Azimuthal anisotropy analysis of walkaround vertical seismic profiling vertical seismic profiling: a case study from Saudi Arabia

Understanding fracture orientations is important for optimal field development of fractured reservoirs because fractures can act as conduits for fluid flow. This is especially true for unconventional reservoirs (e.g., tight gas sands and shale gas). Using walkaround Vertical Seismic Profiling (VSP) technology presents a unique opportunity to identify seismic azimuthal anisotropy for use in mapping potential fracture zones and their orientation around a borehole. Saudi Aramco recently completed the acquisition, processing and analysis of a walkaround VSP survey through an unconventional tight gas sand reservoir to help characterize fractures. In this paper, we present the results of the seismic azimuthal anisotropy analysis using seismic traveltime, shear‐wave splitting and amplitude attenuation. The azimuthal anisotropy results are compared to the fracture orientations derived from dipole sonic and image logs. The image log interpretation suggests that an orthorhombic fracture system is present. VSP data show that the P‐wave traveltime anisotropy direction is NE to SW. This is consistent with the cemented fractures from the image log interpretation. The seismic amplitude attenuation anisotropy direction is NW to SE. This is consistent with one of the two orientations obtained using transverse to radial amplitude ratio analysis, with the dipole sonic and with open fracture directions interpreted from image log data.     

Seismic characterization of reservoirs with multiple fracture sets using velocity and attenuation anisotropy data

Knowledge about the spatial distribution of the fracture density and the azimuthal fracture orientation can greatly help in optimizing production from fractured reservoirs. Frequency-dependent seismic velocity and attenuation anisotropy data contain information about the fractures present in the reservoir. In this study, we use the measurements of velocity and attenuation anisotropy data corresponding to different seismic frequencies and azimuths to infer information about the multiple fracture sets present in the reservoir. We consider a reservoir model with two sets of vertical fractures characterized by unknown azimuthal fracture orientations and fracture densities. Frequency-dependent seismic velocity and attenuation anisotropy data is computed using the effective viscoelastic stiffness tensor and solving the Christoffel equation. A Bayesian inversion method is then applied to measurements of velocity and attenuation anisotropy data corresponding to different seismic frequencies and azimuth to estimate the azimuthal fracture orientations and the fracture densities, as well as their uncertainties. Our numerical examples suggest that velocity anisotropy data alone cannot recover the unknown fracture parameters. However, an improved estimation of the unknown fracture parameters can be obtained by joint inversion of velocity and attenuation anisotropy data.     

Modelling frequency-dependent seismic anisotropy in fluid-saturated rock with aligned fractures: implication of fracture size estimation from anisotropic measurements

Measurements of seismic anisotropy in fractured rock are used at present to deduce information about the fracture orientation and the spatial distribution of fracture intensity. Analysis of the data is based upon equivalent-medium theories that describe the elastic response of a rock containing cracks or fractures in the long-wavelength limit. Conventional models assume frequency independence and cannot distinguish between microcracks and macrofractures. The latter, however, control the fluid flow in many subsurface reservoirs. Therefore, the fracture size is essential information for reservoir engineers. In this study we apply a new equivalent-medium theory that models frequency-dependent anisotropy and is sensitive to the length scale of fractures. The model considers velocity dispersion and attenuation due to a squirt-flow mechanism at two different scales: the grain scale (microcracks and equant matrix porosity) and formation-scale fractures. The theory is first tested and calibrated against published laboratory data. Then we present the analysis and modelling of frequency-dependent shear-wave splitting in multicomponent VSP data from a tight gas reservoir. We invert for fracture density and fracture size from the frequency dependence of the time delay between split shear waves. The derived fracture length matches independent observations from borehole data.     

