Liu et al. During the VSP wave (P-wave and converted S-wave) imaging process, the velocity of both P- and S-waves should be provided. In areas where l

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1 APPLIED GEOPHYSICS, Vol. 4 No.3 (September 2007), P , 14 Figures. DOI: /s Pure S-waves in land P-wave source VSP data Liu Yang 1, Zhang Qinghong 2, Bao Leiying 2,and Wei Xiucheng 3 Abstract: Conventional land vertical seismic profiling (VSP) exploration usually uses P-wave sources and three-component geophones for receivers, emphasizing P- and converted S-waves. Previous studies show that both dynamite borehole shots and vertical vibrations from controllable seismic sources at the surface will produce relatively strong pure P-waves and weaker pure S-waves. Interfaces with a large Poisson s ratio difference have a positive influence on the formation of strong transmitted converted S-waves. By a comparative analysis of pure S-waves from sources and converted downgoing S-waves, we believe that the main frequency of pure S-waves is usually lower than pure P-waves while the main frequency of downgoing converted S-waves is close to that of P-waves. We have studied zero-offset and offset VSP data from land P-wave sources. Results show that pure S-waves commonly exist in these data with differences in wave intensity. S-wave velocity can be obtained from the P-wave source zero-offset VSP data. Finally, we discuss the bright future of joint application of VSP P-and S-waves and the full use of S-waves in P-wave source VSP data. Keywords: Land VSP, P-wave source, pure S-wave. Introduction VSP technology is a method of observing seismic signals at different depths of a well when the seismic source is near the surface. Compared with surface seismic surveys, VSP technology shows less energy attenuation and higher spatial resolution near the borehole because the seismic waves propagate through the low-velocity layer one time and the propagation distance is shorter. VSP results can depict accurate velocities, strata, structure near the hole, and the vertical distribution of stratigraphic reservoirs. It is a bridge between seismic reflections and geologic horizons which provides reliable data for detailed structure interpretation, reservoir prediction, and reservoir description. VSP technology usually uses three-component geophones to receive seismic waves. VSP seismic exploration can be divided into full wave VSP, S-wave, and P-wave exploration according to the source characteristics. Full-wave exploration uses P-wave, SV-wave, and SH-wave sources and three-component geophones. Full-wave VSP surveys can record up to nine seismic wave components which include PP-, SS-, SP-, and PS-waves. S-wave VSP exploration uses SV- and SH-wave sources, whereas P-wave VSP exploration uses P-wave sources. In spite of the numerous advantages S-wave VSP exploration possesses for fracture surveys and seismic anisotropy studies, it is difficult for S-wave source shooting to produce high quality S-waves. Moreover, the high cost of S-wave exploration to some degree constrains the use of S-wave VSP surveys. Combining P-waves received from three-component geophones with PS converted waves not only reduces non-uniqueness but improves the accuracy and chance of success for structural interpretation, lithology and fracture determination, and hydrocarbon recognition. Manuscript received by the Editor 2007; revised manuscript received August 19, Key Laboratory of Geophysical Exploration of CNPC, China University of Petroleum, Beijing, , China. 2. Borehole Seismic Center, East Geophysical Company of CNPC, Zhuozhou, Zhuozhou, , China. 3. Exploration and Production Research Institute of SINOPEC, Beijing, , China. 173

