STUDY OF TRAVELTIME AND AMPLITUDE TIME-LAPSE TOMOGRAPHY USING PHYSICAL MODEL DATA1

In seismic tomography the observed traveltimes or amplitudes of direct waves are inverted to obtain an estimate of seismic velocity or absorption of the section surveyed. There has been much recent interest in using cross-well traveltime tomography to observe the progress of fluids injected into the reservoir rocks during enhanced oil recovery (EOR) processes. If repeated surveys are carried out, then EOR processes may be monitored over a period of time. This paper describes the results of a simulated time-lapse tomography experiment to image the flood zone in an EOR process. Two physical models were made out of epoxy resins to simulate an essentially plane-layered sedimentary sequence containing a reservoir layer and simple geological structure. The models differed only in the reservoir layer, which was uniform in the ‘pre-flood’ model and contained a flood zone of known geometry in the ‘post-flood’ model. Data sets were acquired from each model using a cross-well survey geometry. Traveltime and amplitude tomographic imaging techniques have been applied to these data in an attempt to locate the extent of the flood zone. Traveltime tomography locates the flood zone quite accurately. Amplitude tomography shows the flood zone as a region of higher absorption, but does not image its boundaries as precisely. This is primarily because of multipathing and diffraction effects, which are not accounted for by the ray-based techniques for inverting seismic amplitudes. Nevertheless, absorption tomograms could complement velocity tomograms in real, heterogeneous reservoirs because absorption and velocity respond differently to changes in liquid/gas saturations for reservoir rocks.     

Traveltime seismic tomography with adaptive wavelet parameterization

An algorithm for solving the inverse kinematic problem of traveltime seismic tomography is developed and tested. The algorithm is intended for imaging the three-dimensional (3D) velocity model composed of a layer underlain by a half-space. This algorithm considers the bottom boundary of the layer as a first-order seismic velocity discontinuity with unknown position that has to be determined in the inversion together with the velocity variations inside the overlying layer and the sub-interface boundary velocities. The inversion can be applied to the travel times of refracted, head and reflected waves. The main idea behind the algorithm is the adaptive parameterization of the medium by the sparse Haar wavelet series expansion. In order to throw off the poorly resolved coefficients of expansion, we suggest using two empirical local resolution measures: the number of seismic rays crossing the support of the corresponding wavelet support area and their angular coverage, i.e., the spread in the azimuths of these rays. The adequacy of these measures is tested by their comparison with the estimation of the diagonal elements of the resolution matrix on the synthetic examples. This comparison proved that the proposed measures can be successfully applied for statistical estimation of the resolution and for constructing the adaptive parameterization. It was shown also that the best results are achieved while using the number of rays normalized to the size of the wavelet support together with their angular coverage. An automated procedure for throwing off poorly resolved unknowns is developed. The parameters of this procedure can be tuned to provide the desired level of detail of the model to be reconstructed. The synthetic checkerboard testing proved the efficiency of the algorithm. The proposed algorithm can be applied to solve different types of problems, including regional seismic studies, as well as exploration and engineering seismology. The use of this algorithm is especially convenient when the medium is essentially three-dimensional and when the conventional seismic methods implying regular network measurements directly above the studied structure (such as the common depth point method) are inapplicable, e.g., in the seismic studies of the foundations of buildings and in rugged terrains.     

速度差对井间走时层析成像质量的影响及其改进方法

在井间地震初至走时层析成像中,随着相邻地质体速度差的增大,使得射线分布不均匀,以及网格剖分不合适,导致层析成像结果不理想.物理和数值模型的井间走时层析成像表明：当速度差超过30.0%时,层析结果畸变较大;在30.0%～15.0%之间时,层析结果较好;低于15.0%时,层析结果好.在此基础上,提出了井间多尺度初至走时层析成像方法,即对同一模型采用多种网格剖分来同时进行层析成像,以获得研究区域的速度图像.数学和物理模型的井间多尺度走时层析结果表明：该方法很好地兼顾了层析成像的分辨率和精度,极大地改善了井间地震层析成像的质量.即使速度差超过30%,其多尺度的层析结果仍然较好.因此,这种方法具有实际应用的潜力.     