中国地震科学台阵两期观测资料近场记录揭示的南北地震带地壳剪切波分裂特征

利用中国地震科学台阵第一期(2011-01-2014-06)及部分中国地震科学台阵第二期(2013-02-2015-12)的流动地震台阵记录到的小震波形资料,运用剪切波分裂系统分析(SAM)方法,分析南北地震带的地壳各向异性,对剪切波分裂参数所反映的区域应力环境及构造特征,以及区域内主压应力方向与断裂分布的关系展开讨论.研究结果表明,南北地震带快剪切波偏振方向自北向南由NE向逐渐转变为NNW向,与南北地震带区域主压应力的方向变化具有一致性.区域内分布的大量NE及WNW或NW向断裂构造同样对快波偏振方向有比较大的影响,位于走滑断裂附近的台站,其快波方向与断裂走向大致平行,部分位于走滑断裂附近的台站其快波方向几乎垂直于断裂走向,而与构造应力场方向一致性较好.个别台站表现出复杂快波优势方向特征,反映出研究区内构造环境的复杂性.慢波时间延迟结果显示,南北地震带南段的平均时间延迟高于北段,反映了受印度板块和欧亚板块的碰撞挤压作用,南段地壳介质各向异性程度更大,构造变形更加剧烈.对比南北地震带上地幔各向异性特征,推测在川滇菱形块体内部可能存在复杂的壳幔耦合现象,地壳剪切波分裂除了反映区域应力特征,还可以揭示出区域构造信息.     

The 3D shear experiment over the Natih field in Oman. Reservoir geology, data acquisition and anisotropy analysis

This paper describes a large-scale reservoir characterization experiment carried out in Oman in 1991 which comprised the acquisition, processing and interpretation of a 28.4 km² 3D multicomponent seismic experiment over the Natih field. The objective of the survey was to obtain information on the fracture network present in the Natih carbonates from shear-wave anisotropy. Shear-wave anisotropy in excess of 20% time splitting was encountered over a large part of the survey. The seismic results are confirmed by geological and well data but provide additional qualitative information on fracturing where this was not available before. Regions of stronger and weaker shear-wave anisotropy appear to be fault-bounded. The average well flow rates (which are fracture-dominated) within such blocks correlate with the average anisotropy of the blocks. The further observation that the anisotropy is largest in the fracture gas cap of the reservoir suggests that shear waves can provide a direct hydrocarbon indicator for fractured rock.     

Imaging pre‐existing natural fractures using microseismic data

In hydraulic fracturing treatments, locating not only hydraulic fractures but also any pre‐existing natural fractures and faults in a subsurface reservoir is very important. Hydraulic fractures can be tracked by locating microseismic events, but to identify the locations of natural fractures, an additional technique is required. In this paper, we present a method to image pre‐existing fractures and faults near a borehole with virtual reverse vertical seismic profiling data or virtual single‐well profiling data (limited to seismic reflection data) created from microseismic monitoring using seismic interferometry. The virtual source data contain reflections from natural fractures and faults, and these features can be imaged by applying migration to the virtual source data. However, the imaging zone of fractures in the proposed method is strongly dependent on the geographic extent of the microseismic events and the location and direction of the fracture. To verify our method, we produced virtual reverse vertical seismic profiling and single‐well profiling data from synthetic microseismic data and compared them with data from real sources in the same relative position as the virtual sources. The results show that the reflection travel times from the fractures in the virtual source data agree well with travel times in the real‐source data. By applying pre‐stack depth migration to the virtual source data, images of the natural fractures were obtained with accurate locations. However, the migrated section of the single‐well profiling data with both real and virtual sources contained spurious fracture images on the opposite side of the borehole. In the case of virtual single‐well profiling data, we could produce correct migration images of fractures by adopting directional redatuming for which the occurrence region of microseismic events is divided into several subdivisions, and fractures located only on the opposite side of the borehole are imaged for each subdivision.     

Anisotropy Effects on Microseismic Event Location

Seismic anisotropy in sedimentary environments is significant—microseismic waveforms often show strong shear-wave splitting, with differences reaching 40% between horizontally and vertically-polarized shear-wave velocities. Failure to account for this anisotropy is shown to result in large microseismic event location errors. A method is presented here for determining the five elastic parameters of a homogeneous, vertical transverse-isotropic (VTI) model from calibration shot data. The method can also use data from mining-induced seismic events, which are then simultaneously located. This simple model provides a good fit to arrival times from coal-environment data, and results in dramatic shifts in interpreted event locations.     

Inversion for seismic anisotropy using genetic algorithms1

A general inversion scheme based on a genetic algorithm is developed to invert seismic observations for anisotropic parameters. The technique is applied to the inversion of shear-wave observations from two azimuthal VSP data sets from the Conoco test site in Oklahoma. Horizontal polarizations and time-delays are inverted for hexagonal and orthorhombic symmetries. The model solutions are consistent with previous studies using trial and error matching of full waveform synthetics. The shear-wave splitting observations suggest the presence of a shear-wave line singularity and are consistent with a dipping fracture system which is known to exist at the test site. Application of the inversion scheme prior to full waveform modelling demonstrates that a considerable saving in time is possible whilst retaining the same degree of accuracy.     