2 Liu et al. During the VSP wave (P-wave and converted S-wave) imaging process, the velocity of both P- and S-waves should be provided. In areas where lateral velocity variation is small, the first break times of the zerooffset P-waves are usually used to calculate the P-wave velocity. In areas where lateral velocity variation is large, zero-offset first break times and offset P-waves can be used to calculate the joint inversion P-wave velocity. The S-wave velocity calculation currently uses the converted S-waves (Ahmed, 1989; Geis et al., 1989). Since the propagation time of converted S-waves is related to the P-wave velocity, which usually has a wide range of values, S-wave velocity calculations have been difficult. Because the geophones receive information only at certain depths of a well, it is difficult to determine the interface locations where converted waves occur outside of these depths which influence the S-wave velocity inversion accuracy. If pure S-waves are recorded in VSP data, using the downgoing pure S-waves in the velocity inversion will certainly produce accurate S-wave velocities. Lash (1980) used explosive sources in a deep well VSP survey and observed pure S-waves and downgoing converted S-waves near the source. O Brien (1992) observed downgoing S-waves in vertical vibroseis VSP records. He showed that when Poisson s ratio of the upper layer is larger than the lower layer, P-waves from the upper layer propagating downward to the interface at small angles can produce transmitted converted S-waves. Zhao et al. (2005) considered that in some P-wave source zero-offset VSP records, the main reasons for the observed pure S-waves produced near the source are: the shear component of the seismic source, near-source heterogeneity, and seismic anisotropy near the source. Li et al. (2005) used the observed VSP downgoing P- and S-waves in a P- and S-wave velocity inversion. Downgoing S-waves observed in zero-offset VSP records can be divided into two categories: pure S-waves produced near the source and downgoing converted S-waves produced when P-waves are transmitted at a high Poisson s ratio interface. By analyzing land P-wave sources, we believe that a land P-wave source is not a pure P-wave source and it can also produce pure S-waves. The comparatively strong pure S-waves can be recovered during processing. Pure S-waves from zerooffset VSP records help the calculation of S-wave layer velocities and stacked profiles. The analysis of conventional land P-wave sources Land P-wave sources are generally comprised of explosive and controlled sources. It is generally believed that explosive sources produce P-waves. When the dynamite has a homogeneous spherical shape, the media around the shooting point is isotropic, and the vibrations generated by the source are the same in various directions, then pure P-waves are (a) Z component (b) H1 component (c) H2 component Fig. 1 The original three-component record of zero-offset VSP of Well A. 174

3 Pure S-waves in land P-wave source VSP data produced. In practice, it is impossible for the dynamite and surrounding media to satisfy all of the conditions and both P- and S-waves are produced. The intensity of the generated S-waves is related to the characteristics of the dynamite and surrounding media. Calculations by Miller and Prusey (1954) show that if the P-wave controlled source is semi-infinite, 7% of the produced energy is downgoing P-waves, 26% is S-wave energy concentrated at 30 to vertical, and 67% surface waves. So a P-wave controlled source can also produce pure S-waves. Pure S-waves from P-wave sources in land zero-offset VSP data Analysis of the zero-offset VSP from Well A Figure 1 is the original three-component zerooffset VSP record from Well A. The basic acquisition parameters are: 226 m offset, the geophone depth range is from 60 to 4040 m, explosive source, the shot depth is a constant 25 m, and the lithology at the shots is sandstone. The geophone interval is 10 m for receiver depths from 60 to 3200 m and 5 m for receiver depths from 3205 to 4040 m. Figure 1 shows that the direct downgoing P-wave energy is concentrated in the vertical component. Since there is a 226 m offset distance between the shot points and borehole, the direct downgoing P-waves have a projection in the horizontal components. Upgoing and downgoing S-waves can be seen in the horizontal components. In three-component VSP data acquisition, the geophone s vertical component direction is usually downward. Since the geophone s horizontal component azimuth cannot be defined and when the geophone moves from one depth to another, the horizontal component azimuth is randomly oriented and the horizontal component azimuth must be calculated in data processing. When the line between shot point and geophone is neither parallel nor vertical to the horizontal component direction, the two horizontal components usually record projections of the direct wave. When an offset exists, after geophone component rotation, the direct wave energy on the radial (R) component is maximized and the energy on the transverse (T) component is minimized. This gives a measure of the geophone azimuth. Figure 2 shows the R and T components after the two horizontal components in Figure 1 are rotated, which illustrates that the downgoing direct P-wave energy mainly is concentrated in the R component which has clear downgoing SV-waves. The T component has comparatively strong downgoing SH waves but, because of poor continuity from the polarity change, the T component S-wave continuity must be improved by a polarity correction. Figure 3 shows the horizontal components of Figure 2 after applying a polarity correction and a bandpass filter. The downgoing waves in both components are clear. Figure 4 shows a comparison (a) R component (b) T component Fig. 2 R and T components after the rotary direction of two horizontal components in Fig