Evaluation of the rockburst potential in longwall coal mining using passive seismic velocity tomography and image subtraction technique

Rockburst is a typical dynamic disaster in underground coal mines which its occurrences relate to the mechanical quality of coal seam and surrounding rock mass and also the condition of stress distribution. The main aim of this paper is to study the potential of rockburst in a longwall coal mine by using of passive seismic velocity tomography and image subtraction technique. For this purpose, first by mounting an array of receivers on the surface above the active panel, the mining-induced seismic data as a passive source for several continuous days were recorded. Then, the three-dimensional tomograms using simultaneous iteration reconstruction technique (SIRT) for each day are created and by employing the velocity filtering, the overstressed zones are detected. In addition, the two-dimensional seismic velocity tomograms in coal seam level by slicing the three-dimensional tomograms are obtained. Then the state of stress changes in successive days by applying the image subtraction technique on these two-dimensional tomograms is considered. The results show that the compilation of filtered three-dimensional tomograms and subtracted images is an appropriate approach for detecting the overstressed zones around the panel and subsequent evaluation of rockburst potential. The research conclusion proves that the applied approach in this study in combination with field observations of rock mass status can effectively identify the rockburst-prone areas during the mining operation and help to improve the safety condition.     

基于小尺度构造约束的网格层析方法及其在火山岩发育区速度建模中的应用

速度场精度是影响偏移成像质量最为关键的因素,因此,速度模型的建立成为解决复杂地质体成像的核心工作.但在火山岩发育区,由于火山岩岩性、岩相复杂,空间相互叠置、尺度小等原因,导致地震波场复杂,成像难度大.常规基于网格的层析成像技术完全是数据驱动,其要求地震数据具有较高信噪比.而火山岩发育区地震反射杂乱,该方法无法满足精细建模需求.为此本文提出一种基于小尺度构造约束的网格层析速度建模方法.该方法既可以通过偏移距共成像点道集的剩余曲率对全局速度进行更新,也可以利用层位约束进行小尺度速度的局部修饰,即,在基于数据驱动的网格层析基础上通过地质约束提高速度模型精度.通过在渤海M油田的实际应用表明该方法在保证计算效率的同时大幅提高小尺度特殊构造体的反演精度,为后续火山岩发育区地震精确成像奠定坚实的基础.     

SOME SOURCES OF DISTORTION IN TOMOGRAPHIC VELOCITY IMAGES1

Two particular sources of distortion, which may be encountered when applying tomographic imaging techniques to crosshole seismic data, have been investigated. Errors in survey locations of the shots and receivers can produce significant distortions in the images obtained. A simple method for solving simultaneously for the velocity field and shot and receiver location errors is presented and applied to synthetic and real data. Reflection and refraction of rays at velocity interfaces may produce poor density and angular coverage of the rays within the region of interest. It is shown that the effect of the velocity field on the ray coverage can significantly affect the resolution in the velocity image, even if ray bending is taken into account. One consequence of this effect is that, in some cases, little improvement in image quality is achieved by using curvi-ray rather than straight-ray inversion techniques, despite the occurrence of pronounced ray bending.     

A comparison of cross-hole electrical and seismic data in fractured rock

Cross‐hole anisotropic electrical and seismic tomograms of fractured metamorphic rock have been obtained at a test site where extensive hydrological data were available. A strong correlation between electrical resistivity anisotropy and seismic compressional‐wave velocity anisotropy has been observed. Analysis of core samples from the site reveal that the shale‐rich rocks have fabric‐related average velocity anisotropy of between 10% and 30%. The cross‐hole seismic data are consistent with these values, indicating that observed anisotropy might be principally due to the inherent rock fabric rather than to the aligned sets of open fractures. One region with velocity anisotropy greater than 30% has been modelled as aligned open fractures within an anisotropic rock matrix and this model is consistent with available fracture density and hydraulic transmissivity data from the boreholes and the cross‐hole resistivity tomography data. However, in general the study highlights the uncertainties that can arise, due to the relative influence of rock fabric and fluid‐filled fractures, when using geophysical techniques for hydrological investigations.     