基于二维三分量伪谱法模拟数据的EDA介质中横波分裂研究

为了检测定向裂隙介质中横波分裂的方位属性特征,分析地震属性随裂隙密度和方位变化,采用人工吸收边界和反周期扩展边界,用伪谱法获得不同裂隙密度和不同方位地质模型三分量地面记录;应用时频分析和剪切波偏振分析研究由于裂隙方位和密度引起的横波分裂.结果显示,裂隙密度和方位决定着横波分裂的时差和偏振.快慢横波的延迟时间随裂隙密度增大而增加,不同方位相同裂隙密度的横波分裂时差有微小的变化.在45°方位检测时间延迟时间最大.通过时频分析,可以看到不同方位的瞬时主频有显著的变化,在横波分裂处瞬时主频有明显变化.因此,瞬时主频和快横波的偏振以及延迟时间可以作为裂隙方位和密度的指示.     

The 3D shear experiment over the Natih field in Oman: the effect of fracture-filling fluids on shear propagation

This is the final paper in a series on the 3D multicomponent seismic experiment in Oman. In this experiment a 3D data set was acquired using three-component geophones and with three source orientations. The data set will subsequently be referred to as the Natih 9C3D data set. We present, for the first time, evidence demonstrating that shear waves are sensitive to fluid type in fractured media. Two observations are examined from the Natih 9C3D data where regions of gas are characterized by slow shear-wave velocities. One is that the shear-wave splitting map of the Natih reservoir exhibits much larger splitting values over the gas cap on the reservoir. This increase in splitting results from a decrease in the slow shear-wave velocity which senses both the fractures and the fracture-filling fluid. Using a new effective-medium model, it was possible to generate a splitting map for the reservoir that is corrected for this fluid effect. Secondly, an anomaly was encountered on the shear-wave data directly above the reservoir. The thick Fiqa shale overburden exhibits a low shear-wave velocity anomaly that is accompanied by higher shear reflectivity and lower frequency content. No such effects are evident in the conventional P-wave data. This feature is interpreted as a gas chimney above the reservoir, a conclusion supported by both effective-medium modelling and the geology.
With this new effective-medium model, we show that introduction of gas into vertically fractured rock appears to decrease the velocity of shear waves (S2), polarized perpendicular to the fracture orientation, whilst leaving the vertical compressional-wave velocity largely unaffected. This conclusion has direct implications for seismic methods in exploration, appraisal and development of fractured reservoirs and suggests that here we should be utilizing S-wave data, as well as the conventional P-wave data, as a direct hydrocarbon indicator.     

Upper mantle anisotropy and crust-mantle deformation pattern beneath the Chinese mainland

Over the past 10 years,the number of broadband seismic stations in China has increased significantly.The broadband seismic records contain information about shear-wave splitting which plays an important role in revealing the upper mantle anisotropy in the Chinese mainland.Based on teleseismic SKS and SKKS phases recorded in the seismic stations,we used the analytical method of minimum transverse energy to determine the fast wave polarization direction and delay time of shear-wave splitting.We also collected results of shear-wave splitting in China and the surrounding regions from previously published papers.From the combined dataset we formed a shear-wave splitting dataset containing 1020 parameter pairs.These splitting parameters reveal the complexity of the upper mantle anisotropy image.Our statistical analysis indicates stronger upper mantle anisotropy in the Chinese mainland,with an average shear-wave time delay of 0.95 s;the anisotropy in the western region is slightly larger(1.01 s)than in the eastern region(0.92 s).On a larger scale,the SKS splitting and surface deformation data in the Tibetan Plateau and the Tianshan region jointly support the lithospheric deformation mode,i.e.the crust-lithospheric mantle coherent deformation.In eastern China,the average fast-wave direction is approximately parallel to the direction of the absolute plate motion;thus,the upper mantle anisotropy can be attributed to the asthenospheric flow.The area from the Ordos block to the Sichuan Basin in central China is the transition zone of deformation modes between the east and the west regions,where the anisotropy images are more complicated,exhibiting"fossil"anisotropy and/or two-layer anisotropy.The collision between the Indian Plate and the Eurasian Plate is the main factor of upper mantle anisotropy in the western region of the Chinese mainland,while the upper mantle anisotropy in the eastern region is related to the subduction of the Pacific Plate and the Philippine Sea Plate beneath the Eurasian Plate.     

