Non-linear Polynomial Clock Drift Estimation for Seismic Data Dating
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Solution Overview
Problem
Current methods for correcting clock drift in seismic data sampling assume linear drift, which is not accurate, leading to errors in dating seismic data samples due to non-linear clock drift caused by factors like aging and temperature changes.
Innovation Solution
A method that estimates clock drift using a non-linear polynomial law, specifically a 3rd-order polynomial equation, to accurately correct the accumulated phase error of clocks, applicable to various types of clocks, including quartz and atomic clocks, and can be implemented within seismic data collection equipment or separately, allowing for robustness against oven heating and temperature changes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If linear correction method is used for clock drift, then calculation simplicity is improved, but dating precision deteriorates due to non-linear drift characteristics
Solution Approach 1:
The patent changes the mathematical model parameters from linear to non-linear (polynomial of order 2 or higher) to accurately represent the actual non-linear drift behavior of clocks. This resolves the contradiction by accepting increased calculation complexity in exchange for significantly improved dating precision, as the non-linear model better captures the true drift characteristics caused by aging and temperature effects.
2Measurement precision
If non-linear polynomial law is used for drift estimation, then dating precision is improved, but calculation complexity increases
Solution Approach 1:
The patent applies a polynomial correction of order 2 or higher, which is more complex than necessary for simple applications but provides sufficient precision for seismic data dating. This partial excessive action resolves the contradiction by implementing just enough non-linearity to capture the drift behavior without over-engineering the solution, balancing precision needs with computational practicality.
3Duration of action of moving object
If clock is used for lengthy seismic campaigns, then data collection duration is improved, but accumulated drift error increases
Solution Approach 1:
The patent implements a feedback mechanism where the non-linear drift model is continuously applied to correct timestamp errors throughout the seismic campaign. By using the polynomial law to calculate and compensate for accumulated drift at each measurement point, the system maintains dating precision even over extended periods, resolving the contradiction between campaign duration and error accumulation.
Data Source
AI summary
A seismic data collection node has a clock for dating samples of seismic data and means for estimating a drift over time of a variable physical operating parameter of the clock. According to a predetermined non-linear law of variation of the variable physical operating parameter, the instantaneous frequency varies according to a polynomial equation of order greater than or equal to 2, such that a phase of the clock varies according to a polynomial equation of order greater than or equal to 3.