Reciprocity Relations Of The Elastic Wavefields In Layered Elastic And Porous Media

Dynamic reciprocity relations reveal the link between the elastic wavefields of two states of a configuration. They are always used for solving geoscience problems, e.g., wave simulation and source inversion for natrual earthquakes, well logging, seismic exploration, and they can also be used for ultrasonic nondestructive testing in industry and medical science. Reciprocity relations for several types of point sources in elastic media have been given by former studies. However, reciprocity relations for point sources in porous media and fluid/solid configurations have not been fully investigated. This hinders applicating reciprocity relations in engineering. In this thesis, dynamic reciprocity relations for several kinds of point sources are derived in fluid/solid configurations and porous media. Numerical experiments are carried out to test the relations, and applications of the relations in wave simulation are discussed. Moment tensor is of great importance in seismology and related with reciprocity relations. However, it was derived for elastic media. The moment tensors of a dislocation in a porous medium are derived in this paper, and the wavefields generated by the moment tensors are calculated.Firstly, the equivalent body forces of a dipole and a quadrupole used in soni c well logging are derived. After that the reciprocity relations for several kinds of point sources in fluid/solid configurations are given, including single forces, explosions, double couples, dipoles and quadrupoles.A 3-D finite-difference time-domain(FDTD) algorithm is used to calculate the wavefields generated by sources located in and outside a fluid filled borehole. The reciprocity relations are tested by a set of numerical experiments implemented by the algorithm. Results of the numerical experiments show that reciprocal waveforms coincide for the situations that both the sources of the two states are located in the borehole fluid and that one of them is located in the formation.When the sources of the two states are located in the borehole fluid, it is shown by numerical experiments that the weak reflection waves from an interface in the formation also satisfies reciprocity relations. In particular, the gudied waves in the received signals can be effectively suppressed by using a monopole source and receiving the horizontal displacement on the borehole axis(or using a horizontal dipole and receiving the pressure on the borehole axis). This can improve the efficiency of extracting the weak reflection waves caused by the interface in the formation, and can guide the design of remote detection imager which is being developed.It is shown by example that reciprocity relations can be used to check numerical algorithms and the implementation of the sources but cannot be used to detect the improper discretization of interfaces. Some applications of the reciprocity relations on simplifying wave simulation are also discussed.Moment tensors of a dislocation in porous media are derived using Biot equations. It is found that a dislocation in a porous medium should be described by two independent moment tensors, which act on the bulk and the fluid phase, respectively. The bulk moment tensor has the conventional meaning of the moment tensor in elastic media, while the fluid moment tensor is a special one for p orous media. Both of the two are caused by the solid dislocation and the fluid injection through the fault towards the surrounding rocks. Both of the moment tensors are needed to describe an opening dislocation; for a shear dislocation, the fluid moment tensor is zero, and the shear dislocation is equivalent to a double couple acting on the bulk; for fluid injection, both of the moment tensors are isotropic and the ratio of their diagonal elements is dependent on medium parameters.The radiation displacement fields generated by the moment tensors in porous media are given. It is found that the fluid moment tensor only causes the compressional waves and does not cause the shear wave. By calculating the radiation fields when both the bulk and fluid moment tensors are unit tensors, it is found that the fluid moment tensor has notable influence only on the slow compressional wave. Therefore, the fluid moment tensor can be ignored when calculating the far field of the radiation wave in an infinite homogeneous poro us medium. However, it cannot be ignored when receivers are near from the source or when the fluid diffusion effect in a long time period is considered. Further, it is found by calculation that the fluid moment tensor will affect the far field when the source is very near an interface in an inhomogeneous medium. That is because the slow compressional wave generated by the fluid moment tensor is converted into the fast compressional wave and the shear wave at the interface. Considering the electrokinetic effect for porous media, it is found that the fluid moment has notable influence on the radiation EM wave.The reciprocity relations for several kinds of point sources in porous media are given, including bulk and fluid single forces, fluid injection, bulk an d fluid moment tensors and explosions. Those for fluid/porous-medium configarations are also obtained. The reciprocity relations are tested by 3-D FDTD numerical experiments in borehole models with porous formations. By the numerical test of the reciprocit y relation between a monopole in the borehole and explosions in the formation, it is shown that the reciprocity relation cannot be simplily replaced by that for elastic media.Based on Pride governing equations for seismoelectric wave propagation in porous media, the dynamic reciprocity relations for seismic sources, electric dipoles, and magnetic dipoles are obtained. The seismoelectric wavefields generated by a single force and a dipole in an infinite homogenous porous medium are simulated using the Green’s function method, and the reciprocity relation for the two sources is tested. It is found that the reciprocal waveforms will not coincide for the radiation EM waves if ignoring the fluid-solid relative displacement in the reciprocity relation. The reciprocity relation is then tested for the reflection seismoelectric wavefields in a horizontally layered model with a highly permeable middle layer, where the single force and electric dipole are located near the free surface. The results show that the reciprocal waveforms coincide even for the weak reflection waves. This indicates that measuring the electric fields generated by single forces is to some extent equivalent to measuring the displacement fields generated by electric dipoles in seismic exploration. After that, the reciprocity relations for an underground double couple, an electric dipole, and a magnetic dipole are tested in a similar layered model. At last, reciprocity relations of seismoelectric fields in fluid/porous-medium configurations are given. This work is of significance for wave simulation in seismoelectric logging, seismoelectric exploration, and studying coseismic EM fields in natural earthquakes.