COMPUTING FIELD STATICS WITH THE HELP OF SEISMIC TOMOGRAPHY*

Field static corrections in general need be applied to all onshore seismic reflection data to eliminate the disturbing effects a weathering layer or near-surface low velocity zone has on the continuity of deep seismic reflections. The traveltimes of waves refracted at the bottom of the low velocity zone (or intermediate refracting interfaces) can often be observed as first breaks on shot records and used to develop a laterally inhomogeneous velocity model for this layer, from which the field static corrections can then be obtained. A simple method is described for computing accurate field statics from first breaks. It is based on a linearization principal for traveltimes and leads to the algorithms that are widely and successfully applied within the framework of seismic tomography. We refine an initial model for the low velocity layer (estimated by a standard traveltime inversion technique) by minimizing the errors between the observed first arrivals on field records and those computed by ray theory through an initial model of the low velocity layer. Thus, one can include more lateral velocity variations within the low velocity layers, which are important to obtain good field static corrections. Traditional first break traveltime inversion methods cannot, in general, provide such refined velocity values. The technique is successfully applied to seismic data from the Amazon Basin. It is based on a simple model for the low velocity layer that consists of an undulating earth surface and one planar horizontal refractor overlain by a laterally changing velocity field.     

地震层析成像技术在岩体完整性测试中的应用

地震波层析成像借鉴了医学上X射线断面扫描的基本原理,利用地震波穿过地质体后走时及能量的改变等物理信息,通过数学处理重建地质体内部图像,从而得到所研究地质体的岩性及构造分布。本文利用这种方法,在一个钻孔中利用电火花震源激了弹性波,在另一个钻孔布设多个检波点同时接收,拾取弹性波初至时间,将接收到的数据利用SIRT方法进行反演迭代计算,最终形成一个弹性波速度谱图,然后利用岩土体的弹性波速度差异推断岩体完整性分布。与其它测试方法比较,该方法分辨率高,空间位置准确,在工程物探、岩土工程勘察中具有较好的应用前景。     

UPPER CRUSTAL VELOCITY STRUCTURE AND CONSTRAINING FAULT INTERPRETATION FROM SHUNYI-TANGGU REFRACTION EXPERIMENT DATA

The urban active fault survey is of great significance to improve the development and utilization of urban underground space, the urban resilience, the regional seismic reference modeling, and the natural hazard prevention. The Beijing-Tianjin metropolitan region with the densest population is one of the most developed and most important urban groups, located at the northeastern North China plain. There are several fault systems crossing and converging in this region, and most of the faults are buried. The tectonic setting of the faults is complex from shallow to deep. There are frequent historical earthquakes in this area, which results in higher earthquake risk and geological hazards. There are two seismicity active belts in this area. One is the NE directed earthquake belt located at the east part of the profile in northern Ninghai near the Tangshan earthquake region. The other is located in the Beijing plain in the northwest of the profile and near the southern end of Yanshan fold belt, where the 1679 M8.0 Sanhe-Pinggu earthquake occurred, the largest historical earthquake of this area. Besides, there are some small earthquake activities related to the Xiadian Fault and the Cangdong Fault at the central part of the profile.
The seismic refraction experiment is an efficient approach for urban active fault survey, especially in large- and medium-size cities. This method was widely applied to the urban hazard assessment of Los Angeles. We applied a regularized tomography method to modeling the upper crustal velocity structure from the high-resolution seismic refraction profile data which is across the Beijing-Tianjin metropolitan region. This seismic refraction profile, with 185km in length, 18 chemical explosive shots and 500m observation space, is the profile with densest seismic acquisition in the Beijing-Tianjin metropolitan region up to now. We used the trial-error method to optimize the starting velocity model for the first-arrival traveltime inversion. The multiple scale checker board tests were applied to the tomographic result assessment, which is a non-linear method to quantitatively estimate the inversion results. The resolution of the tomographic model is 2km to 4km through the ray-path coverage when the threshold value is 0.5 and is 4km to 7km through the ray-path coverage when the threshold value is 0.7. The tomographic model reveals a very thick sediment cover on the crystalline basement beneath the Beijing-Tianjin metropolitan region. The P wave velocity of near surface is 1.6km/s. The thickest sediment cover area locates in the Huanghua sag and the Wuqing sag with a thickness of 8km, and the thinnest area is located at the Beijing sag with a thickness of 2km. The thickness of the sediment cover is 4km and 5km in the Cangxian uplift and the Dacang sag, respectively. The depth of crystalline basement and the tectonic features of the geological subunits are related to the extension and rift movement since the Cenozoic, which is the dynamics of formation of the giant basins.
It is difficult to identify a buried fault system, for a tomographic regularization process includes velocity smoothing, and limited by the seismic reflection imaging method, it is more difficult to image the steep fault. Velocity and seismic phase variations usually provide important references that describe the geometry of the faults where there are velocity differences between the two sides of fault. In this paper, we analyzed the structural features of the faults with big velocity difference between the two sides of the fault system using the velocity difference revealed by tomography and the lateral seismic variations in seismograms, and constrained the geometry of the major faults in the study region from near surface to upper crust. Both the Baodi Fault and the Xiadian Fault are very steep with clear velocity difference between their two sides. The seismic refraction phases and the tomographic model indicate that they both cut the crystalline basement and extend to 12km deep. The Baodi Fault is the boundary between the Dachang sag and the Wuqing sag. The Xiadian Fault is a listric fault and a boundary between the Tongxian uplift and the Dachang sag. The tomographic model and the earthquake locations show that the near-vertical Shunyi-Liangxiang Fault, with a certain amount of velocity difference between its two sides, cuts the crystalline basement, and the seismicity on the fault is frequent since Cenozoic. The Shunyi-Liangxiang Fault can be identified deep to 20km according to the seismicity hypocenters.
The dense acquisition seismic refraction is a good approach to construct velocity model of the upper crust and helpful to identify the buried faults where there are velocity differences between their two sides. Our results show that the seismic refraction survey is a useful implement which provides comprehensive references for imaging the fault geometry in urban active fault survey.     

