficiency of the tomography method. The method is applied to the reconstruction of lateral variations of Rayleigh wave phase velocities in the Carpathian-Balkan region. The variations of phase velocities obtained from data on azimuthal anomalies are found to be correlated with group-velocity variations obtained from travel-time data.