Abstract
Marine spark sources are widely used in high-resolution marine seismic surveys. The characteristic of a wavelet is a critical part in seismic exploration; thus, the formation and numerical simulation of spark source wavelets should be explored. In studies on spark source excitation, the acoustic field generated by the interaction between bubbles constitutes the near-field wavelet of a source. Therefore, this interaction should be revealed by studying complex multibubble motion laws. In this study, actual discharge conditions were combined to derive the multibubble equation of motion. Energy conservation, ideal gas equation, and environmental factors in the discharge of spark source wavelets were studied, and the simulation method of an ocean spark source wavelet was established. The accuracy of the simulation calculation method was verified through a comparison of indoor-measured signals using three electrodes and the spark source wavelet obtained in the field. Results revealed that the accuracy of the model is related to the number of electrodes. The fewer the number of electrodes used, the lower will be the model’s accuracy. This finding is attributed to the statistical hypothesis factor introduced to eliminate the coupling term of the interaction of the multibubble motion equation. This study presents a method for analyzing the wavelet characteristics of an indoor-simulated spark source wavelet.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bruggeman, P., and Leys, C., 2009. Non-thermal plasmas in and in contact with liquids. Journal of Physics D: Applied Physics, 42(5): 53001, DOI: https://doi.org/10.1088/0022-3727/42/5/053001.
Cook, J. A., 1993. Interaction of multiple spark-generated bubbles in a compressible liquid. PhD thesis. University of Texas.
Cook, J. A., Gleeson, A. M., and Roberts, R. M., 1997. A spark-generated bubble model with semi-empirical mass transport. The Journal of the Acoustical Society of America, 101(4): 1908–1920, DOI: https://doi.org/10.1121/1.418236.
Duchesne, M. J., Bellefleur, G., Galbraith, M., Koesar, R., and Kuzmiski, R., 2007. Strategies for waveform processing in sparker data. Marine Geophysical Researches, 28(2): 153–164, DOI: https://doi.org/10.1007/s11001-007-9023-8.
Eubank, P. T., Patel, M. R., Barrufet, M. A., and Bozkurt, B., 1993. Theoretical models of the electrical discharge machining process. III. The variable mass, cylindrical plasma model. Journal of Applied Physics, 73(11): 7900–7909, DOI: https://doi.org/10.1063/1.353942.
Fujikawa, S., and Akamatsu, T., 1980. Effects of the non-equilibrium condensation of vapor on the pressure wave produced by the collapse of a bubble in a liquid. Journal of Fluid Mechanics, 97(3): 481–512, DOI: https://doi.org/10.1017/S0022112080002662.
Fujikawa, S., and Takahira, H., 1986. A theoretical study on the interaction between two spherical bubbles and radiated pressure waves in liquid. Acustica, 61: 188–199.
Garipov, R. M., 1973. Closed equations for the motion of liquid containing bubbles (survey). Journal of Applied Mechanics and Technical Physics, 14(6): 737–756, DOI: https://doi.org/10.1007/BF00853186.
Huang, P. Z., and Chen, S. C., 1981. Study on spark source in marine seismic exploration. Oil Geophysical Prospecting, 5: 74–83, DOI: https://doi.org/10.13810/j.cnki.issn.1000-7210.1981.05.010 (in Chinese with English abstract).
Huang, Y. F., Yan, H., Wang, B. Z., Zhang, X. M., Liu, Z., and Yan, K. P., 2014. The electro-acoustic transition process of pulsed corona discharge in conductive water. Journal of Physics D: Applied Physics, 47(25): 255204, DOI: https://doi.org/10.1088/00223727/47/25/255204.
Jiang, Z. T., Han, R., and Li, S., 2015. Numerical study on non-spherical bubble dynamics in multiple-bubble interactions. Journal of Harbin Engineering University, 36(8): 1019–1023 (in Chinese with English abstract).
Liang, Z., Dai, Y. F., and Cheng, L. J., 1998. Dynamic equation of two spherical bubbles in multiphase flow. Journal of Hydrodynamics, 13(1): 28–34, DOI: https://doi.org/10.16076/j.cnki.cjhd.1998.01.005 (in Chinese with English abstract).
Loffe, A. I., and Naugol’nykh, K. A., 1968. Formation of shock waves by an electric discharge in water. Journal of Applied Mechanics and Technical Physics, 9(1): 96–100, DOI: https://doi.org/10.1007/BF00923476.
Lu, J. M., 1993. Principle of Seismic Exploration. Petroleum Industry Press, Beijing, 121–126 (in Chinese).
Lu, X. P., Pan, Y., and Liu, K. F., 2000. Radiation characteristics of plasma in a pulsed discharge in water. Journal of Huazhong University of Science and Technology, 28(12): 85–87, DOI: https://doi.org/10.13245/j.hust.2000.12.031 (in Chinese with English abstract).
Lu, X. P., Pan, Y., and Zhang, H. H., 2002a. A study on the characteristic of plasma and bubble break process of pulsed discharge in water. Acta Physica Sinica, 51(8): 1768–1772, DOI: https://doi.org/10.3321/j.issn:1000-3290.2002.08.021 (in Chinese with English abstract).
