Naked Science Forum
Non Life Sciences => Geology, Palaeontology & Archaeology => Topic started by: Chondrally on 12/10/2017 00:44:13
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Average number of Earthquakes for Various Countries for 10,20 and 30 years and time till at least one quake of each magnitude. Raw data from the USGS earthquake catalag website:
https://earthquake.usgs.gov/earthquakes/search/
I did not Use the Gutenberg-Richter law, i generated the probability distributions of the quakes versus magnitude and time difference between quakes. The fat tail was extended with a Pareto type distribution fitted to the real distribution where it ended. This was used to simulate earthquakes of various magnitudes with attention to the phase distribution of magnitudes and time-distributions.....i believe this is a more sophisticated analysis than can be achieved with Gutenberg-Richter alone. I solved for an average count close to 1,, some times its 2 or 3 over 20000 paths into the future, but the average is close to 1. The sd gives you an idea of how many paths might be greater than 1. Russia has the most frequent and highest magnitude earthquakes of any region on Earth. It is because of the asteroid strike 230 million years ago, on the opposite side of the Earth. The fragmented continental plate is prone to having large and frequent earthquakes. Japan sits in the "ring of fire" and so does California.
Japan
magnitude cutoff = 5. , years = 0.0060782 , Probability= 1.7442*10-6 per quake or 1.51211*10-6 per day, count = 1.0302 , sd = 0.856922 , mean number of quakes in time period is: 0.641533 , Number of days in period = 2.22001
magnitude cutoff = 5. , years = 10. , Probability= 1.44319*10-6 per quake or 6.60575*10-7 per day, count = 519.05 , sd = 163.281 , mean number of quakes in time period is: 1253.83 , Number of days in period = 3652.42
magnitude cutoff = 5. , years = 20. , Probability= 1.45356*10-6 per quake or 6.55754*10-7 per day, count = 1028.07 , sd = 225.086 , mean number of quakes in time period is: 2471.61 , Number of days in period = 7304.84
magnitude cutoff = 5. , years = 30. , Probability= 1.44113*10-6 per quake or 6.47719*10-7 per day, count = 1521.93 , sd = 287.442 , mean number of quakes in time period is: 3693.57 , Number of days in period = 10957.3
magnitude cutoff = 5.5 , years = 0.00824855 , Probability= 1.2463*10-6 per quake or 1.05116*10-6 per day, count = 1.0604 , sd = 0.903376 , mean number of quakes in time period is: 0.847 , Number of days in period = 3.01272
magnitude cutoff = 5.5 , years = 10. , Probability= 8.55162*10-7 per quake or 3.91423*10-7 per day, count = 341.551 , sd = 117.962 , mean number of quakes in time period is: 1253.83 , Number of days in period = 3652.42
magnitude cutoff = 5.5 , years = 20. , Probability= 8.55461*10-7 per quake or 3.85929*10-7 per day, count = 672.222 , sd = 160.519 , mean number of quakes in time period is: 2471.61 , Number of days in period = 7304.84
magnitude cutoff = 5.5 , years = 30. , Probability= 8.45805*10-7 per quake or 3.80148*10-7 per day, count = 992.598 , sd = 202.782 , mean number of quakes in time period is: 3693.57 , Number of days in period = 10957.3
magnitude cutoff = 6. , years = 0.0120464 , Probability= 7.9613*10-7 per quake or 6.46189*10-7 per day, count = 1.035 , sd = 0.92168 , mean number of quakes in time period is: 1.1904 , Number of days in period = 4.39986
magnitude cutoff = 6. , years = 10. , Probability= 4.63133*10-7 per quake or 2.11984*10-7 per day, count = 208.3 , sd = 76.0192 , mean number of quakes in time period is: 1253.83 , Number of days in period = 3652.42
magnitude cutoff = 6. , years = 20. , Probability= 4.58509*10-7 per quake or 2.0685*10-7 per day, count = 406.31 , sd = 102.645 , mean number of quakes in time period is: 2471.61 , Number of days in period = 7304.84
magnitude cutoff = 6. , years = 30. , Probability= 4.51742*10-7 per quake or 2.03036*10-7 per day, count = 598.145 , sd = 128.835 , mean number of quakes in time period is: 3693.57 , Number of days in period = 10957.3
