Modeling of borehole radar for well logging using pseudo-spectral time domain algorithm

Abstract

In this article, numerical modeling of borehole radar for well logging in time domain is developed using pseudo-spectral time domain algorithm in axisymmetric cylindrical coordinate for proximate true formation model. The conductivity and relative permittivity logging curves are obtained from the data of borehole radar for well logging. Since the relative permittivity logging curve is not affected by salinity of formation water, borehole radar for well logging has obvious advantages as compared with conventional electrical logging. The borehole radar for well logging is a one-transmitter and two-receiver logging tool. The conductivity and relative permittivity logging curves are obtained successfully by measuring the amplitude radio and the time difference of pulse waveform from two receivers. The calculated conductivity and relative permittivity logging curves are close to the true value of surrounding formation, which tests the usability and reliability of borehole radar for well logging. The numerical modeling of borehole radar for well logging laid the important foundation for researching its logging tool.

Keywords

borehole radar / well logging / pseudo-spectral time domain algorithm / conductivity / permittivity

References

[1] Bentley L. R., Trenholm N. M.. The Accurate of Water Table Elevation Estimates Determined from Ground Penetrating Radar Data. Journal of Environmental and Engineering Geophysics, 2002, 7: 37-53.

[2] Bourgeois J. M., Smith G. S.. A Fully Three-Dimensional Simulation of Ground-Penetrating Radar: FDTD Theory Compared with Experiment. IEEE Trans. Geosci. Remote Sensing, 1996, 34: 36-44.

[3] Chen H. W.. Staggered-Grid Pseudo-spectral Acoustic Wave Field Simulation in Two-Dimensional Media. J. Acoust. Soc. Am., 1996, 100: 120-131.

[4] Chen Y. C.. Finite-Difference Time-Domain Algorithm for Solving Maxwell’s Equations in Rotationally Symmetric Geometries. IEEE Trans. Microwave Theory Tech., 1996, 44: 832-839.

[5] Chen Y. H., Oristaglio M. L.. A Modeling Study of Borehole Radar for Oil-Field Applications. Geophysics, 2002, 67: 1486-1494.

[6] Fornberg B.. The Pseudo-spectral Method—Comparisons with Finite Difference for the Elastic Wave Equation. Geophysics, 1997, 52: 483-501.

[7] Greaves R. J., Lesmes D. P., Lee J. M., . Velocity Variations and Water Content Estimated from Multi-offset Ground-Penetrating Radar. Geophysics, 1996, 61: 683-695.

[8] Lin S. H., Zhao L. Y.. High Precision Time Domain Forward Modeling for Crosshole Electromagnetic Tomography. Journal of China University of Geosciences, 2007, 18(4): 320-325.

[9] Liu Q. H.. The PSTD Algorithm: A Time-Domain Method Requiring Only Two Cells per Wavelength. Microwave Opt. Technol. Lett., 1997, 15(2): 158-165.

[10] Liu Q. H.. Large-Scale Simulations of Electromagnetic and Acoustic Measurements Using the Pseudospectral Time-Domain Algorithm. IEEE Transaction on Geoscience and Remote Sensing, 1999, 37(2): 917-926.

[11] Liu Q. H., He J.. An Efficient PSTD Algorithm for Cylindrical Coordinates. IEEE Trans., Antennas Propagat, 2001, 49: 1349-1351.

[12] Reshef M., Kosloff D., Edwards M., . Three-Dimensional Acoustic Modeling by the Fourier Method. Geophysics, 1988, 53: 1175-1183.

[13] Sanada Y.. The Study of High Precision Modeling and Imaging of the Ground Penetration Radar (GPR) [Dissertation], 2000, Kyoto: Kyoto University

[14] Taflove A., Hagness S. C.. Computational Electrodynamics: The Finite Difference Time Domain Method, 2000 2 Boston, London: Artech House 67-107.

[15] The Writer Group on the Borehole Electromagnetic Wave Method The Borehole Electromagnetic Wave Method, 1982, Beijing: Geological Publishing House

[16] The Writer Group on the Well Logging The Well Logging, 2004, Beijing: Petroleum Industry Press

[17] Uno, T., 1998. Analysis of Electromagnetic Field and Antenna Using FDTD Method. Korona, Japan

[18] Wang T., Tripp A. C.. FDTD Simulation of EM Wave Propagation in 3-D Media. Geophysics, 1996, 61: 110-120.

[19] Witte D. C., Richards P. G.. The Pseudo-spectral Method for Simulating Wave Propagating. Computational Acoustics, 1990, 3: 1-18.