Magnetic Field Models
- Industry requests higher degree, smaller scale magnetic models:
- Are these justified by the data available?
- What are the associated reduction (or otherwise) in uncertainties?
- What are the main sources of uncertainty and how to quantify them?
- We examine and quantify the main sources of error:
- (i) high degree crustal field and
- (ii) spatial limitations of crustal field input data
- (iii) forecasting uncertainty;
- (iv) external field
High degree models (degree > 133)
- Satellite data can be used to consistently model the field to degree 133 [wavelengths ~300 km]
- Adding in ground aeromagnetic and marine surveys; Global grid compilations at 0.05°
- Theoretical degree = 7200 [~4km]
- Realistically, available memory/computation time are limiting factors e.g. 800--1440 [~28-50 km]
- Look at errors in X, Y and Z (linear) and convert to Dec, Inc and Total Field (F) at the end
- Use 95.4% CI divided by 2 = 1 sigma equivalent
Analysis in XYZ
- Working with magnetic field values in X, Y and Z is linear
- Computing errors and differences in DIF is non-linear (e.g. angles with cosine/sine, square roots)
- Errors computed in XYZ and converted to DIF (using main field, H and F values) at the end
Errors in magnetic data
- Errors in magnetic data are not Gaussian
- 1σ = 68.3%
- 2 x 1σ = 95.4%
- 3 x 1σ = 99.7%, etc
- Usually, better described by Laplacian
- 2 x 1σ ≠ 95.4%!
- To compute confidence intervals: sort the residuals, then find the 68.3%, 95.4% values
- Typically, CI 68.3% < 1σ; CI 95.4% > 2σ
- To be conservative: use CI 95.4% divided by 2; call this a scalable 1 sigma equivalent
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View the entire Presentation:
Quantifying Uncertainties in High-resolution Magnetic Field Models
Ciaran Beggan (Speaker), Susan Macmillan, Brian Hamilton, William Brown