Looking for a formula to describe this graph, related to wave mechanics

I’m working on a statistics problem looking to understand why some very simple periodic models are causing even cutting-edge Bayesian sampling tools to fail catastrophically. I think I’ve traced the failure down to a fundamental issue with the likelihood topography associated with periodic models whereby there are many local peaks that can cause samplers to miss the global peak.

Here’s a graphic of the likelihood topography for a 10s signal sampled at 100Hz and generated with zero phase and a frequency of 1 Hz, where each location’s color is determined by the likelihood of the signal given a model with that point’s corresponding frequency and phase:

The upper left is the full bivariate topography with color indicating relative log-likelihood (scaled to range between -1 to 0), the upper right is the likelihood as a function of model frequency for a model with zero phase, and the lower left is the likelihood as a function of model phase for a model with a 1Hz frequency.

I’m getting the feeling that there is a physical systems analogue to this, possibly related to coherence and interference/beating? Does this structure resonate with anyone in any sense?

If I can work out a closed-form solution to capture this topography, I think it would help me work out a reparameterization to achieve more reliable sampling. Thanks in advance for any thoughts!