Borehole wave field modeling, reflection extraction and reverse time migration in acoustic reflection imaging logging

Junxiao Li

ABSTRACT

This thesis systematically examines, develops and refines the basic procedures of acoustic reflection imaging logging. The reflections derived from the energy that leaks away from the borehole and is reflected back to the receivers after interacting with the structures outside the borehole, can be extracted from the full waveforms recorded by the downhole receivers. A three-dimensional finite difference method based on the first order velocity and stress hyperbolic equations is then developed to simulate wave propagation in both isotropic and anisotropic media. A hybrid-perfectly matched layer absorbing boundary condition is proposed to mitigate the artificial reflections. Finally, the borehole reverse time migration is developed to image the near borehole structures.

The reflection extraction from the borehole full waveforms is not straightforward. Under acoustic well logging conditions, reflected wave signals used in sonic reflection logging are generally submerged in the full waveform records, hidden by the dominant direct waves (direct P- and Swaves, and the Stoneley wave). It is critical, therefore, to effectively extract the reflection signals from the acoustic full waveforms in acoustic reflection well logging data processing. The Karhunen-Lo`eve transformations combined with a band limiting filter is used to extract reflections of interest out of dominant direct waves. Under the assumption that large energy (squaredamplitude) differences exist between each wave component, the direct Stoneley wave, S-wave and the P-wave are eliminated sequentially by subtracting the most significant principle components, after which the remaining signal is seen to be dominated by reflected events. The extracted reflections can then be used in migration so as to get a clear image of the structures outside of the borehole.

During wavefield modeling, an issue faced by finite difference methods, which has particular importance in borehole applications, is the mitigation of artificial reflections from computational boundaries. This computational boundary artificial reflection problem has been a persistent topic in the literature of wave modelling, no complete solution has yet been found. To address this, a hybrid perfectly matched layer methodology is introduced and discussed in the context of standard perfectly matched layer, convolutional perfectly matched layer, and multiaxial perfectly matched layer methods, and their abilities relative to the suppression of artificial reflections are compared. The method is a hybrid in the sense of combining aspects of the convolutional perfectly matched layer and the multiaxial perfectly matched layer schemes.

The fact that waves can impinge on the borehole instrument from all azimuths is an important source of ambiguity. This azimuthal ambiguity has been an issue ever since the beginning of borehole acoustic reflection imaging. The data (which actually may be from every possible direction of underneath formations) is considered in standard imaging and processing to have come from one direction. The 4-component dipole acoustic well logging technique is designed to solve the azimuth ambiguity problem by analyzing the azimuthal information contained in the recorded shear wave signals. Thereafter, standard migration procedure can be applied to get the imaging result. In this thesis, the 3D reverse time migration in the borehole environment is proposed and applied in the simulated data set with a similar source and receiver system as sonic scanner tool developed by Schlumberger. The staggered-grid finite difference RTM performs perfectly in fluid-solid boundary with a source located in the fluid-filled borehole. The imaging result shows the directional information of the structures outside the borehole can be directly obtained.

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