Continuous Spatial Functions for Resistivity Inversion
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Solution Overview
Problem
Current well drilling operations face challenges in generating geologically realistic earth models due to over-fitting of data below noise levels and the absence of constraints, leading to unrealistic artefacts in resistivity inversion models.
Innovation Solution
The use of continuous spatial functions, such as splines and polynomial functions, to parameterize earth models, allowing for real-time computation of geological formation characteristics without the need for stitching discrete 1D models, reducing computational complexity and generating continuous images of formations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If point-by-point 1D inversion is used to generate resistivity models at each measurement point, then detailed formation characteristics can be obtained, but geologically unrealistic artefacts are introduced due to over-fitting and absence of constraints
Solution Approach 1:
The patent combines multiple discrete 1D inversion models into a single continuous 2D earth model by representing formation properties as continuous spatial functions. This merging process integrates information from multiple measurement points while enforcing geological continuity constraints, thereby reducing over-fitting artefacts and improving the reliability of the inversion results.
Solution Approach 2:
The patent transitions from one-dimensional point-by-point inversion models to a two-dimensional continuous earth model. By introducing the spatial dimension and representing formation properties as continuous functions across the survey area, the method constrains the inversion to produce geologically plausible results while maintaining measurement precision.
2Loss of information
If discrete 1D models are generated at each measurement point, then detailed local formation information is obtained, but computational complexity increases due to the need to stitch multiple models together
Solution Approach 1:
Instead of generating discrete 1D models at each measurement point and then stitching them together, the patent inverts the approach by directly computing a continuous 2D earth model from all measurement data simultaneously. This eliminates the stitching process and reduces algorithmic complexity while preserving local formation information through the continuous spatial representation.
3Productivity
If continuous spatial functions are used to parameterize earth models, then real-time computation is enabled with reduced complexity, but the ability to capture discrete geological features may be reduced
Solution Approach 1:
The patent employs dynamic spatial functions (such as splines or other continuous functions) to parameterize the earth model, allowing the model to adapt its complexity to the underlying data. This dynamic approach enables real-time computation while maintaining the ability to capture discrete geological features through appropriate function selection and parameterization.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach reduces computational load, facilitates real-time data processing, and provides more accurate geological formation characterization, enhancing the performance of drilling operations by generating continuous 2D and 3D earth models with reduced algorithmic complexity.
Implementation Method 1
a transmitter of the induction logging tool transmits an electromagnetic signal that passes through the geological formation around the borehole and induces a signal in one or more receivers in the induction logging tool
Data Source
AI summary
An example method for modeling a geological formation includes receiving a set of measurements from an electromagnetic logging tool and representing at least one characteristic of the geological formation as at least one continuous spatial function. At least one coefficient of the at least one continuous spatial function may be determined based, at least in part, on the set of measurements. At least one characteristic of the geological formation may be determined based, at least in part, on the at least one continuous spatial function.