Becoming Certain About Deterministic Inversion Uncertainty

Logging-While-Drilling (LWD) tools have shown that electromagnetic (EM) measurements can be used to determine the subsurface’sunknown electrical properties away from the trajectory of horizontally drilled wells. Modern LWD technologies can produce a model of the formation's electrical resistivity to depths of investigation (DOI) in excess of 150ft radially (Seydoux et al., 2014, Yankai, et al., 2018), in real-time. In LWD applications, measurements of the different components of the magnetic field, excited by multiple loop antennas, are performed at various measured depths (MD) along the logging bottom hole assembly (BHA), at multiple frequencies of excitation. The magnetic-field components are then converted to deep and ultra-deep azimuthal resistivity measurements (DAR and UDAR respectively), which are used to estimate the resistivity distribution of the formation surrounding the wellbore via inversion. The resulting resistivity maps are interpreted to geological models and provide end-users with geosteering insights in real-time, or after drilling has been completed. The model is also used to estimate structural settings, productivity expectations, to evaluate fluid reserves or to plan additional wells. Resistivity models are determined through different inversion methods (Tarantola, 1987, Meju, 2009), approximating the EM solution describing the acquired data. Accordingly, the development of more advanced inversion algorithms to determine resistivity models from LWD measurements while drilling, has received considerable attention (e.g., Li et al., 2005; Yankai et al., 2018; Thiel et al., 2018). These algorithms, which initially were developed to approximate a 1D local solution, first illustrated by Li et al., (2005) and have been increasing their dimensionality, to aid in the fitting of more complex data, recently moving to 2D solutions (Thiel, et al., 2016, 2018) and 3D (Omar et al., 2024).