magnitude cutoff = 6.5 , years = 0.0195717 , Probability= 5.07479*10-7 per quake or 3.89278*10-7 per day, count = 1.0166 , sd = 0.969414 , mean number of quakes in time period is: 1.8278 , Number of days in period = 7.14839
magnitude cutoff = 6.5 , years = 10. , Probability= 2.51166*10-7 per quake or 1.14963*10-7 per day, count = 113.234 , sd = 42.7155 , mean number of quakes in time period is: 1253.83 , Number of days in period = 3652.42
magnitude cutoff = 6.5 , years = 20. , Probability= 2.46348*10-7 per quake or 1.11136*10-7 per day, count = 218.746 , sd = 57.2696 , mean number of quakes in time period is: 2471.61 , Number of days in period = 7304.84
magnitude cutoff = 6.5 , years = 30. , Probability= 2.42086*10-7 per quake or 1.08806*10-7 per day, count = 321.161 , sd = 71.4552 , mean number of quakes in time period is: 3693.57 , Number of days in period = 10957.3
magnitude cutoff = 7. , years = 0.0348961 , Probability= 3.00222*10-7 per quake or 2.1828*10-7 per day, count = 1.0294 , sd = 1.05266 , mean number of quakes in time period is: 3.08893 , Number of days in period = 12.7455
magnitude cutoff = 7. , years = 10. , Probability= 1.29309*10-7 per quake or 5.91869*10-8 per day, count = 59.3048 , sd = 22.7366 , mean number of quakes in time period is: 1253.83 , Number of days in period = 3652.42
magnitude cutoff = 7. , years = 20. , Probability= 1.26*10-7 per quake or 5.68433*10-8 per day, count = 113.8 , sd = 30.485 , mean number of quakes in time period is: 2471.61 , Number of days in period = 7304.84
magnitude cutoff = 7. , years = 30. , Probability= 1.23574*10-7 per quake or 5.55407*10-8 per day, count = 166.735 , sd = 37.8672 , mean number of quakes in time period is: 3693.57 , Number of days in period = 10957.3
magnitude cutoff = 7.5 , years = 0.130559 , Probability= 9.87637*10-8 per quake or 6.02525*10-8 per day, count = 1.1212 , sd = 1.10939 , mean number of quakes in time period is: 9.69713 , Number of days in period = 47.6856
magnitude cutoff = 7.5 , years = 10. , Probability= 4.23031*10-8 per quake or 1.93629*10-8 per day, count = 20.6904 , sd = 8.10272 , mean number of quakes in time period is: 1253.83 , Number of days in period = 3652.42
magnitude cutoff = 7.5 , years = 20. , Probability= 4.07312*10-8 per quake or 1.83753*10-8 per day, count = 39.2638 , sd = 10.8333 , mean number of quakes in time period is: 2471.61 , Number of days in period = 7304.84
magnitude cutoff = 7.5 , years = 30. , Probability= 3.98033*10-8 per quake or 1.78897*10-8 per day, count = 57.336 , sd = 13.3958 , mean number of quakes in time period is: 3693.57 , Number of days in period = 10957.3
magnitude cutoff = 8. , years = 6.99321 , Probability= 2.74019*10-9 per quake or 9.47766*10-10 per day, count = 0.9428 , sd = 0.760083 , mean number of quakes in time period is: 294.48 , Number of days in period = 2554.21
magnitude cutoff = 8. , years = 10. , Probability= 2.51323*10-9 per quake or 1.15035*10-9 per day, count = 1.22725 , sd = 0.666565 , mean number of quakes in time period is: 1253.83 , Number of days in period = 3652.42
magnitude cutoff = 8. , years = 20. , Probability= 2.20265*10-9 per quake or 9.93696*10-10 per day, count = 2.12025 , sd = 0.880572 , mean number of quakes in time period is: 2471.61 , Number of days in period = 7304.84
magnitude cutoff = 8. , years = 30. , Probability= 2.08597*10-9 per quake or 9.37542*10-10 per day, count = 3.00065 , sd = 1.06559 , mean number of quakes in time period is: 3693.57 , Number of days in period = 10957.3
Russia
magnitude cutoff = 5., years = 0.00186865, Probability= 2.5366*10^-6 per quake or 5.19207*10^-6 per day, count = 0.9985, sd = 0.912767 , mean number of quakes in time period is: 0.155222 , Number of days in period = 0.682508
magnitude cutoff = 5., years = 10., Probability= 2.99883*10^-6 per quake or 2.01279*10^-6 per day, count = 1535.4, sd = 306.957 , mean number of quakes in time period is: 2206.33 , Number of days in period = 3652.42