4 Liu et al. between the Z and R components. The downgoing SVwave energy is mainly focused on the R component while the Z component hardly registers the SV-waves. According to O Brien (1992), strong downgoing transmitted converted S-waves result from a high Poisson s ratio difference across an interface. Usually the velocity of the overlying velocity layer is low and the Poisson s ratio is high, so downgoing transmitted converted S-waves can be produced at the top of highvelocity layer. The primary frequency of the S-waves should be close to that of the P waves. However, it can be easily seen from Figure 2a that the downgoing S-wave frequency is lower than that of the P-waves, especially for depths from 3000 to 4000 m. Figure 1a shows that the amplitude and wave shape of the direct P-waves produced by explosive sources tend to be static with depth. If S-waves are converted and transmitted, they should also be static with depth. In addition, when (a) R component (b) T component Fig. 3 The record of the two horizontal components in Fig. 2 after polarity correcting and bandpass filtering. (a) R component (b) Z component Fig. 4 The record of Z component in Fig. 1 and R component in Fig. 3 after bandpass filtering. 176

5 Pure S-waves in land P-wave source VSP data the P-wave angle of incidence is nearly perpendicular to a velocity boundary, converted SH-waves will not be generated. As a result, pure S-waves should be produced at the top of a high-velocity layer. The changes over depth of the direct arrival amplitude and shape are most likely due to changing shot conditions. Figure 5 is the R component downgoing wave record of Figure 4a showing the downgoing SV-wave first arrival times. The P- and S-wave interval velocities and Vs/Vp velocity ratio can be calculated from the arrival times. The results are shown in Figure 6, which illustrates that P- and S-wave velocities generally increase and the Vs/Vp velocity ratio remains approximately 0.55 with increasing depth. Figure 7 shows the results of extracting, flattening, and corridor muting the R component upgoing SV-waves of Figure 4. Figure 8 shows the P- and SV-wave corridor stacks; notice the abundant SV-wave reflections. Due to the lack of wavelet match processing, large arrival shape differences, and differences in reflection strength, it is difficult to identify the relationships between corresponding P and SV reflections events. Analysis of the zero-offset VSP from Well B Figure 9 is the original three-component zero-offset VSP record from Well B with a 61 m offset, same shot positions, 20 m shot depth, shots in loess, and geophone depths from 270 to 2100 m. Figure 10 shows the horizontal components from Figure 9 after the rotation to radial and transverse directions, polarity correction, and bandpass filtering. The seismic traces in these two figures are amplitude balanced with relative amplitude preserved on each trace. The two figures also show the strong P and S multiples. If the conversion of the downgoing S-waves occurs at the high-velocity layer or deeper interfaces, the primary frequency should be similar to the transmitted P-wave Time (ms) Velocity (m/s) Tp Ts (a) The picked direct P-wave and SV-wave arrival time Vp Vs Depth (m) Depth (m) (b) P-wave and S-wave interval velocity calculated from direct wave arrival time Vs/ Vp Fig. 5 The first break time picking of the S waves from the record of downgoing waves of R component in Fig Depth (m) (c) Velocity ratio of P-wave to S-wave interval velocity calculated from direct arrival time Fig. 6 P-wave interval velocity, S-wave interval velocity, and velocity ratio derived from direct wave arrival time. 177

6 Liu et al. frequency. Since the shots are in the low velocity loess layer, the pure S-waves produced by the explosion should possess a relatively low primary frequency. The frequency of the downgoing S-waves in Figure 10 is obviously lower than that of the downgoing P-waves. Take the example of the trace at 270 m depth, the downgoing P multiple energy from 170 to 970 ms apparently decreases. If pure S-waves are converted from transmitted P-waves, the downgoing S multiples from 250 to 1050 ms should also show an apparent decrease. However, the observed situation is different. Lash (1980) believed that the multicycle downgoing S-waves created from a dynamite explosion in a borehole should be pure waves produced at the source. In conclusion, the downgoing S-waves in Figure 10 should be pure S-waves produced at the source. Pure S-waves in land P-wave source offset VSP data Analysis of the offset VSP from Well A The offset VSP survey of Well A (see Figure 11) uses a shot offset of m, a dynamite shot depth of 25 m, sandstone lithology surrounding the shots, and geophone depths from 480 to 4040 m. The downgoing S-waves after wave field separation of the rotated R and T components are shown in Figure 12. At a depth of about 2000 m, we see relatively strong downgoing S-waves from 1200 to 1400 ms. The frequency is (a) Upgoing waves (b) Upgoing wave flatting (c) Corridor muting Fig. 7 Extracting, flatting and corridor muting to upgoing SV waves of R component in Fig. 4. obviously lower than the downgoing P-waves. The S-waves should be pure S-waves generated near the explosion but are not converted S-waves from the top of the high-velocity layer. Analysis of the offset VSP from Well B Figure 13 shows the original three-component offset VSP record from Well B. The main acquisition parameters are: 1614 m shot offset, geophone depths from 2110 to 520 m, 20 m shot depth, and loess surrounds the shots. Figure 14 shows the R and T components after rotation of the two horizontal components from Figure 13. Downgoing S-waves can be clearly seen in the T component, with the primary frequency being lower than the P-waves. The S-waves should be pure SH-waves generated by the dynamite explosion. The SH-waves are reflected from at a velocity boundary. Discussion Our analysis shows that explosive and controlled seismic sources are not pure P-wave sources but also produce pure S-waves. Since on land there are usually near-surface low-velocity horizons, the primary S-wave frequency formed from controlled sources at the surface 178