基于MSFM的复杂近地表模型走时计算

地震走时层析成像方法是解决复杂近地表模型速度建模问题的重要技术.该方法是一种迭代反演方法,在反演过程中需要反复计算地震射线走时.故而,高效高精度且能适应复杂模型的走时计算方法是地震走时层析成像实用化的关键技术之一.本文引入医学成像领域研究的MSFM(Multi-stencils Fast Marching Methods)用于地震层析反演中的走时计算.该方法在标准FMM(Fast Marching Methods)基础上利用坐标旋转生成新的FMM计算模板,使计算网格点对角方向邻点参与计算,改善了标准FMM存在对角方向误差大的缺陷.本文分析对比了MSFM和标准FMM的计算精度和计算效率;针对地震层析成像技术解决的起伏地表模型建模问题,研究了起伏地表模型地震走时计算的MSFM实现方法;采用炮点邻近区域局部细分网格技术只需增加很少的计算量即可大幅提高计算精度.理论分析和模型试算表明MSFM算法明显改善了FMM的计算精度,同时保持了FMM算法的高效性.文章通过对崎岖地表模型的正演和层析反演试算,验证了基于MSFM的地震走时计算方法对复杂模型有很强的适应能力.研究表明该方法作为地震走时层析反演中高效高精度的正演算法,有很好的应用价值.     

Generalized acoustic diffraction tomogra phy1

A generalized diffraction tomography algorithm is developed, which in principle can handle irregularly spaced data, curved acquisition lines and non-uniform background models. By direct comparison with medical diffraction tomography, it is shown that the generalized method involves the same two processing steps: data filtering and back-propagation. The filter handles the irregular sampling of the model space and the uneven energy coverage, while the back-propagation operator removes the wave propagation effects. Paraxial ray-tracing techniques are employed to compute both these quantities. In medical diffraction tomography, the resolution vector (i.e. the Fourier vector of the model space) is defined by the incident and scattered plane-wave directions. It is shown here that a similar relationship exists for a non-uniform background, where the resolution vector at a particular image point is defined by the incident and scattered ray directions. Consequently, the impulse response of the generalized algorithm becomes space variant. Finally, a general processing procedure for transmission mode seismic data, based on this generalized algorithm, is proposed. The potential of the method is demonstrated using synthetic cross-hole data.     

二阶Born近似有限频率走时敏感核

有限频率层析成像考虑了非均匀介质中波的散射、衍射、波前愈合等物理性质,使得其对速度异常体的分辨能力远大于射线层析成像.推导和计算有限频率敏感核是进行有限频率层析成像的关键,当前推导有限频率敏感核多借助一阶Born近似,但这只适用于弱散射介质的情况.本文基于二阶Born近似并利用傅里叶变换推导了三维均匀介质情况下有限频率敏感核的解析表达式,并将其推广到非均匀介质中得到了三维非均匀介质中有限频率敏感核.研究表明:当介质中速度扰动小于2%时,基于二阶Born近似的有限频率敏感核与基于一阶Born近似的有限频率敏感核差别很小,可近似认为相同;当介质中速度扰动大于5%时,基于二阶Born近似的有限频率敏感核与基于一阶Born近似的有限频率敏感核有较大不同,表明此时已不能忽略二次散射.     

