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There's always more one can do in modeling, and the path is fraught with false starts and dead ends, but this is really zeroing in on the essential common mode. The two keys are (1) a well-calibrated LOD forcing and (2) a specific annualized impulse. The first is a solid premise, but the second has the feel of an ansatz, since it feels a bit random. The idea is that every 4th year, the impulse strength is much stronger. Why this would happen is not close to obvious but it might be related to the fact that both As it turns out I long ago ran into a similar bifurcation, with the commonality being derived from a Fourier series and the orthogonality being in the spatial (not time) domain. The results were reported in refs [1,2,3] with two different material systems (Silicon and Germanium) and the last being a conference submission. This was big news in condensed matter systems at the time, as getting a paper published in Applied Physics Letters is no easy task. This quickly became a study on the effect of surfactants on crystal growth [4] (we regrettably missed using the term surfactant in our papers). The experiment and resolution is pretty simple. At the time, we were using electron diffraction to infer surface periodicity of atoms via a Fourier series analysis -- which is direct, kind of like having waves in a fluid directly identified by their frequency. When the surface was quenched with an arsenic (As) gas, both the silicon (Si) and germanium (Ge) surfaces rearrange in a spatial bifurcation. This figure from ref [3]: Figure 1 is what we observed in the diffraction and Figure 2 is what we inferred from the inverse Fourier series reconstruction of the surface re-arrangement. Essentially the surface transformed from a single stepped staircase periodicity to a 3 + 1 stepped periodicity. A decade after this, direct observations were available via scanning tunneling microscopy (STEM) and the results were validated in ref [5]
The STM view looked like this, where the bunching into a 3 layer step is clearly seen, and thus not inferred On single crystal surfaces, this super-periodicity or bifurcation into longer range periodicities is common and related to reduction in free energy of the surface, in this case changing it from a More to follow Refs
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Clean runs assuming a 3+1 annual impulse with precisely calibrated dLOD. Data from the GIST at GitHub below: Typical signature is a double sideband suppressed carrier modulation (at the annual frequency), folding as shown below The tidal forcing exactly matches the dLOD of the Earth's rotation. Since measured dLOD only goes back to 1962, we calibrate a model to this data and extraopolate backwards to allow model cross-validation back to pre-1900 dates. |
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With nonlinear math, there are many ways to arrive at the same result, especially in comparison to a linear model. So forever evolving. Several findings to consider with the common-mode model.
With these in place, the following indices can be solved with identical tidal forcing factors
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Not going to repeat the whole post here
https://geoenergymath.com/2025/03/07/teleconnection-vs-common-mode/
Example of an EMI cross-validation based on a common-mode tidal forcing.
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