A review of a quarter century of International Workshops on Seismic Anisotropy in the crust (0IWSA–12IWSA)

In 25 years, the presence of azimuthally varying seismic anisotropy throughout the Earth’s crust has progressed from general denial to universal acceptance, so that many international geophysical meetings now have sessions on seismic anisotropy. Over this period, the proceedings of the biennial series of International Workshops in Seismic Anisotropy (IWSAs) have captured many of the notable advances in the theory, calculation, observation and interpretation of particularly shear-wave splitting (seismic birefringence) in the Earth’s crust. Shear-wave splitting is the almost-infallible indicator of seismic anisotropy along the ray path. This paper reviews 13 IWSA meetings (0IWSA–12IWSA) as a catalogue of 25 years of progress in seismic anisotropy. The evidence now suggests that shear-wave splitting monitors the low-level pre-fracturing deformation of the stress-aligned fluid-saturated microcracks pervading almost all in situ rocks in the crust. Shear-wave splitting indicates that microcracks are so closely spaced they are critical systems with all the universality, calculability, predictability, “butterfly wing’s” sensitivity, and deterministic chaos that that implies. This leads to a New Geophysics, where low-level deformation can be monitored with shear-wave splitting, future behaviour calculated–predicted with the anisotropic poro-elastic model of rock evolution, and in some circumstances even potentially controlled by feedback. We anticipate the New Geophysics will greatly invigorate IWSA.     

Estimating azimuthal stress‐induced P‐wave anisotropy from S‐wave anisotropy using sonic log or vertical seismic profile data

Most sedimentary rocks are anisotropic, yet it is often difficult to accurately incorporate anisotropy into seismic workflows because analysis of anisotropy requires knowledge of a number of parameters that are difficult to estimate from standard seismic data. In this study, we provide a methodology to infer azimuthal P‐wave anisotropy from S‐wave anisotropy calculated from log or vertical seismic profile data. This methodology involves a number of steps. First, we compute the azimuthal P‐wave anisotropy in the dry medium as a function of the azimuthal S‐wave anisotropy using a rock physics model, which accounts for the stress dependency of seismic wave velocities in dry isotropic elastic media subjected to triaxial compression. Once the P‐wave anisotropy in the dry medium is known, we use the anisotropic Gassmann equations to estimate the anisotropy of the saturated medium. We test this workflow on the log data acquired in the North West Shelf of Australia, where azimuthal anisotropy is likely caused by large differences between minimum and maximum horizontal stresses. The obtained results are compared to azimuthal P‐wave anisotropy obtained via orthorhombic tomography in the same area. In the clean sandstone layers, anisotropy parameters obtained by both methods are fairly consistent. In the shale and shaly sandstone layers, however, there is a significant discrepancy between results since the stress‐induced anisotropy model we use is not applicable to rocks exhibiting intrinsic anisotropy. This methodology could be useful for building the initial anisotropic velocity model for imaging, which is to be refined through migration velocity analysis.     

Preliminary seismic anisotropy in the upper crust of the south segment of Xiaojiang faults and its tectonic implications