7 Pure S-waves in land P-wave source VSP data (a) P waves (b) SV waves Fig. 8 Zero-offset VSP corridor stack profiles of P and SV waves of Well A. and dynamite sources at some depth is much lower than P-waves. Furthermore, SH-waves can usually be observed in the VSP records. When a large Poisson s ratio difference exists across an interface, strong downgoing converted S-waves may be formed. The upper interface of the near-surface high-velocity layer is an example. Downgoing converted S-waves are usually SV-waves produced when P-waves from the seismic sources are transmitted to the high-velocity layer. The primary SV-wave frequency is nearly the same as the P-waves. The analyses of many zero-offset and far-offset land VSP records have proved that pure S-waves are generated at the source. In VSP and surface observations, the low-velocity layer has the same influence on S-waves when they are transmitted downward. Why is it difficult to observe pure S-waves in surface three-component seismic records? The reason is, in surface observations S-waves pass through the low-velocity layer when they (a) Z component (b) H1 component (c) H2 component Fig. 9 The original three-component record of zero-offset VSP of Well B. 179

8 Liu et al. are transmitted upward to the surface geophones. Since the low-velocity layer strongly absorbs and attenuates S-waves, the S-wave energy will be extremely weak when the arrivals reach the surface. In contrast, the nearsurface influence does not exist in VSP observations. Since pure S-waves are usually produced from conventional P-wave sources, not only pure P- and converted PS-waves but pure S-waves should be considered in the following aspects of three-component VSP data: Make full use of direct wave propagation times. The direct P- and S-wave arrival time picks should be used in the inversion of P- and S-wave interval velocities to calculate Poisson s ratio for lithology and fluid characteristics, imaging accuracy improvements in PSwave imaging from offset VSP data, improvements in calibration of surface converted PS-wave synthetics, and time to depth conversion of surface PS-waves. (a) R component (b) T component Fig. 10 The record of the two horizontal components in Fig. 9 after polarity correcting and bandpass filtering. (a) Z component (b) H1 component (c) H2 component Fig. 11 The original three-component record of offset VSP of Well A. 180

9 Pure S-waves in land P-wave source VSP data Make full use of direct transmitted wave motion information. P- and S-wave quality factors can be estimated from PP-and SS-waves. The quality factors can be applied in reservoir description and the improvement of surface seismic data resolution. Make full use of the upgoing reflected wave fields. Compared with PP reflected waves, converted PS reflected waves have a small imaging range and a high fold number, which does not benefit a joint interpretation. SS-wave imaging range and fold number are basically the same as PP reflected waves, consequently positively influencing joint interpretation and interpretation (a) Downgoing S waves (SV waves) obtained from R and Z component wave field separation (b) Downgoing S waves (SH waves) obtained from T component wave field separation Fig. 12 Downgoing S-wave record derived from rotary direction and wave field separation to the three-component record in Fig.11. (a) Z component (b) H1 component (c) H2 component Fig. 13 The original three-component record of offset VSP of Well B. 181

