| Both acoustic sources and detectors are put in the same borehole in routineacoustic logging. The main frequent of acoustic sources are commonlycomparatively high. It has high precision and particularity depict on stratumnear the hole. But acoustic logging is not very good on stratum far from the hole.This is a obvious lack of acoustic logging. Seismic on the ground can detect largerange. But it has low Signal-Noise, and can not particularity depict on stratum.Cross well is one of method remedy the lack of acoustic logging and seismic. Itput up a bridge between acoustic logging and seismic. Cross well can acquirehigh precision seismic signal. It can incept direct waves, reflect waves, diffractwaves, scattering waves, guide waves, canal waves and all kinds of conversionwaves. Acoustic fields have abundant information. So we can obtain much moreinformation on stratum. The application of cross well technology is increasingin recently years.The theoretical study of cross well have two ways: one is base on themethod of geometry optics or radial theory, the other one is base on the methodof wave-equation. Radial theory can be applied when seismic wavelength greatfor the scale of anuniformity body. But radial theory can not applied whenseismic wavelength close to the scale of anunfoumity body. Because diffractionand scattering rise leading action in this time. We must apply the method ofwave-equation.We must establish physics model base on the fact circs on cross well seismic.Resolving and computing acoustic field radiation, propagation and effectbetween boreholes from strict wave-equation are the foundation of comprehendand explain for the method of measure.This text advise a simple model that excited by an external explosive pointsource of cross well in the first part. The direct field only have longitudinalwave. The theoretical expressions were solved in and out borehole about all offrequency. We also study the full wave and the response of frequency-wavenumber. The acoustic field in borehole excited by an external explosive pointsource is quite to the summation of acoustic field excited by infinite ordersmultipole sources located at the axis of borehole. For a certain center frequency,summation of definite order of multipole field may offer the approximate wavefield that satisfied the need of precision. We must take into account more orderof multipole term with increasing of center frequency, speed of stratum, receivedistance offset the axis of borehole and degree of eccentricity. Results ofnumerical analysis showed that the amplitude of Stoneley will increase whenreduce the center frequency in the same distance and stratum. This is the sameas acoustic logging. Stoneley wave excited in fast stratum is much more intensitythan in slow stratum at the same distance and center frequency. So it is thereason that we could receive intensity Stoneley wave, but we could not receiveStoneley wave sometimes.It is insufficient that we only measure the speed of longitudinal wave. It ismore important that we measure the velocity of transverse wave. This text hassimulated the model of external single point force source about this lack. Thedirect field is not only has longitudinal wave but also has SV wave in this modelof external single point force source. It can receive longitudinal wave, transversewave and all kinds of mode waves. It is also resemble to the model of cross well.So it has the great meaning for the model of cross well. We solve the theoreticalexpressions in and out borehole about all of frequency. The acoustic field inborehole excited by an external explosive point source is quite to the summationof acoustic field excited by infinite orders multipole sources located at the axisof borehole. Results of numerical analysis showed it is very resemble to themodel of external explosive point source. For example the select order ofacoustic field. But it has some particular characteristic of acoustic field inborehole. It can receive longitudinal wave, transverse wave and all kinds ofmode waves. We can acquire details about configuration. We can receive criticalrefractive longitudinal wave and receive critical refractive transverse wave insoft stratum. It is because that the speed of transverse wave in stratum less thanthe speed of water in borehole. The numerical results show that the chart offrequency and wave number when the source near the wall of well is same asthe chart in the borehole. But it has same drape near the formant oflongitudinal wave when the source far from the wall of well. We are nor veryclearly and have to more realize. Theory and numerical simulation have somemeanings to cross well in fact. Numerical simulation is in favor of cross wellseismic for us. It can minish the affect of Stoneley wave by us to selectappropriate frequency. The model of external explosive point source and singlepoint force source is not only help us to comprehend cross well, but also hasmeanings to comprehend nucleus explosive and shake in strtum.We had simulated the model of cross well base on wave-equation. Explosivepoint source located at axis. We solve the theoretical expressions in and outborehole about all of frequency. Acoustic field had been simulated. We onlycalculate one time scattering. Because acoustic field has become comparativelyinfirmness once transmission and scattering. Especially for large distance crosswell seismic. Numerical value showed that the result of full wave is alike toexternal single point force. There is not critical wave in soft stratum whencenter frequency is 2000Hz about external single point source. But there iscritical wave in the model of cross well seismic. I think it should be thattransverse wave intensity in the model of cross well seismic. It has manycomponent of acoustic field in cross well seismic. There may be has all kinds ofwaves. We should identify the style of wave in the chart of full wave. It is help usto further understand to cross well seismic by theoretical and numericalsimulation.
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