magnitude cutoff = 5., years = 20., Probability= 3.03846*10^-6 per quake or 2.28295*10^-6 per day, count = 3491.88, sd = 721.309 , mean number of quakes in time period is: 4939.65 , Number of days in period = 7304.84
magnitude cutoff = 5., years = 30., Probability= 3.04936*10^-6 per quake or 2.53076*10^-6 per day, count = 5810.84, sd = 1219.12 , mean number of quakes in time period is: 8184.41 , Number of days in period = 10957.3
magnitude cutoff = 5.5, years = 0.00233525, Probability= 1.76559*10^-6 per quake or 3.34516*10^-6 per day, count = 0.9945, sd = 0.91098 , mean number of quakes in time period is: 0.179556 , Number of days in period = 0.852931
magnitude cutoff = 5.5, years = 10., Probability= 1.73651*10^-6 per quake or 1.16553*10^-6 per day, count = 1198.99, sd = 254.746 , mean number of quakes in time period is: 2206.33 , Number of days in period = 3652.42
magnitude cutoff = 5.5, years = 20., Probability= 1.76932*10^-6 per quake or 1.32938*10^-6 per day, count = 2734.17, sd = 576.09 , mean number of quakes in time period is: 4939.65 , Number of days in period = 7304.84
magnitude cutoff = 5.5, years = 30., Probability= 1.77825*10^-6 per quake or 1.47583*10^-6 per day, count = 4553.17, sd = 966.725 , mean number of quakes in time period is: 8184.41 , Number of days in period = 10957.3
magnitude cutoff = 6., years = 0.00310678, Probability= 1.22512*10^-6 per quake or 2.11128*10^-6 per day, count = 0.9775, sd = 0.897704 , mean number of quakes in time period is: 0.217278 , Number of days in period = 1.13473
magnitude cutoff = 6., years = 10., Probability= 1.06769*10^-6 per quake or 7.16624*10^-7 per day, count = 890.862, sd = 198.484 , mean number of quakes in time period is: 2206.33 , Number of days in period = 3652.42
magnitude cutoff = 6., years = 20., Probability= 1.08888*10^-6 per quake or 8.18127*10^-7 per day, count = 2032.13, sd = 436.191 , mean number of quakes in time period is: 4939.65 , Number of days in period = 7304.84
magnitude cutoff = 6., years = 30., Probability= 1.09475*10^-6 per quake or 9.08572*10^-7 per day, count = 3384.64, sd = 726.487 , mean number of quakes in time period is: 8184.41 , Number of days in period = 10957.3
magnitude cutoff = 6.5, years = 0.00458933, Probability= 8.58061*10^-7 per quake or 1.26671*10^-6 per day, count = 0.9475, sd = 0.87437 , mean number of quakes in time period is: 0.274944 , Number of days in period = 1.67622
magnitude cutoff = 6.5, years = 10., Probability= 6.54016*10^-7 per quake or 4.3897*10^-7 per day, count = 614.914, sd = 142.483 , mean number of quakes in time period is: 2206.33 , Number of days in period = 3652.42
magnitude cutoff = 6.5, years = 20., Probability= 6.65099*10^-7 per quake or 4.99722*10^-7 per day, count = 1399.07, sd = 304.53 , mean number of quakes in time period is: 4939.65 , Number of days in period = 7304.84
magnitude cutoff = 6.5, years = 30., Probability= 6.68494*10^-7 per quake or 5.54805*10^-7 per day, count = 2329.55, sd = 504.441 , mean number of quakes in time period is: 8184.41 , Number of days in period = 10957.3
magnitude cutoff = 7., years = 0.00759372, Probability= 6.05815*10^-7 per quake or 7.76068*10^-7 per day, count = 0.9975, sd = 0.925974 , mean number of quakes in time period is: 0.394778 , Number of days in period = 2.77355
magnitude cutoff = 7., years = 10., Probability= 3.73107*10^-7 per quake or 2.50426*10^-7 per day, count = 375.321, sd = 89.4567 , mean number of quakes in time period is: 2206.33 , Number of days in period = 3652.42
magnitude cutoff = 7., years = 20., Probability= 3.77871*10^-7 per quake or 2.83914*10^-7 per day, count = 850.754, sd = 186.978 , mean number of quakes in time period is: 4939.65 , Number of days in period = 7304.84
magnitude cutoff = 7., years = 30., Probability= 3.79499*10^-7 per quake or 3.14958*10^-7 per day, count = 1415.49, sd = 308.254 , mean number of quakes in time period is: 8184.41 , Number of days in period = 10957.3