10 Liu et al. accuracy. If converted SP-waves are acquired, a much larger imaging range can be obtained as well. This analysis has shown the bright future for the joint application of both P- and S-waves. Our next emphasis will be on the full development and application of pure S-waves in land P-wave source VSP data. (a) R component (b) T component Fig. 14 The record of rotary direction to the two horizontal components in Fig. 13. References Ahmed, H., 1989, Application of mode-converted shear waves to rock-property estimation from vertical seismic profiling data: Geophysics, 54, Geis, W. T., Stewart, R. R., Jones, M. J., and Katapodis, P. E., 1989, Processing, correlating, and interpreting converted S-waves in Southern Alberta: 59th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, Lash, C. C., 1980, Shear waves, multiple reflections, and converted waves found by a deep vertical wave test (vertical seismic profiling): Geophysics, 45 (9), Li, Y. P., Zhao, X. M., Zhou, R., and Dushman, D.,2005, 3C VSP tomography inversion for subsurface P- and S-wave velocity distribution: 75th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, Miller, G. F., Pursey, H., 1954, The field and radiation impedance of mechanical radiators on the free surface of a semi-infinite isotropic solid. Proceeding of the Royal Society of London, Series A, 223, O Brien, J., 1992, VSP measurement of shear-wave velocities in consolidated and poorly consolidated formations: Geophysics, 57 (12), Zhao, X. M., Zhou, R., Li, Y. P., Janak, P., and Dushman, D., 2005, Shear waves from near-offset VSP survey and applications: 75th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, Liu Yang, is a professor at China University of Petroleum. He received his PhD in applied geophysics in 1998 from the University of Petroleum (Beijing). His research interests are seismic anisotropy and surface and borehole multi-component seismic exploration. wliuyang@vip.sina.com. 182

