Analytical And Numerical Simulation Of Wavefields In Borehole Acoustic Reflection Survey

In recent years,the sonic logging technique has been develpoed a lot with the increasing demand in the oil and gas resvior exploration and production.The detection distance of the convetional sonic logging technique is small(e.g.,the distance of 10 k Hz monopole logging is about 1 m from the borehole),while borehole acoustic reflection survey(BARS)technique can obtain the geological structures of more than ten meters or even tens of meters away from the borehole.When compared with the seismic exploration,BARS has the higher resolution,and is a frontier reseach area in the field of geophysics exploration.Due to the complexity of the BARS structure,simulating the wave propagation is a challenge The forward modelling and simulation is of great signaficane for studying the wave propagation and the instrucment development.The thesis focuses on BARS,studying the efficient algorithm to simulate the wavefields in the complicated formation,analyzing the characteristic of waves induced by the formation interface,the three-dimensional objects,and the fractures.For the formation interface outside the borehole,we first use the steepest descent integration method to calculate the radiated waves in the formation.Then,the reflected waves from the interface are replaced with the radiated waves generated by the virtual forces.Finally,based on the reciprocity relation,we derive the analytical solutions of the wavefields generated by the reflected wavefields.We validate the accuracy of the analytical solutions by comaparing with the 3D finite-difference time-domain results.Compared with the numerical method,the analytical method significantly enhances the computation effeciency.Based on the analytical solutions of the reflected waves,to solve the problem of azimuth ambiguity of dipole BARS,We analyze the characteristics of the reflcted pressure and displacement waveforms.Based on the wavefield property,we propose a method recording pressure and displacements simultaneously to uniqu ely determine the azimuth angle of the interface outside borehole.When the logging tool is eccentric,we derive the analytical solutions of the reflected waves and analyze the effects of the source frequency and eccentric distance on the wavefields.It is found that the source frequency is the dominant factor influencing the radiated wavefields.When the frequency is below 300 Hz,the eccentric source generates the radiated waves independent on the eccentric distance.When the source frequency is larger than 3000 Hz,the amplitudes of the high-order wave components increase with the eccentric distance.We study the azimuth-dependent characteristics of the reflected waves.It found that magnitude of the P/S waves is sensitive to the azimuth angle and the sensitivity is independent on the distance of reflector.We propose a BARS system with both eccentric source and receiver to determine the azimuth angle of the geological interface,giving certain theoretical guideline for the development of sonic logging ins trument.We derive the analytical solutions of the wavefields inside borehole due to the converted waves(P-SV/SV-P)from the interface outside borehole.Prior theoretical research ignores the converted waves from the interface,leading to the difference between the analytical solutions and the 3D finite difference method results.We study the effects of the source type,receiver-source offset,tilted angle,and the source-reflector distance on the converted wave amplitudes.The contribution of converted waves to the full waveforms is analyzed.The results show that with the increasing of the distance ratio(the ratio of reflector distance to the source-receiver offset),the ratio of the converted waves amplitudes to the reflected P-P wave amplitudes first increases and then decreases.When the distance ratio is smaller than 4,it necessary to consider the contribution of converted waves.However,when the distance ratio is larger than 10,the converted waves is so small that can be ignored.In addition,the numerical example shows that the amplitudes of converted waves are sensitive to the tilt angle of the interface.The converted waves amplitudes increase with the tilt angle,demonstrating that the converted waves can be used to inverse the tilt angle.For the far-field objects outside the borehole,we propose a hybrid method combining analytical solutions and finite-difference time-domain method.the borehole radiated waves are implemented into the region involved the object.Inside the regional domain,we use finite-difference time-domain method to obtain the scattered wavefields due to the object.Based on the reciprocity equations in terms of surface integral,we transform the scattered waves into the wavefields inside borehole.We apply this algorithm to simulate the wavefields due to a single object outside the borehole.The simulated results agree well with the solutions by the whole domain finite-difference method,illustrating the accuracy of the method.The proposed algorithm only needs regional finite difference model including the objects and avoid the whole domain simulation,leading to considerable reduction of computational costs.The numerical example demonstrates the method can accurately and efficiently simulate the large-scale and double-scale wave propagation in BARS.To modelling the scattered waves due to the fractured media,w e developed an efficient 3D time domain spectral method.The algorithm employs the general slip model to describe the fracture rather than meshing the fracture along the thickness direction directly,thus reducing the computational costs.The results from spectral element method show good agreement with the reference solutions of the thin-layer modelling,validating the accuracy of the method.We simulate the scattered wavefields due to the arbitrary finite-length,tilted and intersecting fractures.It is found the three components of scattered wavefields due to the anisotropy of the fractures are coupled,which is meaningful for the recognition and inversion of the anisotropy of the fracture.We apply the algorithm to simulate the borehole acoustics in the fractured media and analyze the effects of various parameters(i.e.,the source type,the fracture parameter,and the spatial interval)on the acoustic wavefields.It found that the wavefields of the dipole source are more sensitive to the fracture than those of monopole source.We recommend using dipole source in the logging to detecting the fractures.For the wave propagation in the porous medium,we propose a simple and non-convolutional perfectly matched layer(PML)technique and implement it into spectral element method to simulate wavefields in the 3D heterogenous porous media.Different form the conventional PML,the new PML preserves the original wave equations in the physical domain,thus can be flexibly incorporated into the existing numerical codes.We introduce the first-order ordinary differential equations to calculate the auxiliary variables inside the PML,thus avoiding the complicated temporary convolution and enhancing the computation efficiency.We apply the algorithm to simulate the wavefields in the isotropic,anisotropic,the elastic-poroelastic coupling and acoustic-poroelastic coupling media.The simulated results show good agreement with the analytical and reference numerical solutions,demonstrating the accuracy of the scheme,and the high efficiency of PML in absorbing in the reflected waves from the artificial boundary.Finally,the algorithm is applied to the borehole acoustics in layered porous medium,illustrating the capacity of the method for simulating wavefields in the compl ex structure.