Theoretical And Numerical Study Of Borehole Coupling Of Oblique Incident Plane P-wave In The Biot Solid

Acoustic logging is a sort of very developed logging method which holds a widespread applied foreground in physical geography filed. A Acoustic logging has the same physics base with the seismic prospecting, it is a tie of combining the geophysical log with the seismic prospecting data. In twenty or thirty years, acoustic logging develops quickly, no matter what theory investigation and open country field working measure or the well logging data treatment application all have great development. However, recognizing of the well sound field is not enough, people can not use the already possess of acoustic wave data sufficiently. Wherefore, it necessitates further investigations of acoustic wave propagation rule in the hole, inspecting characteristic outside the hole and formation bounding surface influence on the full wave sound field and the partial wave sound field, building more perfect logging interpretation model . These are physics base of acoustic logging, these are also the research subject which geological prospecting scholar and petroleum developing scientific worker are interested in.As a matter of fact, ideal elastic formation not exists. Formation frequently belongs to multiphase mixture-small opening medium, belonging to mixture is on account for solid part (then rock frame) often being made up particles, which has different chemical characteristic and crystal characteristic, this kind of solid part always combining gas phase and liquid phase of holding loophole space among particles, so it belongs multiphase. Microinhomogeneities of the porous medium cause a complex macrophysics shape, the shape treats comparing sensitization of minimal change group of fluid content or solid constitution, porous medium acoustic of the porous medium combines strictness of mechanics rule with natural random of porous medium, besides attempting to describe its state characteristic.The theoretical study of cross well have two ways: one is base on the method of geometry optics or radial theory, the other one is base on the method of wave-equation. Radial theory can be applied when seismic wavelength great for the scale of anuniformity body. But radial theory can not applied when seismic wavelength close to the scale of anunfoumity body. Because diffraction and scattering rise leading action in this time. We must apply the method of wave-equation. We must establish physics model base on the fact circs on cross well seismic. Resolving and computing acoustic field radiation, propagation and effect between boreholes from strict wave-equation are the foundation of comprehend and explain for the method of measure.This article consider a comparison simple model, incident wave outside the hole is plane P-wave case. An exact parsed expression of the coupling of an external oblique plane P-wave to a fluid-filled in Biot saturation porous solid is present. Discussing angle of incidence is 90 degree, sound field of the pressure in a hole is analyzed theoretically and numerically, the theory is compared with literature to testify the correctness of the theory. The mechanism of the resonance response of the pressure in a hole is analyzed numerically in different angles of incidence. In different angles of incidence, resonance hump of the pressure in a hole is not linearity variation, resonance hump of the pressure in a hole appear minimal value in angles of incidence between 30 and 40 degree. The changes of the pressure for off-axis are investigated in different angles of incidence. The frequency of signal is under 500Hz, the difference that the pressure in a hole ( ) and the sidewall ( ) of different points following frequency variation curve may neglect, the frequency of signal is over 1 kHz, they divided obviously. The frequency of signal is about 3 kHz, two pressure curve of polar angle and appear concurrent hump, but angles of incidence is less than 60 degree the concurrent hump vanish. The effect of the difference of permeability and porosity for the pressure in a hole are investigated emphatically. In low frequency region magnification of r=0r =bθ=00θ=1800 permeability leads to rise of the pressure in a hole, the frequency of signal is over 3 kHz that high frequency lead to falling of the pressure in a hole. In higher frequency of signal the difference of permeability only homologize identical pressure in a hole. The angle of incidence is 90 degrees, no matter what is low and high frequency, the pressure in a hole even drives to stable value in high or low permeability, the limit of low permeability is corresponded to the case of elastic solid. At the variation angles of incidence, the width of different permeability curve also generates variation. In low frequency region magnification of porosity leads to falling of the pressure in a hole, the frequency of signal is over 3 kHz that high frequency lead to rise of the pressure in a hole. In higher frequency of signal the difference of porosity only homologize identical pressure in a hole. No matter what is low and high frequency, the pressure in a hole even not drive to stable value. The angle of incidence is 90 degree, at the magnification of the pressure in a hole reduce in size. The angle of incidence is 60 and 15 degree, in low frequency region magnification of porosity leads to falling of the pressure in a hole, in high frequency region magnification of porosity leads to magnification of the pressure in a hole. The magnification of porosity leads to falling of the pressure outside a hole. The angle of incidence is only 60 degree, the magnification of porosity leads to falling of the pressure outside a hole and magnification again. The results show that the well hole has a significant effect on the pressure measured in the hole over the complete frequency range. The different angles of incidence have effect on resonance hump of the pressure in a hole. When the frequency of the seismic signal measured is over 500Hz, the effect of the off-axis measurement and the difference azimuth must be considered. The effect of permeability and porosity dimension must be considered obviously. It made us recognized more deep recognition of porous solid formation.Total teachings, through assuming the different angles of incidence carry on calculation and analogue. Body work is research work that nobody do hitherto, have definite innovation. Its result have definite reference value on identify and separation of the wave field in Biot solid and explanation of seismic exploration data between two holes.