Rayleigh Surface Wave Least Squares Inversion

Rayleigh surface wave least squares inversion is a method commonly used in geophysical exploration, primarily for inverting shear wave velocity structures of subsurface media. This approach infers formation parameters by analyzing the dispersion characteristics of Rayleigh surface waves, making it particularly suitable for detecting shallow geological structures.

The core concept of least squares inversion involves iterative optimization to minimize residuals between theoretical dispersion curves and actual observational data. In Rayleigh wave inversion, implementation typically requires constructing an initial model and using least squares algorithms to gradually adjust model parameters (such as shear wave velocity and layer thickness) until the fitting error reaches an acceptable range. Code implementation generally involves setting up an objective function that calculates the L2-norm difference between observed and predicted dispersion data, followed by gradient-based optimization methods like Gauss-Newton or Levenberg-Marquardt algorithms for parameter updates.

The advantages of this method lie in its concise mathematical formulation and computational stability, making it suitable for researchers new to inversion techniques. However, inversion results may be influenced by the initial model, making appropriate initial parameter selection crucial. Furthermore, to enhance inversion reliability, additional constraints or regularization techniques are typically incorporated to optimize solution uniqueness and stability. From a programming perspective, this often involves adding Tikhonov regularization terms to the objective function or implementing bound constraints on model parameters during optimization.

For beginners, understanding Rayleigh wave dispersion characteristics, constructing inversion objective functions, and mastering least squares optimization workflows are key steps in mastering this technique. Practical implementation would include coding dispersion curve calculation using matrix methods for layered media, implementing sensitivity analysis through partial derivative computations, and establishing convergence criteria for the iterative optimization process.