magnitude cutoff = 7.5, years = 0.0142664, Probability= 3.25774*10^-7 per quake or 3.66524*10^-7 per day, count = 0.9605, sd = 0.904119 , mean number of quakes in time period is: 0.651389 , Number of days in period = 5.21071
magnitude cutoff = 7.5, years = 10., Probability= 1.64764*10^-7 per quake or 1.10588*10^-7 per day, count = 182.158, sd = 44.0865 , mean number of quakes in time period is: 2206.33 , Number of days in period = 3652.42
magnitude cutoff = 7.5, years = 20., Probability= 1.66161*10^-7 per quake or 1.24845*10^-7 per day, count = 411.323, sd = 90.761 , mean number of quakes in time period is: 4939.65 , Number of days in period = 7304.84
magnitude cutoff = 7.5, years = 30., Probability= 1.66633*10^-7 per quake or 1.38294*10^-7 per day, count = 683.458, sd = 149.198 , mean number of quakes in time period is: 8184.41 , Number of days in period = 10957.3
magnitude cutoff = 8., years = 0.041706, Probability= 1.23749*10^-7 per quake or 1.19055*10^-7 per day, count = 0.945, sd = 0.900642 , mean number of quakes in time period is: 1.62833 , Number of days in period = 15.2328
magnitude cutoff = 8., years = 10., Probability= 5.23464*10^-8 per quake or 3.51345*10^-8 per day, count = 60.1813, sd = 14.8164 , mean number of quakes in time period is: 2206.33 , Number of days in period = 3652.42
magnitude cutoff = 8., years = 20., Probability= 5.24572*10^-8 per quake or 3.94138*10^-8 per day, count = 135.022, sd = 29.9889 , mean number of quakes in time period is: 4939.65 , Number of days in period = 7304.84
magnitude cutoff = 8., years = 30., Probability= 5.24986*10^-8 per quake or 4.35703*10^-8 per day, count = 223.893, sd = 49.0215 , mean number of quakes in time period is: 8184.41 , Number of days in period = 10957.3
magnitude cutoff = 8.5, years = 0.188188, Probability= 3.42762*10^-8 per quake or 2.67478*10^-8 per day, count = 0.958, sd = 0.890454 , mean number of quakes in time period is: 5.95972 , Number of days in period = 68.7342
magnitude cutoff = 8.5, years = 10., Probability= 1.7296*10^-8 per quake or 1.1609*10^-8 per day, count = 19.8848, sd = 4.94735 , mean number of quakes in time period is: 2206.33 , Number of days in period = 3652.42
magnitude cutoff = 8.5, years = 20., Probability= 1.72456*10^-8 per quake or 1.29575*10^-8 per day, count = 44.3893, sd = 9.9018 , mean number of quakes in time period is: 4939.65 , Number of days in period = 7304.84
magnitude cutoff = 8.5, years = 30., Probability= 1.72334*10^-8 per quake or 1.43026*10^-8 per day, count = 73.4961, sd = 16.1398 , mean number of quakes in time period is: 8184.41 , Number of days in period = 10957.3
magnitude cutoff = 9., years = 30., Probability= 7.2059*10^-12 per quake or 5.25429*10^-12 per day, count = 0.03, sd = 0.0321016 , mean number of quakes in time period is: 887.74 , Number of days in period = 10957.3
magnitude cutoff = 9., years = 10., Probability= 8.56765*10^-12 per quake or 5.75053*10^-12 per day, count = 0.00985, sd = 0.0319137 , mean number of quakes in time period is: 2206.33 , Number of days in period = 3652.42
magnitude cutoff = 9., years = 20., Probability= 7.07084*10^-12 per quake or 5.31268*10^-12 per day, count = 0.0182, sd = 0.0434707 , mean number of quakes in time period is: 4939.65 , Number of days in period = 7304.84
magnitude cutoff = 9., years = 30., Probability= 6.81168*10^-12 per quake or 5.65323*10^-12 per day, count = 0.02905, sd = 0.0559702 , mean number of quakes in time period is: 8184.41 , Number of days in period = 10957.3
California
magnitude cutoff = 5. , years = 0.031119 , Probability= 4.10051*10-6 per quake or 1.11027*10-6 per day, count = 0.965 , sd = 0.886568 , mean number of quakes in time period is: 0.341944 , Number of days in period = 11.366
magnitude cutoff = 5. , years = 10. , Probability= 2.1294*10-6 per quake or 4.97301*10-7 per day, count = 119.507 , sd = 18.6931 , mean number of quakes in time period is: 767.687 , Number of days in period = 3652.42
