Stability Does Not Guarantee Accuracy: CFL-Compliant 1D Acoustic FDTD and Its Consequences for Near-Surface Layered Modeling

Explicit finite-difference time-domain (FDTD) solvers for the 1D acoustic wave equation are routinely configured by enforcing the Courant–Friedrichs–Lewy (CFL) stability limit. In near-surface settings, this practice can create a false sense of model fidelity because stability constrains time stepping but does not control phase and amplitude errors induced by numerical dispersion. This report isolates the gap between stable time marching and accurate waveform synthesis in layered, strongly contrasting near-surface media. Beyond the well-known stability–accuracy distinction, the specific contribution is a reproducible near-surface verification workflow that couples a transfer-matrix stratified benchmark with controlled bandwidth variation at fixed CFL and converts the resulting waveform misfits into an explicit dispersion budget and pass–fail acceptance gate. The intended deliverable is an independent verification note that demonstrates, with quantitative evidence, that CFL compliance is necessary for stability but insufficient for accuracy, and that near-surface forward modeling requires an explicit dispersion budget expressed in points per minimum wavelength and validated by waveform misfit diagnostics.