基于鞍点法与互易性的远探测波场模拟
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摘要
声波远探测中波场是非轴对称的,采用数值算法计算波场会耗费大量时间,无法满足实际测井数据实时处理的需求。为了解决这一问题,该文采用解析法分别计算辐射场和井外界面反射波激发的井内响应。首先利用鞍点法获得井内声源的远场辐射波场,并与实轴积分获得的精确结果进行比较验证解的正确性。然后将反射波等效为集中力的辐射波,利用集中力与井内声源的互易关系获得反射波激发的井内波场解,该解答与有限差分模拟结果一致。该方法为远探测的正演模拟和远探测结果的及时评价提供了有效手段。
The wave field of single-well imaging is asymmetric. It takes a lot of time to calculate the wave field by numerical algorithm, which cannot meet the needs of real-time processing of logging data. In this study,the analytical solution to the radiation wave from the source in a borehole and the borehole wave excited by reflections from the interface outside the borehole is obtained. Firstly, the far-field radiated wave field of borehole acoustic source is obtained by steepest descent method, and the correctness of the solution is verified by comparing with the exact results obtained by real-axis integration. The reflected wave is taken as equivalent to the radiated wave of a concentrated force. The asymptotic solution to the wave field in the borehole excited by reflected wave is obtained using the reciprocal relationship between the concentrated force and the source in the borehole. The results agree with those obtained by finite difference method. This method provides an efficient tool for feasibility study for downhole acoustic distant detection and quick evaluation of the detection results.
The wave field of single-well imaging is asymmetric. It takes a lot of time to calculate the wave field by numerical algorithm, which cannot meet the needs of real-time processing of logging data. In this study,the analytical solution to the radiation wave from the source in a borehole and the borehole wave excited by reflections from the interface outside the borehole is obtained. Firstly, the far-field radiated wave field of borehole acoustic source is obtained by steepest descent method, and the correctness of the solution is verified by comparing with the exact results obtained by real-axis integration. The reflected wave is taken as equivalent to the radiated wave of a concentrated force. The asymptotic solution to the wave field in the borehole excited by reflected wave is obtained using the reciprocal relationship between the concentrated force and the source in the borehole. The results agree with those obtained by finite difference method. This method provides an efficient tool for feasibility study for downhole acoustic distant detection and quick evaluation of the detection results.
引文
[1]Hornby B E.Imaging of near-borehole structure using fullwaveform sonic data[J].Geophysics,1989,54(6):747-757.
[2]薛梅.远探测声波反射波测井研究[D].北京:中国石油大学,2002.
[3]乔文孝,车小花,李刚,等.反射声波成像测井的物理模拟[J].石油物探,2004,43(3):294-297,7.Qiao Wenxiao,Che Xiaohua,Li Gang,et al.Physical simulation of single-well imaging[J].Geophys Prosp Petrol,2004,43(3):294-297,7.
[4]何峰江.声反射成像测井仪器仿真及波形处理技术研究[D].北京:中国石油大学,2005.
[5]Tang X M.Imaging near borehole structure using directional acoustic wave measurement[J].Geophysics,2004,69(6):1378-1386.
[6]Tang X M,Patterson D.Single-well S-wave imaging using multi component dipole acoustic log date[J].Geophysics,2009,74(6):211-223.
[7]Wei Z T,Tang X M.Numerical simulation of radiation,reflection,and reception of elastic waves from a borehole dipole source[J].Geophysics,2012,77(6):D253-D261.
[8]Zhang Y D,Hu H S.A technique to eliminate the azimuth ambiguity in single-well imaging[J].Geophysics,2014,79(6):D409-D416.
[9]Wang Z,Hu H S,Yang Y F.Reciprocity relations for the elastodynamic fields generated by multipole sources in a fluid-solid configuration[J].Geophysical Journal International,2015,203(2):883-892.
[10]Lee M W,Balch A H.Theoretical seismic wave radiation from a fluid-filled borehole[J].Geophysics,1982,47(9):1308-1314.
[11]Gibson Jr R L.Radiation from seismic sources in cased and cemented boreholes[J].Geophysics,1994,59(4):518-533.
[12]Schoenberg M.Fluid and solid motion in the neighborhood of a fluid-filled borehole due to the passage of a lowfrequency elastic plane wave[J].Geophysics,1986,51(6):1191-1205.
[13]Lee M W.Particle displacements on the wall of a borehole from incident plane waves[J].Geophysics,1987,52(9):1290-1296.
[14]Lovell J R,Hornby B E.Borehole coupling at sonic frequencies[J].Geophysics,1990,55(7):806-814.