Field and synthetic experiments for virtual source crosswell tomography in vertical wells: Perth Basin,Western Australia

It is common for at least one monitoring well to be located proximally to a production well. This presents the possibility of applying crosswell technologies to resolve a range of earth properties between the wells. We present both field and synthetic examples of dual well walk-away vertical seismic profiling in vertical wells and show how the direct arrivals from a virtual source may be used to create velocity images between the wells. The synthetic experiments highlight the potential of virtual source crosswell tomography where large numbers of closely spaced receivers can be deployed in multiple wells. The field experiment is completed in two monitoring wells at an aquifer storage and recovery site near Perth, Western Australia. For this site, the crosswell velocity distribution recovered from inversion of travel times between in-hole virtual sources and receivers is highly consistent with what is expected from sonic logging and detailed zero-offset vertical seismic profiling. When compared to conventional walkaway vertical seismic profiling, the only additional effort required to complete dual-well walkaway vertical seismic profiling is the deployment of seismic sensors in the second well. The significant advantage of virtual source crosswell tomography is realised where strong near surface heterogeneity results in large travel time statics.     

Exploring some issues in acoustic full waveform inversion

The least‐squares error measures the difference between observed and modelled seismic data. Because it suffers from local minima, a good initial velocity model is required to avoid convergence to the wrong model when using a gradient‐based minimization method. If a data set mainly contains reflection events, it is difficult to update the velocity model with the least‐squares error because the minimization method easily ends up in the nearest local minimum without ever reaching the global minimum. Several authors observed that the model could be updated by diving waves, requiring a wide‐angle or large‐offset data set. This full waveform tomography is limited to a maximum depth. Here, we use a linear velocity model to obtain estimates for the maximum depth. In addition, we investigate how frequencies should be selected if the seismic data are modelled in the frequency domain. In the presence of noise, the condition to avoid local minima requires more frequencies than needed for sufficient spectral coverage. We also considered acoustic inversion of a synthetic marine data set created by an elastic time‐domain finite‐difference code. This allowed us to validate the estimates made for the linear velocity model. The acoustic approximation leads to a number of problems when using long‐offset data. Nevertheless, we obtained reasonable results. The use of a variable density in the acoustic inversion helped to match the data at the expense of accuracy in the inversion result for the density.     

基于交叉梯度交替结构约束的二维地震走时与全通道直流电阻率联合反演

在利用不同的地球物理勘探方法对地下复杂介质成像时,因观测系统的非完备性及数据本身对某些岩石物性的不敏感性,单独成像的结果存在较大的不确定性和不一致性.对于地震体波走时成像与直流电阻率成像,均面临着成像阴影区问题.对于地震走时成像,地震射线对低速区域覆盖较差形成阴影区,造成低速区域分辨率降低.对于电阻率成像,电场线在高阻区域分布较少,造成高阻区域分辨率较低.为了提高地下介质成像的精度,Gallado和Meju（2003）提出了基于交叉梯度结构约束的联合地球物理成像方法.在要求不同的物性模型拟合各自对应的数据同时,模型之间的结构要求一致,即交叉梯度趋于零.为了更有效地实现基于交叉梯度的结构约束,我们提出了一种新的交替结构约束的联合反演流程,即交替反演不同的数据而且在反演一种数据时要求对应的模型与另一个模型结构一致.新的算法能够更容易地把单独的反演系统耦合在一起,而且也更容易建立结构约束和数据拟合之间的平衡.基于新的联合反演流程,我们测试了基于交叉梯度结构约束的二维跨孔地震走时和直流电阻率联合成像.合成数据测试表明,我们提出的交替结构约束流程能够很好地实现基于交叉梯度结构约束的联合成像.与单独成像结果相比,地震走时和全通道电阻率联合成像更可靠地确定了速度和电阻率异常.     

