Rayleigh wave waveform-amplitude spectrum joint inversion: an advanced resolution-stability approach for loess near-surface imaging

Rayleigh wave methods are widely utilized in near-surface geophysical exploration within loess regions. However, conventional dispersion curve inversion methods are constrained by the horizontally layered media assumption, which restricts their lateral resolution and prevents the identification of collapsible voids, hidden faults, and other concealed defects. With advances in computational power, wave-equation-based waveform inversion and amplitude spectrum inversion have emerged as promising techniques for characterizing shallow subsurface structures. Nevertheless, waveform inversion often converges to local minima due to insufficient low-frequency components and a strong dependence on the initial model. Although amplitude spectrum inversion can partially alleviate these issues by exploiting low-frequency Rayleigh waves, it neglects the critical role of high-frequency waveform components and the effective use of single-trace data in improving inversion resolution. To address these limitations, this study proposes a joint inversion method that integrates the Rayleigh wave amplitude spectrum with full waveform data. A joint objective function with dynamically variable weights is constructed. By dynamically adjusting the relative weights of the two components during the iteration process, amplitude spectrum inversion is prioritized in the early stages to build a stable background velocity model and mitigate cycle-skipping problems. In later stages, the weight of waveform inversion is gradually increased to leverage high-frequency information for improving model resolution. This strategy simultaneously compensates for the shortcomings of each individual approach and enhances convergence efficiency. Numerical simulation results demonstrate that compared with conventional individual waveform inversion or amplitude spectrum inversion, the proposed joint inversion method achieves higher accuracy and stability in 2D shear-wave velocity inversion. Furthermore, field data applications from the loess area substantiate the practical value of this method in engineering-scale near-surface exploration.