Lu, X. P., Pan, Y., Liu, K. F., Liu, M. H., and Zhang, H. H., 2002b. Spark model of pulsed discharge in water. Journal of Applied Physics, 91(1): 24–31, DOI: https://doi.org/10.1063/1.1420765 (in Chinese with English abstract).
Luo, D., and Cai, F., 2017. Numerical simulation for accuracy of velocity analysis in small-scale high-resolution marine multichannel seismic technology. Journal of Ocean University of China, 16(3): 370–382, DOI: https://doi.org/10.1007/s11802-017-3145-7.
Morioka, M., 1974. Theory of natural frequencies of two pulsating bubbles in infinite liquid. Journal of Nuclear Science and Technology, 11(12): 554–560, DOI: https://doi.org/10.1080/18811248.1974.9730710.
Müller-Michaelis, A., and Uenzelmann-Neben, G., 2015. Using seismic reflection data to reveal high-resolution structure and pathway of the upper Western Boundary Undercurrent core at Eirik drift. Marine Geophysical Research, 36(4): 343–353, DOI: https://doi.org/10.1007/s11001-015-9255-y.
Pei, Y. L., Wang, K. Y., Li, G. B., Li, S. X., and Liu, C. G., 2007. Application study of marine engineering seismic sources. Petroleum Instruments, 21(2): 20–23, DOI: https://doi.org/10.3969/j.issn.1004-9134.2007.02.008 (in Chinese with English abstract).
Plesset, M. S., and Prosperetti, A., 2003. Bubble dynamics and cavitation. Annual Review of Fluid Mechanics, 9(1): 145–185, DOI: https://doi.org/10.1146/annurev.fl.09.010177.001045.
Pu, Z. Q., Zhang, W., Shi, K. R., Zhang, J. H., and Wu, Y. L., 2005. Modeling of double cavitation collapse and cavitation noise. Journal of Tsinghua University, 15(11): 1450–1452, DOI: https://doi.org/10.3321/j.issn:1000-0054.2005.11.003 (in Chinese with English abstract).
Ramana, M. V., Goli, A., Desa, M., Ramprasad, T., and Pawan, D., 2014. Synthesis of deep multichannel seismic and high resolution sparker data: Implications for the geological environment of the Krishna-Godavari offshore, eastern continental margin of India. Marine and Petroleum Geology, 58(3): 339–355, DOI: https://doi.org/10.1016/j.marpetgeo.2014.08.006.
Rayleigh, L., 1917. On the pressure developed in a liquid during the collapse of spherical cavity. Philosophical Magazine, 34: 94–99, DOI: https://doi.org/10.1016/b978-0-08-006821-3.50028-3.
Shima, A., 1971. The natural frequencies of two spherical bubbles oscillating in water. Journal of Basic Engineering, 93: 426–431, DOI: https://doi.org/10.1115/1.3425268.
Ushakov, V. Y., Klimkin, V. F., and Korobeynikov, S. M., 2007. Impulse Breakdown in Liquids. Springer, Berlin Heidelberg, 109–132.
Xing, L., 2012. Study of the key technologies of high-precision marine multichannel seismic survey. PhD thesis. Ocean University of China.
Yan, D., Bian, D. C., and Que, M. H., 2014. Basic phenomenon analysis of high voltage discharge in water. Coal Technology, 33(7): 294–296, DOI: https://doi.org/10.13301/j.cnki.ct.2014.07.112 (in Chinese with English abstract).
Zel’dovich, Y. B., and Raizer, Y. P., 1967. Physics of Shock Waves and High Temperature Hydrodynamic Phenomena. Dover Publications Inc., New York, 1–896.
Zhang, J., Liu, H. S., Tong, S. Y., Wang, L. F., and Wang, R. M., 2009. A study on bubble effect mechanism and characteristics of high-frequency sparker source. International Forum on Information Technology and Applications. Chengdu, 287–290, DOI: https://doi.org/10.1109/IFITA.2009.330.
Zhu, B. K., 1985. Effects of sea surface reflection on frequency spectrum of the sparker source and the way to remove them. Donghai Marine Science, 3(1): 17–23 (in Chinese with English abstract).
Ziolkowski, A., 1970. A method for calculating the output pressure waveform from an air gun. Geophysical Journal of the Royal Astronomical Society, 21(2): 137–161.
Acknowledgements
The indoor test data and technical support were provided by Drs. Y. F. Huang (Shenzhen Institutes of Advanced Technology) and L. C. Zhang (Zhejiang University). This study was supported by the Geological Survey of China (No. DD20191003), and the National Key Research and Development Plan (No. 2016YFC0303901).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wei, J., Yang, H., Feng, J. et al. Simulation of Spark Source Wavelet Under Multibubble Motion. J. Ocean Univ. China 20, 67–74 (2021). https://doi.org/10.1007/s11802-021-4303-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11802-021-4303-5