Dispersion Curve Fitting for Slowness Estimation in Acoustic Logging
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Solution Overview
Problem
Existing methods for accurately determining compressional and shear velocity in earth formations face challenges due to dispersion effects in acoustic logging data, particularly in wireline and LWD measurements, where model-based approaches suffer from significant errors due to complex borehole conditions and noise interference.
Innovation Solution
A data-driven curve-fitting method is employed to estimate slowness by transforming acoustic waveform data into the frequency domain, calculating a slowness-frequency coherence function, selecting dispersion data from peaks, and fitting a curve using a hyper tangent or arc tangent function with minimal parameters to capture dispersion characteristics, thereby reducing noise effects and improving accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If model-based dispersion estimation is used, then theoretical dispersion curves can be calculated, but significant errors occur when borehole conditions deviate from ideal theoretical conditions
Solution Approach 1:
The patent creates a synthetic dispersion curve that copies the essential characteristics of theoretical dispersion curves but is generated from measured data rather than complex models. This synthetic curve captures the dominant dispersion behavior without requiring detailed knowledge of borehole conditions, fluid properties, or tool configurations, thus resolving the contradiction between accuracy and adaptability.
Solution Approach 2:
The invention changes the approach from using numerous model parameters (borehole size, formation velocities, fluid properties, tool effects) to using a minimal set of parameters fitted directly to measured data. By fitting a simple functional form to the measured dispersion data, the method achieves accuracy without requiring detailed parameter knowledge, thus adapting to various borehole conditions.
2Measurement precision
If histogram approach is used for data-driven dispersion analysis, then formation slowness can be estimated from peak distribution, but data noise and mode interference create spurious peaks that mislead edge detection
Solution Approach 1:
The patent extracts only the essential dispersion characteristics from the measured data by fitting a synthetic dispersion curve to the measured slowness values. This extraction process separates the dominant dispersion behavior from noise and interference, removing the harmful effects that plague the histogram approach while retaining the useful information needed for accurate slowness estimation.
Solution Approach 2:
The synthetic dispersion curve acts as an intermediary between the raw measured data and the final slowness estimation. Rather than directly analyzing the noisy measured data through histogram edge detection, the method uses the synthetic curve as a mediator that smooths out noise and interference while preserving the essential dispersion characteristics needed for accurate slowness determination.
3Reliability
If full theoretical modeling is used for dispersion analysis, then comprehensive waveguide structure can be represented, but numerous model parameters are required and processing complexity increases
Solution Approach 1:
The patent extracts only the essential dispersion characteristics from the complex theoretical modeling framework. Instead of requiring complete waveguide structure modeling with numerous parameters, the method extracts the dominant dispersion behavior directly from measured data, achieving reliability without the complexity of full theoretical modeling.
Solution Approach 2:
The synthetic dispersion curve is a simplified, computationally inexpensive alternative to full theoretical modeling. It uses a simple functional form with minimal parameters that can be quickly fitted to data, providing reliable dispersion analysis without the computational burden and parameter complexity of comprehensive theoretical models.
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 method provides more accurate and reliable estimates of formation slowness by effectively handling dispersion and noise, improving the accuracy of compressional and shear velocity measurements in both wireline and LWD data sets, and is applicable to various guided wave modes.
Implementation Method 1
transmitting acoustic energy into the earth formation using an acoustic source
Implementation Method 2
receiving the acoustic energy with an array of acoustic receivers, each acoustic receiver being configured to provide acoustic waveform data related to the received acoustic energy
Implementation Method 3
transforming the acoustic waveform data into a frequency domain to provide frequency domain data
Implementation Method 4
calculating a slowness-frequency coherence function using the frequency domain data; selecting slowness dispersion data from peaks of the slowness-frequency coherence function
Data Source
AI summary
A method for estimating a slowness of an earth formation, the method including: transmitting acoustic energy into the earth formation using an acoustic source; receiving the acoustic energy with an array of acoustic receivers, each acoustic receiver being configured to provide acoustic waveform data related to the received acoustic energy; transforming the acoustic waveform data into a frequency domain to provide frequency domain data; calculating a slowness-frequency coherence function using the frequency domain data; selecting slowness dispersion data from peaks of the slowness-frequency coherence function; fitting a curve to the slowness dispersion data; and estimating the slowness from the curve.