Electromagnetic propagation logging has been primarily used to measure formation resistivity. A sensitivity study shows that the formation dielectric constant becomes detectable when it is larger than 10 for the typical LWD 2 MHz propagation measurements. At this frequency, in some field cases, the dielectric constant can be tens to hundreds, making it measurable directly from propagation data. Factors causing this high dielectric constant include connate water volume, the interfacial polarization due to clays, and the Maxwell-Wagner effect as a result of coexistence of conducting and insulating materials. Current methods for determining dielectric constant are based on a homogeneous assumption for the formation regardless of its actual complexity. These methods give reasonable results in thick beds (larger than 10 ft) and low-resistivity-contrast (less than 5) formations. In thinner beds with larger resistivity contrast, both resistivity and dielectric constant logs can be adversely affected by the strong shoulder bed effect. The dip effect in dipping formations can only exacerbate the situation. Like resistivity, dielectric constant can also be anisotropic, but the anisotropy will be ignored here. These effects must be corrected to mitigate undesirable results in the quantitative use of resistivity and dielectric constant logs. The goal of this paper is to address this problem by incorporating the layered structure in the formation model to correct for the shoulder bed and dip effects on resistivity and dielectric constant logs. To account for these effects, we first take advantage of our previous work (Wang et al., 2019) on induction dielectric processing for its fast convergence, robustness to data noise, and weak dependence on initial formation model. The regularization popular for feature selection problems in supervised learning is then added to the existing method. An attractive feature of this regularization is its unique noise-suppression capability while being able to preserve bed boundaries on resistivity and dielectric constant logs. Numerical experiments with synthetic data demonstrate the clear benefits of the new processing in comparison to current methods that have been popular for dielectric constant processing. Field testing also confirms that this data processing is superior to the current methods as far as dip and shoulder bed effects are concerned. Both synthetic and field results indicate that this advanced data processing should be run preferentially as long as the relative dip is not extremely high (less than 70 deg). Some questions with practical importance are addressed in detail that provides insight into the characteristics and performance of the processing. These questions include the effects of data noise, inaccurate dip input, and drilling fluid invasion. In addition, the depth of investigation and vertical resolution are studied for resistivity and dielectric constant to enable a quantitative comparison with other logs. The limitations of the processing and guidelines are also discussed before field applications.
Improved Deep Learning Model Based on Self-Paced Learning for Multiscale Short-Term Electricity Load Forecasting
