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Introduction:
Due to a recent conundrum revolving around the limits of earthquake formulas and their questionable accuracy on planets larger than Earth. It was deemed that such use of formulas were not acceptable by VSBW standards and as such the One Piece verse suffered immensely for it, as its greatest feats revolve around the planet and earthquakes. While this is mainly aimed towards One Piece, I suppose this would be valid for any other verse with the same problem.The formula “(Magnitude at distance)+6.399+1.66×log10((r÷110)×((2×π)÷360))” is what is normally used but due to being reliant on Earth values was deemed inaccurate to use on larger planets as the attenuation value should be different.
What is Seismic Attenuation and How is it Determined?
Seismic Attenuation is, essentially, the rate at which earthquakes lose energy over the distance they travel. The current formula uses a value of 1.66 and it is derived from factors such as Pore Water Pressure, Temperature, Crustal Heterogeneity, Composition, and Melt and Fluid Content.How it Compares to Blue:
Let’s go over each one and how each affects Seismic Attenuation.Pore Water Pressure:
PWP is the “pressure of groundwater held within a soil or rock, in gaps between particles (pores).” higher pressure translates to more energy loss. The exact pressure would either be the same or be higher due to phenomena like this existing on Blue, which increases the attenuation value.Temperature:
The temperature of the planet directly affects Seismic Attenuation, the higher the temperature of the medium is, the more energy is lost meaning a higher Seismic Attenuation value. Larger planets have an innate higher temperature compared to Earth, which Blue is accepted to be larger than Earth.Crustal Heterogeneity and Composition:
Crustal Heterogeneity refers to the “variation in physical, chemical, and structural properties within the Earth's crust”, due to Blue already using Earth like composition to determine its density; it’s safe to say seismic attenuation shouldn’t change too much from Earth.Melt and Fluid Content:
Again, Blue was already accepted to use Earth like density, meaning the Melt and Fluid content should proportionally increase, increasing attenuation value.How It Affects The Formula:
“(Magnitude at distance)+6.399+1.66×log10((r÷110)×((2×π)÷360))” is the initial formula, with the 1.66 value representing Seismic Attenuation.Let’s plug in our values and see how things turn out with a control formula.
r = Half the circumference of the planet
Since we are assuming complete planet wide shaking, that is the maximum distance a quake can realistically travel.
(6)+6.399+1.66×log10((2,476,085÷110)×((2×π)÷360)) = 16.7054553846
10^(1.5×(16.7054553846)+4.8) = 7.2141153e+29 Joules = 172.42 Exatons of TNT (Moon level)
Now let’s see how different attenuation values affect the outcome, we’ll start with lowering it by .33.
(6)+6.399+1.33×log10((2,476,085÷110)×((2×π)÷360)) = 15.8493
This gives us a lower value. Now let’s do another where the attenuation is .33 higher.
(6)+6.399+1.99×log10((2,476,085÷110)×((2×π)÷360)) = 17.5615
This gives us a result that is higher.
What does this mean for us? Well, the evidence I’ve presented for how seismic attenuation is found points towards Blue having a higher seismic attenuation value than one we normally use, which in turn gives us a higher yield. While it is impossible to find the exact attenuation value, my point I am trying to make is that whatever yield “1.66” gives us is a lowball yield and is still perfectly fine for ascertaining the yield of quakes on planets larger than Earth.
Additionally, due to the previous formula using the planet’s circumference, another formula brought to my attention by Floxy178, should result in a better value as it is not reliant on the planet’s circumference.
"(Magnitude at distance) + 0.084 + 1.66*log10(arc length in KM)"
(6) + 0.084 + 1.66*log10(2,476,085) = 16.6977
(6) + 0.084 + 1.99*log10(2,476,085) = 18.807593443
Even using this new formula gives a higher value when using a higher attenuation value, again, a lowball value. Whether the actual value is 1.67 or 1000, it doesn’t matter as whatever 1.66 gives us is lower than what it should be.
Conclusion:
Proposal: Allow this formula to be used "(Magnitude at distance) + 0.084 + 1.66*log10(arc length in KM)" as I’ve proven, it results in a lower yield than it should and doesn’t overestimate the final result.
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