The Xiaojiang faults,striking north-to-south(NS),and the Honghe faults,striking north-to-west(NW),are first-order block boundaries that intersect to form a concentrated stress zone at an acute angle in the southern part of the Sichuan-Yunnan rhombic block(SYB).It is also a crucial zone for material escaping from the Tibetan Plateau(TP)due to the collision between the Indian Plate and the Eurasian Plate.In December 2017,the Institute of Earthquake Forecasting of the China Earthquake Administration(CEA)deployed a linear temporary seismic broadband array,the Honghe-Xiaojiang temporary Seismic Array(HX Array),across first-order block boundaries in the southern SYB.By using the waveform data of small earthquakes recorded by stations in the HX Array across Xiaojiang faults from 2017 to 2019,and by permanent seismic stations of the China National Earthquake Networks from 2012 to 2019,this paper adopts the systematic analysis method of shear-wave splitting(SWS),SAM method,to obtain preliminary results for seismic anisotropy in the upper crust.The study area can be divided into two subzones according to the spatial distribution of the directions of polarization of the fast shear-wave(PFS)at the stations:the northern zone(zone A,where the HX Array is located)and the southern zone(zone B,to the south of the HX Array).The results show that the directions of the PFS at stations in zone A were highly consistent,dominant in the NE direction,correlated with the in-situ principal compressive stress,and were seemingly unaffected by the Xiaojiang faults.The directions of the PFS as recorded at stations in zone B were more complicated,and were dominant in the NS direction parallel to that of the regional principal compressive stress.This suggests the joint influence of complex tectonics and regional stress in this narrow wedge area.By referring to the azimuthal anisotropy derived from seismic ambient noise in the southeast margin of the TP,the NS direction of the PFS in the middle and lower crust,and its EW direction in the upper mantle,this paper concludes that azimuthal anisotropy in the upper crust differed from that in the lower crust in the south segment of Xiaojiang faults,at least beneath the observation area,and azimuthal anisotropy in the crust was different from that in the upper mantle.The results support the pattern of deformation of ductile flow in the lower crust,and the decoupling between the upper and lower crusts as well as that between the crust and the mantle in the study area.The crustal directions of the PFS appeared to be independent of the Xiaojiang faults,suggesting that the influence of the South China block on the SYB passed through the Xiaojiang faults to the Yimen region.The results of this study indicate that anisotropic studies based on data on the dense temporary seismic array can yield clearer tectonic information,and reveal the complex spatial distribution of stress and deformation in the upper crust of the south segment of Xiaojiang faults.     

ANISOTROPY DETECTED IN SHALLOW CLAYS USING SHEAR-WAVE SPLITTING IN A VSP SURVEY1

Shear waves can provide valuable information about seismic anisotropy. On entering an anisotropic medium, a shear wave generally splits (shear-wave splitting) into a fast and a slow quasi-shear wave with polarizations fixed by the elastic properties of the medium and direction of travel. If the medium contains planar discontinuities with common normals, the fast shear wave will be suitably propagated if its polarization lies in the plane of the discontinuities. Measuring this polarization, using a VSP geometry with oriented three-component geophones in the borehole, offers the possibility of monitoring the orientation and density of the discontinuities as a function of depth. Such a shear-wave VSP was carried out in an uncased 0.3 m diameter borehole drilled to a depth of 120 m in the north of The Netherlands. The upper 80 m of the sequence, consisting of a glacial till and sands and clays of Pleistocene age, was studied. The clays in this sequence have been subjected to glacial deformation and as a result are overconsolidated and locally fissured. In our shallow VSP experiment, shear-wave splitting and therefore anisotropy was identified at various geophone depths for one source offset. Hodograms showed a consistent polarization of the fast shear-wave component over a large depth interval. Under the assumption that the anisotropy was caused by planar discontinuities with common normals, this polarization direction gives the strike of the fissures in this interval. The polarization direction of the fast S-wave did not correspond exactly with the strike which was obtained from geological information on the fissures. The geological information was from undisturbed oriented 70 mm core samples taken at 3 m intervals in the borehole. The discrepancy, however, could be explained in terms of dipping fissures, and such a dip was confirmed by the geological and geotechnical information. The orientation of fissures is an important factor in the directional deformation and strength characteristics of clays as far as geotechnical behaviour is concerned. This study thus illustrates a practical application of shear-wave splitting observed in shallow shear-wave VSP for geology and geotechnical engineering.     

Numerical analysis of seismic wave propagation in fluid-saturated porous multifractured media