[15]Peng C.Borehole effects on downhole seismic measurements[D].Massachusetts:Massachusetts Institute of Technology,1994.
[16]Tang X M,Cao J J,Wei Z T.Shear-wave radiation,reception,and reciprocity of a borehole dipole source:with application to modeling of shear-wave reflection survey[J].Geophysics,2014,79(20):T43-T50.
[17]Kurkjian A L,Chang S K.Acoustic multipole sources in fluid-filled boreholes[J].Geophysics,1986,51(1):148-163.
[18]Tang X M,Cheng C H.Quantitative borehole acoustic methods[M].Amsterdam,Boston:Elsevier Science Publishing,2004.
[19]Tsang L,Rader D.Numerical evaluation of the transient acoustic waveform due to a point source in a fluid-filled borehole[J].Geophysics,1979,44(10):1706-1720.
[20]Aki K,Richards P.Quantitative seismology:theory and methods[M].San Francisco,California:W.H.Freeman&Co,1998.
[21]Love A E H.A treatise on the mathematical theory of elasticity[M].New York:Dover Publications,1944.
[22]王治.分层弹性与孔隙介质中弹性波场的互易关系[D].哈尔滨:哈尔滨工业大学,2016.
[2]薛梅.远探测声波反射波测井研究[D].北京:中国石油大学,2002.
[3]乔文孝,车小花,李刚,等.反射声波成像测井的物理模拟[J].石油物探,2004,43(3):294-297,7.Qiao Wenxiao,Che Xiaohua,Li Gang,et al.Physical simulation of single-well imaging[J].Geophys Prosp Petrol,2004,43(3):294-297,7.
[4]何峰江.声反射成像测井仪器仿真及波形处理技术研究[D].北京:中国石油大学,2005.
[5]Tang X M.Imaging near borehole structure using directional acoustic wave measurement[J].Geophysics,2004,69(6):1378-1386.
[6]Tang X M,Patterson D.Single-well S-wave imaging using multi component dipole acoustic log date[J].Geophysics,2009,74(6):211-223.
[7]Wei Z T,Tang X M.Numerical simulation of radiation,reflection,and reception of elastic waves from a borehole dipole source[J].Geophysics,2012,77(6):D253-D261.
[8]Zhang Y D,Hu H S.A technique to eliminate the azimuth ambiguity in single-well imaging[J].Geophysics,2014,79(6):D409-D416.
[9]Wang Z,Hu H S,Yang Y F.Reciprocity relations for the elastodynamic fields generated by multipole sources in a fluid-solid configuration[J].Geophysical Journal International,2015,203(2):883-892.
[10]Lee M W,Balch A H.Theoretical seismic wave radiation from a fluid-filled borehole[J].Geophysics,1982,47(9):1308-1314.
[11]Gibson Jr R L.Radiation from seismic sources in cased and cemented boreholes[J].Geophysics,1994,59(4):518-533.
[12]Schoenberg M.Fluid and solid motion in the neighborhood of a fluid-filled borehole due to the passage of a lowfrequency elastic plane wave[J].Geophysics,1986,51(6):1191-1205.
[13]Lee M W.Particle displacements on the wall of a borehole from incident plane waves[J].Geophysics,1987,52(9):1290-1296.
[14]Lovell J R,Hornby B E.Borehole coupling at sonic frequencies[J].Geophysics,1990,55(7):806-814.
[15]Peng C.Borehole effects on downhole seismic measurements[D].Massachusetts:Massachusetts Institute of Technology,1994.
[16]Tang X M,Cao J J,Wei Z T.Shear-wave radiation,reception,and reciprocity of a borehole dipole source:with application to modeling of shear-wave reflection survey[J].Geophysics,2014,79(20):T43-T50.
[17]Kurkjian A L,Chang S K.Acoustic multipole sources in fluid-filled boreholes[J].Geophysics,1986,51(1):148-163.
[18]Tang X M,Cheng C H.Quantitative borehole acoustic methods[M].Amsterdam,Boston:Elsevier Science Publishing,2004.
[19]Tsang L,Rader D.Numerical evaluation of the transient acoustic waveform due to a point source in a fluid-filled borehole[J].Geophysics,1979,44(10):1706-1720.
[20]Aki K,Richards P.Quantitative seismology:theory and methods[M].San Francisco,California:W.H.Freeman&Co,1998.
[21]Love A E H.A treatise on the mathematical theory of elasticity[M].New York:Dover Publications,1944.
[22]王治.分层弹性与孔隙介质中弹性波场的互易关系[D].哈尔滨:哈尔滨工业大学,2016.