各向异性双相介质中多极源声波测井理论研究

将各向异性地层模拟为横向各向同性双相介质 ,使其对称主轴与井孔中心轴线相垂直 .本文针对井孔模型下的多极源声波测井问题提出了一种解析的摄动方法 .将各向异性双相介质看作是由对应的各向同性双相介质加上摄动部分而组成 ,并引入 5个关于弹性模量偏离各向同性时的摄动量 ,对对称主轴与井轴垂直的各向异性双相介质的多极源声波测井问题进行了系统的理论研究和分析 ,严格求解了井孔内外的零级和一级近似声波场 .发现在n级多极源激发下 ,井孔中不仅出现n级多极声场 ,而且还能激发出与各向同性地层时不相同的高于和低于n级的多极声波场

Theoretical Study of Multipole Acoustic Logging in Anisotropic Two-phase Medium Formation

Anisotropic formation is modeled as a transversely isotropic two phase medium with the symmetric principal axis perpendicular to the borehole axis. An effective analytical perturbation method is presented and applied to multipole acoustic logging in this formation borehole model. The anisotropic formation is regarded as the perturbations added to the relevant isotropic two phase medium. Five perturbation quantities about moduli deviated from the isotropic formation are introduced. The acoustic multipole logging in anisotropy is theoretically studied and analyzed. The zero and first order perturbation solutions of the multipole acoustic fields inside and outside the borehole are derived. It is found that not only the n th multipole acoustic field can be excited by the n th multipole source, but the multipole fields whose orders are higher and lower that n can also be excited in such a formation borehole system.