Elastic wave propagation and attenuation in porous rock layers with oriented sets of fractures, especially in carbonate reservoirs, are anisotropic owing to fracture sealing, fracture size, fracture density, filling fluid, and fracture strike orientation. To address this problem, we adopt the Chapman effective medium model and carry out numerical experiments to assess the variation in P-wave velocity and attenuation, and the shear-wave splitting anisotropy with the frequency and azimuth of the incident wave. The results suggest that velocity, attenuation, and anisotropy vary as function of azimuth and frequency. The azimuths of the minimum attenuation and maximum P-wave velocity are nearly coincident with the average strike of the two sets of open fractures. P-wave velocity is greater in sealed fractures than open fractures, whereas the attenuation of energy and anisotropy is stronger in open fractures than sealed fractures. For fractures of different sizes, the maximum velocity together with the minimum attenuation correspond to the average orientation of the fracture sets. Small fractures affect the wave propagation less. Azimuth-dependent anisotropy is low and varies more than the other attributes. Fracture density strongly affects the P-wave velocity, attenuation, and shear-wave anisotropy. The attenuation is more sensitive to the variation of fracture size than that of velocity and anisotropy. In the seismic frequency band, the effect of oil and gas saturation on attenuation is very different from that for brine saturation and varies weakly over azimuth. It is demonstrated that for two sets of fractures with the same density, the fast shear-wave polarization angle is almost linearly related with the orientation of one of the fracture sets.     

剪切波分裂分析系统SAM(2007)——区域地震台网资料应用实例

通过对云南、辽宁、福建遥测地震台网的波形资料分析实例,介绍了"剪切波分裂系统分析方法"软件SAM(2007)的用法。通过对区域台网资料的处理分析,表明SAM(2007)是研究剪切波分裂的一个比较实用的软件,能够有效的处理快、慢剪切波识别的问题,研究地壳介质的地震各向异性问题,能普遍用于分析国内区域地震台网资料。     

卢龙地区S波偏振与上地壳裂隙各向异性

由三分量数字地震仪组成的小孔径流动台网记录了1982年10月19日河北卢龙M_s=6.1级地震的部分余震.用质点运动图的方法对横波的偏振进行了分析。研究结果表明,在横波窗内的各观测点都存在横波的分裂现象.不同离源角和方位角快波偏振的水平投影都具有近NE40°方向的优势取向,与根据卢龙地震两组断层错动在各向同性介质中所辐射的横波的偏振方向不一致.这可以由传播介质中应力所导致裂隙的定向排列来解释.这一观测结果提供了卢龙地区脆性上地壳大范围膨胀各向异性（EDA）的证据,并表明这一地区直立平行排列裂隙取向和水平主压应力的方向为NE40°.     

青藏高原东北缘中上地壳介质各向异性及其构造意义

青藏高原东北缘(94°E—105°E,32°N-40°N)是高原北东向扩张的前沿地带,亦是研究高原生长过程的重要区域.本文利用青海省数字地震台网(2008-2014年)共7年的地震目录和波形数据,首先使用双差定位获取精定位震源位置,在此基础上,挑选位于S波窗口内(射线入射角≤45°)的地震事件,依据S波分裂分析方法(SAM),获取研究区域内共26个台站的S波分裂参数.研究结果表明:地处多个块体交汇部位的西宁及其周缘,地壳各向异性呈现两个优势偏振方向,表明该区中上地壳应力环境由区域主压应力场和活动断层共同约束;玉树地震序列的地壳各向异性优势偏振方向与区域主压应力场一致.     

Shear-wave splitting and reservoir crack characterization: the Coso geothermal field

This paper aims to improve current understanding of the subsurface fracture system in the Coso geothermal field, located in east-central California. The Coso reservoir is in active economic development, so that knowledge of the subsurface fracture system is of vital importance for an accurate evaluation of its geothermal potential and day-to-day production. To detect the geometry and density of fracture systems we applied the shear-wave splitting technique to a large number of high-quality seismograms from local microearthquakes recorded by a permanent, 16-station, down-hole, 3-component seismic array running at 480 samples/s. The analysis of shear-wave splitting (seismic birefringence) provides parameters directly related to the strike of the subsurface fractures and their density (number of cracks per unit volume), and, consequently, is an important technique to outline zones of high permeability. Three major fracture directions N10–30W, N0–20E, and N40–50E, of which the first and the second are the most prominent, were identified from the seismograms recorded by the 16-station down-hole array. All orientations are consistent with the known strike of local sets of faults and fractures in local wells and at the surface, as well as with previous analyses of seismic anisotropy in the region. The high quality of the recordings has allowed us to launch an unprecedented investigation into the characteristics of the temporal variations in crack polarization and crack density in a producing geothermal environment. Preliminary results point to significant temporal changes in shear-wave time delays, probably influenced by temporal changes in crack density within a period of 5 years (1996–2000). They are tentatively interpreted as due to a local 3% increase in shear-wave velocity in the southwestern part of the field during 1999.