Magnetotelluric Data Inversion Using Nonlinear Conjugate Gradient Method

Magnetotelluric (MT) data inversion serves as a vital technique in geophysical exploration, inferring subsurface resistivity structures by analyzing natural electromagnetic field signals. The Nonlinear Conjugate Gradient (NLCG) inversion algorithm is widely adopted due to its computational efficiency and stability. However, preprocessing and post-processing stages significantly impact the reliability and interpretability of inversion results.

Preprocessing Stage Preprocessing aims to enhance the signal-to-noise ratio and consistency of raw data. First, time-series data requires denoising to remove power-line interference and outliers. Second, power spectrum analysis validates data stationarity to prevent inversion biases from local anomalies. For multi-station data, impedance tensor rotation aligns coordinate systems, ensuring geometrical consistency in subsequent inversions. For missing or distorted high-frequency data, interpolation or physics-based correction methods can be applied. Code implementations typically involve FFT-based filtering, robust statistical outlier detection, and coordinate transformation routines using matrix operations.

Core Inversion: NLCG Algorithm NLCG inversion iteratively optimizes an objective function (e.g., weighted sum of data misfit and model roughness) to approximate true resistivity structures. Its advantages include low memory usage and flexibility in handling large-scale model parameters. The algorithm updates model parameters along conjugate gradient directions, combined with line search to determine optimal step sizes and avoid local minima. In MT inversion, regularization terms balance data fitting and model smoothness, while frequency-dependent weighting accounts for varying data quality. Implementation involves gradient computation using adjoint methods, preconditioning for convergence acceleration, and adaptive regularization parameter tuning.

Post-processing Stage Post-processing validates result rationality and stability through: Resolution analysis: Evaluating model credibility at different depths via sensitivity matrix or point spread function calculations; Multi-dimensional visualization: Overlaying resistivity models with geological information to generate profiles or 3D volume renderings; Cross-validation: Testing model predictive capability using withheld stations or frequency bands; Uncertainty quantification: Estimating boundary uncertainties of key structures through inversion covariance matrices or Monte Carlo methods. Code implementations may include parallelized sensitivity computations, GPU-accelerated visualization tools, and statistical resampling algorithms.

Systematic preprocessing and post-processing enable NLCG inversion to reliably reveal subsurface electrical structures, providing robust foundations for resource exploration or tectonic studies.