Abstract
Numerical geometrical factors (GFs) are developed for array laterolog measurements in 1D cylindrically and planarly layered formations. The kernel of GFs assumes that laterolog responses can be expressed in terms of the linear superposition of formation resistivities at different units. Two techniques, namely physics-driven modeling and data-driven approximation, have been used to ensure the computational accuracy and efficiency of GFs. Physics-driven modeling uses a 3D finite-element algorithm to generate high-precision and fully labeled GF data and library. Subsequently, these predetermined data are trained offline using classical neural network algorithms to establish an implicit relationship between the formation parameters and GFs. The joint physics and data-driven GFs present three main advantages. First, they enable the direct representation of the spatial sensitivity of layered formations laterally and horizontally in vertical and horizontal wells. Second, GFs can be used to calculate the array laterolog responses rapidly. The computation speed can be enhanced thousands of times in comparison with traditional physic-driven modeling, allowing for real-time data processing. Another noteworthy aspect is that GF forward modeling can handle formations with arbitrary layers, thereby resolving the fixed-layer modeling issue inherent in traditional data-driven methods. Third, the GFs can be used to approximate the derivative of the logging response with respect to formation resistivity, significantly reducing the complexity of the Jacobian matrix calculation for deterministic inversion. These numerical GFs not only serve as an excellent alternative simulator for the array laterolog but will also be helpful to accelerate the modeling and inversion of other logging measurements in layered structures.
Paper Information:
Lei Wang, Yueyang Han, Zhiqiang Li*, Donghan Hao and Shaogui Deng, 2025, The Joint Physics and Data Driven Geometrical Factor of Array Laterolog in Layered Formations. Geophysics, https://library.seg.org/doi/full/10.1190/geo2024-0112.1