Non‐uniqueness with refraction inversion – the Mt Bulga shear zone

The tau‐p inversion algorithm is widely employed to generate starting models with many computer programs that implement refraction tomography. However, this algorithm can frequently fail to detect even major lateral variations in seismic velocities, such as a 50 m wide shear zone, which is the subject of this study. By contrast, the shear zone is successfully defined with the inversion algorithms of the generalized reciprocal method. The shear zone is confirmed with a 2D analysis of the head wave amplitudes, a spectral analysis of the refraction convolution section and with numerous closely spaced orthogonal seismic profiles recorded for a later 3D refraction investigation. Further improvements in resolution, which facilitate the recognition of additional zones with moderate reductions in seismic velocity, are achieved with a novel application of the Hilbert transform to the refractor velocity analysis algorithm. However, the improved resolution also requires the use of a lower average vertical seismic velocity, which accommodates a velocity reversal in the weathering. The lower seismic velocity is derived with the generalized reciprocal method, whereas most refraction tomography programs assume vertical velocity gradients as the default. Although all of the tomograms are consistent with the traveltime data, the resolution of each tomogram is comparable only with that of the starting model. Therefore, it is essential to employ inversion algorithms that can generate detailed starting models, where detailed lateral resolution is the objective. Non‐uniqueness can often be readily resolved with head wave amplitudes, attribute processing of the refraction convolution section and additional seismic traverses, prior to the acquisition of any borehole data. It is concluded that, unless specific measures are taken to address non‐uniqueness, the production of a single refraction tomogram that fits the traveltime data to sufficient accuracy does not necessarily demonstrate that the result is either correct, or even the most probable.     

基于微动技术探测盆地浅部地层速度结构1

本文介绍了利用微动技术探测地表浅层速度结构的方法,并在江苏常州地区一个凹陷盆地内进行了一次野外台阵观测试验,采集场地数据的质量良好.利用空间自相关法得到了不同半径下的自相关函数曲线,该场地的自相关函数显示,对于半径较大的台阵,其自相关系数较好;根据自相关函数提取了场地的频散曲线.通过设定初始模型,利用邻域反演算法得到了该场地的基本速度结构和各层深度分布范围;最后通过与场地附近的人工地震剖面进行对比分析表明,试验结果所揭示的土层结构与浅层人工地震勘探解释结果接近.     

Imaging weak zones in the foundation using frequency domain attenuation tomography

Cross-hole imaging method using Time Domain (TD) and Frequency Domain (FD) parts of cross-hole radar tomography data acquired using Step Frequency Ground Penetrating Radar (SFGPR) was implemented. This method was adopted for imaging foundation of a dam to check if the foundation was free of geological weak zones. The dam site is characterised by massive and jointed-phyllites associated with major and minor shears. The cross-hole radar tomography data was acquired in the frequency bandwidth of 250 MHz, from the deepest level gallery up to a depth of 40 m in the foundation. In TD, first arrival time and amplitudes of radio waves were inverted using Simultaneous Iterative Reconstruction Technique (SIRT) resulting in velocity and attenuation tomograms. The tomograms showed nearly uniform velocity or attenuation structure in the respective tomographic plane. Subsequently, cross-hole radar tomography data was analysed in FD for a variation of spectrum-amplitude at different frequencies. Amplitudes picked at each single frequency were then inverted using SIRT for obtaining frequency domain attenuation tomogram (FDAT). The FDAT clearly showed presence of anomalous high attenuation zones in the depth range of 23–33 m of the tomographic plane. The anomalous zones in the attenuation tomogram are weak zones in the foundation. To validate the above observations, cross-hole seismic tomography was also done in the same boreholes. Cross-hole seismic tomography results showed low velocity (p-wave) zones around the same location corresponding to the high attenuation zone in FDAT, bringing the dormant weak zone to light. This enabled fine-tuning of the reinforcement design and strengthening the weak zone. This paper discusses the cross-hole radar tomography imaging method, the results of its application in imaging weak zones in the foundation and the comparison of cross-hole radar tomography results (in TD and FD) with the cross-hole seismic tomography results.     

Detection of Local Inhomogeneities by Means of Cross-borehole Seismic Tomography

—This numerical study is devoted to distortions of local anomalies which are revealed by 2-D and 3-D cross-borehole seismic tomography based on first arrival travel times. The fact that prolonged subvertical anomalies may disappear in the final velocity model is well known. But distortions are also inherent to images of local inhomogeneities. These distortions are accompanied with false anomalies of the opposite sign located just above and below true ones. I offer a semi-empirical explanation of their existence, proving that they are an inherent consequence of observation geometry incompleteness. To improve the quality of the model obtained with cross-borehole tomography, a 3-D acquisition geometry may be used when additional boreholes are positioned around the target object. Results of 3-D tomographic experiments however may be considerably distorted for another reason nonaccounted bending of seismic rays.¶To generate the travel times, a ray-tracing procedure making use of the graph theory was applied. Tomographic inversion was performed by an algorithm based on the assumption of the unknown function smoothness.