By adopting the method of controlling parameters this paper describes the construction of various kinds of cubic curve segment and curved surface fragment with rational and non rational parameters, and discusses the ...By adopting the method of controlling parameters this paper describes the construction of various kinds of cubic curve segment and curved surface fragment with rational and non rational parameters, and discusses the relationship between controlling parameters, weighted factors and types, kinds and characteristics of curve segments and curved surface fragments. A mathematical method is provided for CAGD with abundant connotations, broad covering region, convenience, flexibility and direct simplicity.展开更多
A wideband dipole signal is required for dipole dispersion correction and nearborehole imaging. To obtain the broadband flexural wave dispersion, we use a nonlinear frequency modulation （NLFM） signal and propose a s...A wideband dipole signal is required for dipole dispersion correction and nearborehole imaging. To obtain the broadband flexural wave dispersion, we use a nonlinear frequency modulation （NLFM） signal and propose a segment linear frequency modulation （SLFM） signal as the dipole excitation signal to compensate for the excitation intensity. The signal-to-noise ratio （SNR） of the signal over the entire frequency band is increased. The finite-difference method is used to simulate the responses from a Ricker wavelet, a linear frequency modulation （LFM） signal, an NLFM signal, and an SLFM signal in two borehole models of a homogeneously hard formation and a radially stratified formation. The dispersion and radial tomography results at low SNR of the sound source signals are compared. Numerical modeling suggests that the energy of the flexural waves excited by the Ricker wavelet source is concentrated near the Airy phase. In this case, the dispersion is incomplete and information regarding the formation near or far from the borehole cannot be obtained. The LFM signal yields dispersion information near the Airy phase and the high-frequency range but not in the low-frequency range. Moreover, the information regarding the formation far from the borehole is not accurate. The NLFM signal extends the frequency range of the flexural waves by compensating for the excitation intensity and yields information regarding the formation information, but it is not easy to obtain. The SLFM signal yields the same results as the NLFM signal and is easier to implement. Consequently, the dipole detection range expands and the S-wave velocity calculation accuracy improves.展开更多
文摘By adopting the method of controlling parameters this paper describes the construction of various kinds of cubic curve segment and curved surface fragment with rational and non rational parameters, and discusses the relationship between controlling parameters, weighted factors and types, kinds and characteristics of curve segments and curved surface fragments. A mathematical method is provided for CAGD with abundant connotations, broad covering region, convenience, flexibility and direct simplicity.
基金This work was supported by the National Natural Science Foundation of China （Nos. 11574347, 11734017, 91630308, and 11374322）, the Youth Talent Project of the Institute of Acoustics of Chinese Academy of Sciences （No. QNYC201619）, and the PetroChina Innovation Foundation （No. 2016D-5007-0304）.
文摘A wideband dipole signal is required for dipole dispersion correction and nearborehole imaging. To obtain the broadband flexural wave dispersion, we use a nonlinear frequency modulation （NLFM） signal and propose a segment linear frequency modulation （SLFM） signal as the dipole excitation signal to compensate for the excitation intensity. The signal-to-noise ratio （SNR） of the signal over the entire frequency band is increased. The finite-difference method is used to simulate the responses from a Ricker wavelet, a linear frequency modulation （LFM） signal, an NLFM signal, and an SLFM signal in two borehole models of a homogeneously hard formation and a radially stratified formation. The dispersion and radial tomography results at low SNR of the sound source signals are compared. Numerical modeling suggests that the energy of the flexural waves excited by the Ricker wavelet source is concentrated near the Airy phase. In this case, the dispersion is incomplete and information regarding the formation near or far from the borehole cannot be obtained. The LFM signal yields dispersion information near the Airy phase and the high-frequency range but not in the low-frequency range. Moreover, the information regarding the formation far from the borehole is not accurate. The NLFM signal extends the frequency range of the flexural waves by compensating for the excitation intensity and yields information regarding the formation information, but it is not easy to obtain. The SLFM signal yields the same results as the NLFM signal and is easier to implement. Consequently, the dipole detection range expands and the S-wave velocity calculation accuracy improves.
