Reverse-learning-enhanced sine cosine algorithm for joint inversion of seismic refraction and Rayleigh-wave dispersion data

Rayleigh-wave dispersion and seismic refraction observations constrain different but coupled aspects of near-surface velocity structure. This study evaluates a reverse-learning-enhanced sine cosine algorithm (ESCA) for jointly estimating layer thickness, shear-wave velocity, and P-wave velocity in a one-dimensional, horizontally layered medium. Reverse learning is added during Tent-map initialization, while the best-solution-centered exponential update follows an earlier sine cosine formulation. The dimensionless joint objective combines root-mean-square relative residuals of fundamental-mode phase velocities and first-arrival times. ESCA, the standard sine cosine algorithm (SCA), and particle swarm optimization (PSO) were evaluated in 30 independent runs using multimodal benchmark functions, synthetic data generated from a model comprising 4 horizontal layers, and previously published field datasets from the Beşirli and MAE sites in Türkiye. The mean final joint-objective values for ESCA, SCA, and PSO, respectively, were 0.0028, 0.0070, and 0.0068 for noise-free synthetic data; 0.0336, 0.0356, and 0.0382 for synthetic data with 10% noise; 0.0343, 0.0393, and 0.0404 for the Beşirli dataset; and 0.0717, 0.0740, and 0.0722 for the MAE dataset. The corresponding runtimes for noise-free synthetic data were 145.32 ± 3.46, 137.89 ± 5.64, and 210.33 ± 4.65 s, respectively. ESCA required 0.99% more objective-function evaluations than the baseline algorithms, although its improvement over PSO for the MAE dataset was small. The field-data results demonstrate consistency within the assumed one-dimensional model but do not account for dipping interfaces or lateral variations in velocity.