11 应用地球物理 ( 英文版 ) 2007 年第 4 卷第 3 期 中文摘要 不规则形状垂直井孔中波传播的 2.5 维边界元模拟 // 2.5D Boundary element simulation of wave propagation in a vertical fluid-filled borehole with Irregular shape, 盖增喜 1, 王灿云 2, 雷厅 3, 陈晓非 1,Applied Geophysics, 2007, 4(3), (1. 北京大学地球与空间科学学院, 地球物理系, 北京, ; 2. 斯伦贝谢公司北京地球科学中心, 北京, ; 3. Schlumberger-Doll Research, Schlumberger.) 摘要 : 本文给出了求解声波测井工作中具有任意形状的垂直井孔中波传播的波数域边界元公式 我们将问题看成是垂向均匀的二维介质, 并沿垂直方向变换到离散波数域 通过与有限差分计算的频散曲线的比较验证了算法和程序的正确性 边界元方法可以处理任意形状的边界, 作为初步应用, 我们研究了垂向裂纹对井孔中波传播的影响 关键词 : 边界元, 声波测井, 频散曲线, 垂向裂纹 岩石物理评价及其在基于常规与 CMR-MDT 测井数据的 AVO 分析中的应用 //Petrophysical evaluation and its application to AVO based on conventional and CMR-MDT logs, 燕军, 刘堂宴, 刘向君, Applied Geophysics, 2007, 4(3), , (1. Fugro-Robertson Ltd (now at Ikon Science, eddington, London, United Kingdom); 2. 同济大学地球海洋科学研究生院, 上海, ; 3. 西南石油大学油气资源地质重点实验室, 成都, ) 摘要 : 常规测井为 AVO 分析提供了基础的资料, 成为联系岩石物理与地震资料的桥梁 然而如果储层存在有复杂的流体系统, 如地层被严重地层流体侵入 电阻率响应低及盐水矿化度复杂等的现象, 则常规测井无法提供高质量的测井资料, 导致得出错误的弹性计算结果, 使 AVO 结果与地震资料不吻合 中国渤海湾地区第三系裂缝性储层复杂, 我们利用常规测井和核磁共振测井与模块地层动态测试相结合的组合仪完成了地层评价和储层描述 研究结果表明岩石物理学家利用上述方法技术可以获得诸如空隙度 渗透率 含水饱和度 束缚流体以及空隙压力等重要的储层参数并进一步综合应用这些结果和以实验室测量数据为基础的岩性分析结果进行在地震域岩石物理研究和 AVO 分析 关键词 : 地层评价,AVO, 测井,CMR-MDT, 岩性分析, 弹性 陆上纵波源 VSP 资料中的纯横波 // Pure S-waves in land P-wave source VSP data, 刘洋 1, 张庆红 2, 鲍磊英 2 3, 魏修成 Applied Geophysics, 2007, 4(3), , (1. 中国石油大学 CNPC 物探重点实验室, 北京 ; 2. 中国石油东方地球物理公司井中地震中心, 涿州 ; 3. 中国石油化工股份有限公司勘探开发研究院, 北京, ) 摘要 : 常规陆上 VSP(Vertical Seismic Profiling) 勘探普遍采用纵波震源激发, 三分量检波器接收, 主要利用的是纵波和转换横波信息 已有的研究表明, 炸药震源在井下激发 可控震源在地面垂向振动, 均会产生较强的纯纵波和一定强度的 纯横波 ; 泊松比差别较大的分界面有利于形成较强的透射转换横波 本文通过对激发形成的纯横波和下行转换形成的横波进行对比分析, 认为纯横波的主频往往低于纯纵波的主频, 而下行转换横波的主频通常接近纵波的主频 本文分别对两个陆上纵波源零偏和非零偏 VSP 资料进行分析, 结果表明这些资料中普遍存在纯横波, 只是横波的强弱存在不同程度的变化 利用纵波源零偏 VSP 资料, 可以获得横波速度信息 最后对 VSP 纵波和横波联合应用前景进行了分析, 应该充分利用纵波源 VSP 资料中的横波信息 关键词 : 陆上 VSP, 纵波震源, 纯横波 玄武岩内非均质性对地震资料的影响 : 印度德干圈闭的一个研究实例 // The effect of intra-trappean heterogeneities on seismic data: A case study from the Deccan Traps, Dhananjai Pandey 1 *, Satish Singh 2, Martin Sinha3, Lucy MacGregor 4, Applied Geophysics, 2007, 4(3), (1.Bullard Laboratories, Madingley Road, University of Cambridge, Cambridge, UK, CB3 0EZ; 2.Laboratoire de G eosciences Marines, IPG Paris 4 Place Jussieu, Paris Cedex 05, France ; 3. SOES, National Oceanography Centre, Southampton, UK, SO14 3ZH; 4, Offshore Hydrocarbon Mapping Plc., Aberdeen, UK, AB23 8GD. 摘要 : 油气勘探需要重新开发玄武岩下目的层的成像技术 我们今天遇到的最重要的问题之一是玄武岩下地震成像 近年来, 由于利用长炮检距这个问题部分已经得到解决 然而, 由于地表以及玄武岩的内部非均质性引起的复杂波形, 近炮检距的资料仍然不能充分地被利用 影响玄武岩下成像的近垂直入射资料对于了解玄武岩层内部结构是十分有用的 对比较均匀的玄武岩目标层可选用转换波 这里我们利用几个合成模型例子重点描述了更接近现实的非均质玄武岩流引起的实际困难 模拟计算了全波地震记录以有助于了解玄武岩内沉积物对地震资料的影响 本文介绍了印度德干圈闭的一个研究实例 首先探讨了夹层沉积物对整个地震成像的影响 其次利用该区声测井资料以反射系数法计算全波场响应与实际地震资料对比, 通过一系列速度 - 深度剖面探讨了利用模式转换波 ( 顶底玄武岩界面上的 P 波转化为 S 波或相反 ) 对印度库奇地区玄武岩下成像的可行性 通过与野外资料相比较证明玄武岩中多个薄层的效应严重恶化我们所要解释和利用的图象的质量 关键词 : 玄武岩下成像, 库奇, 德干高原, 反射系数, 全波形模拟 基于 VSP 直达波资料的粘弹介质参数遗传算法反演 //Parametric inversion of viscoelastic media from VSP data using a genetic algorithm, 胡彬, 唐刚, 马坚伟, 杨慧珠, Applied Geophysics, 2007, 4(3), (1. 清华大学地震波勘探开发研究所, 北京,100084) 摘要 : 粘弹性参数变得越来越重要, 其反演算法也逐渐成为众多研究者的研究热点 而遗传算法是一种随机 自适应 启发式的算法, 具有很好的鲁棒性和全局收敛性, 本文基于 VSP 直达波方程, 引入了遗传算法来进行粘弹参数反演, 首先将频率域直达波方程表示为复速度的函数, 然后通过遗传算法反演出复速度 而复速度和品质因子又是复速度的函数, 从而便可很容易的得出 但若直接反演复速度, 反演参数太多, 不容易实现, 所以又将复速度表示成参数 C 0 和 C 的函数, 以减少反演参数数量 最后给出了理论模型实验, 以证明该算法的有效性