Simulation Of Acoustic Fields In Borehole Excited By An Off Centered Multipole Source In Transversely Isotropic Formation

In transonic seismic exploration,especially in multipole acoustic logging,transversely isotropic media is the most important and most common anisotropic model.Many sedimentary rocks exhibit transversely isotropic properties of this anisotropy.At present,the multipole acoustic logging instrument can emit monopole,dipole and quadrupole mode sound waves,and four sets of unipolar pressure array receivers are used to receive the combined acoustic signals to obtain the monopole,dipole and quadrupole waveform.In the actual operation of logging,it is inevitable that the logging instrument deviated from the borehole center.In order to correct the influence of the eccentricity of the multipole acoustic logging tool,this paper studies the eccentric multipole source in the transversely isotropic formation.There is an analytical solution in the transverse isotropic stratum(VTI)parallel to the well axis.Based on the theoretical derivation of the eccentric point source,the eccentric point source field in the transversely isotropic strata is obtained,and the eccentric multipole source is regarded as the superposition of the eccentric point source.We use MATLAB programming software to simulate the eccentric multipole tool in the well model.The acoustic potential function is obtained in the frequency domain and the wave number domain,and the acoustic field at the arbitrary position of the well excited by the eccentric multipole source is calculated by the real axis integral method.For the dipole source to study the three directions of eccentricity,respectively,clockwise eccentric 0 °,eccentric 45 °,eccentric 90 °.For the quadrupole source,the eccentricity of the two directions is studied,which are clockwise eccentric0 ° and eccentricity 45 °,respectively.The eccentric point source excitation of the sound field is equivalent to the n-order multi-pole source field superposition.Through the study of this paper,we findthat the eccentric dipole source and the eccentric quadrupole source are also true.The center of the dipole source can only stimulate the bending wave of this mode(ignoring the high order mode),while the eccentric dipole source excites the non-dipole mode;The center of the quadrupole source can only stimulate the spiral wave of this model,and eccentric quadrupole source excites the non-quadrupole mode.Except that the orthogonal eccentricity and the central situation are similar,In general,by combining the signals of several different azimuth receivers,the interference of the other modes can be greatly filtered out.So that the bending wave of the dipole and the helical wave energy of the quadrupole can be accurately received,and then the shear wave velocity is obtained.However,in the receiver of a single azimuth,a distinct non dipole mode and non quadrupole mode can be received.Then,extract the stoneley wave and the other modes from the non-dipole,non-quadrupole modes,the amplitude of these modes change with the eccentric position.Comparing the off centered multipole source and the center multipole source,the waveform formed by multi-directional reception and combination shows that the influence of eccentricity is very small.The research results in this paper can provide theoretical basis for the eccentricity of multipole acoustic logging in borehole in transversely isotropic formation.