This thesis focuses on statistical approaches to mainly single-well acoustic imaging data for (1) analyzing characteristics of these data and (2) denoising. Single-well acoustic imaging is a generic name to imply both data acquisition by hardware and data processing by software in order for delineating geological structural features or subsurface bedding boundaries in the vicinity of wellbores.

Chapter 1 is intended to introduce background of single-well acoustic imaging and notations. This includes introducing sonic logging tool and concepts of single-well acoustic imaging. Our target data domain is also defined. The importance of single-well acoustic imaging is explained in terms of a resolution gap that lies in between seismic method and borehole logs. Key oilfield related terminologies are described for self-completeness.

Chapter 2 attempts to study Principal Component Analysis (PCA) and its related techniques such as PCA on-line and local PCA. We studied these techniques on both synthetic and single-well acoustic data to observe functional features. Specifically we use local PCA for migrated images from single-well acoustic data and found that crisscross like patterns or annoying noises on the migrated images are effectively eliminated.

The core methodology of this thesis, local likelihood regression, appears in Chapter 3. We intend to (1) formulate our model and estimation methods; and to (2) present their applicability to single-well acoustic data. Therefore, we first formulate the local regression model, whose predictor variable is a scalar and response variables have a vector shape, in the 2-d (space, time) domain. An optimal parameter selection is also dealt. In our model we consider polynomial models up to the cubic order. In order to measure the performance of model fitting we introduce the leave-one-out cross validation (CV) criteria. Then we apply our local regression model to the real data and present estimate results. The use of CV is attempted to identify an optimal parameter, which defines a degree of locality in the selected model. This single bandwidth selection is then extended to multiple bandwidth selection that takes into account the variant locality over the time domain. Our results demonstrate that the applied method successfully achieved: (1) identification of continuous reflectors, and (2) suppression of random noise in the data processed.

In Chapter 4 local approaches are attempted in another geophysical analysis domain. It is spatial interpolation named kriging. Both local constant and local linear regressions are considered between a scalar predictor variable and scalar response variable. This Chapter concentrates on the semi-variogram cloud from the porosity data with local regression approaches. This cloud indicates the dissimilarities against the spatial separation of sample pairs and is important when determining a sequence of average dissimilarities over the lateral direction. Normally this sequence is fitted with a theoretical curve, however this process may be practically difficult because a wrong model selection falls away from key features embraced by the original data. This local regression approach facilitates easy computation for forming an appropriate sequence of average dissimilarities with no worry about selecting an optimal model from theoretical models such as exponential, Gaussian, spherical and so on. We have demonstrated that the local regression approach produces reasonable kriged maps under an optimal locality and regression model.

Lastly conclusive remarks are stated in Conclusion. Single-well acoustic imaging is still emerging technology. On this technically new field what we have contributed can be re-phrased as follows:

・ Local analysis of PCA is found to be effective for removing crisscross like patterns on migrated images from single-well acoustic imaging.

・ Local regression approach is introduced on the single-well acoustic data mainly for denoising.

・ The vector-valued response variable is considered for a scalar predictor in the local regression approach.

・ Visualization of local regression results is made.

・ The bandwidth selection is made along the depth axis.

・ The cross validation is used for selecting an optimal bandwidth.

・ Multiple bandwidth selection is proposed by additionally taking account for the time axis.

Generated Matlab codes are listed in this thesis., application/pdf, 総研大甲第854号}, title = {Principal Component Analysis and Local Regression Analysis on Acoustic Logging Data}, year = {} }