Theoretical And Numerical Study Of Borehole Acoustic Field Excited By External Acoustic Sources In The Biot Solid

Acoustic logging is a variety of specific acoustic technology logging collectively. The theoretical foundation is the elastic Wave's excitation and propagation in the columnar layered medium. Theoretically studies the rule of acoustic excitation, propagation and reception in the borehole. The acoustic logging theory's main content researches the interaction of the elastic wave and the borehole entrance from different angle, so we should not only consider the different type of acoustic source, but also consider the type of stratum medium and the borehole system's geometry structure and so on in theoretical research. This work is also the main subject in the theoretical studies of acoustic logging.For many years , acoustic logging get a rapid development. Conventional acoustic logging put acoustic sources and detectors in the same borehole, but acoustic logging is not very good on stratum far from the hole. Although seismic on the ground can detect large range, but it has not high precision on stratum. Cross well is one of methods that can remedy the lack of acoustic logging and seismic. It put up a bridge between acoustic logging and seismic. Measuring the stratum across the borehole and reservoir specificity can remedy the lack of cross detectability in the borehole. It also can settle many questions such as the unbalance of gathering the information type and the information abundance between the borehole and the cross well.So we should 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 and further studies on the rule of sound wave in cross well seismic are necessary. We should research the dielectric feature out the borehole and the effect stratum interface to the full wave field and the partial wave field in the borehole. This work can make the mode perfect and help us comprehend the actual measuring method and the results. My subject launches based on such goal.In this paper I discuss apart three models in the Biot solid these excited by an external explosive point source of cross well, the model of external single point force source, the model of explosive point source located at axis in two wells through theoretical analysis and numerical simulation. Actually all these models belong to the model of cross well seismic.In the model that excited by an external explosive point source of cross well, the theoretical expressions were solved in and out borehole about all of frequency. The direct field only have longitudinal wave. According to the theoretical expressions, I found that the acoustic field in borehole excited by an external explosive point source is quite to the summation of acoustic field excited by infinite orders multipole sources located at the axis of borehole. This article puts up the numerical simulation and frequency wave-number analysis of full wave to acoustic sound field in the borehole which selects different center frequency, different radial spacing and different stratum. The stimulation shows that we must take into account more order of multipole term with increasing of center frequency, different stratum, receive distance offset the axis of borehole and degree of eccentricity. At the same time, Results of numerical analysis showed that the amplitude of Stoneley excited by the borehole will increase when reduce the center frequency in the same distance and stratum. The rule is uniform as acoustic logging. The amplitude of Stoneley wave excited in the borehole and other waves will be reduced even disappeared with the increasing of the distance. It will only left the longitudinal wave because the effect between the spherical wave excited by an external explosive point source of cross well and the borehole become lower with the increasing of the distance. The amplitude of Stoneley wave is larger in hard stratum than in soft stratum in the same distance and center frequency.The model of external explosive point source of cross well can only measure the speed of longitudinal wave. It can't reflect all the stratum information accurately. This paper has simulated the model of external single point force source about this lack. The direct field is not only has longitudinal wave but also has SV wave in this model of external single point force source. It can receive longitudinal wave, transverse wave and all kinds of mode waves. We solve the theoretical expressions in and out borehole about all of frequency. The acoustic field in borehole excited by an external explosive point source is quite to the summation of acoustic field excited by infinite orders multipole sources located at the axis of borehole. Results of numerical analysis showed that the effect by different center frequency, different stratum and receive distance offset the axis of borehole in model of external single point force source is very resemble to the model of external explosive point source. It can receive longitudinal wave, transverse wave and all kinds of mode waves. We can acquire details about configuration. We can receive critical refractive longitudinal wave and receive critical refractive longitudinal wave in soft and hard stratum. The amplitude of transition critical longitudinal wave main associated with center frequency of sound source, stratum parameter, incident transversal wave's strength. At the same time, I also considered the influence to full wave about some pore parameter and the position angle. The results show that porosity and the rate of permeation widely impact Stoneley wave and dipole flexural wave. In numerical simulation of frequency-wave number, it obviously shows that the comparation of phase velocity about the model wave's of unipolar field, dipole field and four-pole field and dispersive situation. Through numerical simulation and analysis, we should comprehend the feature of seismic wave field in the pore stratum borehole. It is advantageous to realize and separate the seismic field in the borehole and receive the seismic field spread along well direction. That can help us obtain the details of reservoir and the stratum structure.At last, we studied the model of explosive point source located at axis in two wells in theory. Its direct field has longitudinal wave and SV wave. At the same time, Critical refractive longitudinal wave , Critical refractive longitudinal wave and all kinds of mode waves are received in the other well. Acoustic field has become comparatively infirmness once transmission and scattering. So we only calculate one time scattering. We solve the theoretical expressions in and out borehole about all of frequency. Acoustic field had been simulated and analyzed. Numerical value showed that the result of full wave is alike to external single point force. But because the distance between two wells is several-ten meters to several-hundred meters, A lot of seismic waves are excitated. It make me obtain abundant information of acoustic field. It is avail to identify and analyze different waves in full wave field.In this paper, I discuss the different models of cross well seismic in the Biot solid, Its theoretical study and numerical simulation to full wave field's identifying and separation, to explaintion of cross well seismic's data has much reference. It also make us have more comprehender and understanding in cross well seismic's field.