magnitude cutoff = 5. , years = 20. , Probability= 2.09242*10-6 per quake or 5.16679*10-7 per day, count = 248.369 , sd = 33.5911 , mean number of quakes in time period is: 1623.4 , Number of days in period = 7304.84
magnitude cutoff = 5. , years = 30. , Probability= 2.0772*10-6 per quake or 5.42477*10-7 per day, count = 391.093 , sd = 48.1261 , mean number of quakes in time period is: 2575.42 , Number of days in period = 10957.3
magnitude cutoff = 5.5 , years = 0.0938086 , Probability= 1.37694*10-6 per quake or 3.24113*10-7 per day, count = 0.956 , sd = 0.878644 , mean number of quakes in time period is: 0.896111 , Number of days in period = 34.2629
magnitude cutoff = 5.5 , years = 10. , Probability= 6.09263*10-7 per quake or 1.42287*10-7 per day, count = 40.0142 , sd = 6.46341 , mean number of quakes in time period is: 767.687 , Number of days in period = 3652.42
magnitude cutoff = 5.5 , years = 20. , Probability= 5.94572*10-7 per quake or 1.46817*10-7 per day, count = 82.7159 , sd = 11.4786 , mean number of quakes in time period is: 1623.4 , Number of days in period = 7304.84
magnitude cutoff = 5.5 , years = 30. , Probability= 5.88655*10-7 per quake or 1.53732*10-7 per day, count = 129.965 , sd = 16.3178 , mean number of quakes in time period is: 2575.42 , Number of days in period = 10957.3
magnitude cutoff = 6. , years = 0.433951 , Probability= 3.13288*10-7 per quake or 6.88286*10-8 per day, count = 0.9645 , sd = 0.877045 , mean number of quakes in time period is: 3.86906 , Number of days in period = 158.497
magnitude cutoff = 6. , years = 10. , Probability= 1.7457*10-7 per quake or 4.07691*10-8 per day, count = 12.0283 , sd = 2.01537 , mean number of quakes in time period is: 767.687 , Number of days in period = 3652.42
magnitude cutoff = 6. , years = 20. , Probability= 1.69619*10-7 per quake or 4.18839*10-8 per day, count = 24.7329 , sd = 3.53038 , mean number of quakes in time period is: 1623.4 , Number of days in period = 7304.84
magnitude cutoff = 6. , years = 30. , Probability= 1.67678*10-7 per quake or 4.37906*10-8 per day, count = 38.7987 , sd = 4.97618 , mean number of quakes in time period is: 2575.42 , Number of days in period = 10957.3
magnitude cutoff = 6.5 , years = 1.36343 , Probability= 9.60229*10-8 per quake or 2.04181*10-8 per day, count = 0.9395 , sd = 0.85297 , mean number of quakes in time period is: 11.7656 , Number of days in period = 497.982
magnitude cutoff = 6.5 , years = 10. , Probability= 7.52768*10-8 per quake or 1.75801*10-8 per day, count = 5.33965 , sd = 1.02292 , mean number of quakes in time period is: 767.687 , Number of days in period = 3652.42
magnitude cutoff = 6.5 , years = 20. , Probability= 7.32186*10-8 per quake or 1.80798*10-8 per day, count = 10.9829 , sd = 1.70657 , mean number of quakes in time period is: 1623.4 , Number of days in period = 7304.84
magnitude cutoff = 6.5 , years = 30. , Probability= 7.2337*10-8 per quake or 1.88914*10-8 per day, count = 17.2138 , sd = 2.37659 , mean number of quakes in time period is: 2575.42 , Number of days in period = 10957.3
magnitude cutoff = 7. , years = 7.67332 , Probability= 1.76445*10-8 per quake or 3.68784*10-9 per day, count = 0.955 , sd = 0.86679 , mean number of quakes in time period is: 65.0854 , Number of days in period = 2802.62
magnitude cutoff = 7. , years = 10. , Probability= 1.75657*10-8 per quake or 4.1023*10-9 per day, count = 1.246 , sd = 0.402275 , mean number of quakes in time period is: 767.687 , Number of days in period = 3652.42
magnitude cutoff = 7. , years = 20. , Probability= 1.66459*10-8 per quake or 4.11037*10-9 per day, count = 2.4969 , sd = 0.607466 , mean number of quakes in time period is: 1623.4 , Number of days in period = 7304.84
magnitude cutoff = 7. , years = 30. , Probability= 1.63439*10-8 per quake or 4.26835*10-9 per day, count = 3.8893 , sd = 0.78934 , mean number of quakes in time period is: 2575.42 , Number of days in period = 10957.3
magnitude cutoff = 7.5 , years = 30. , Probability= 0. per quake or 0. per day, count = 0. , sd = 0. , mean number of quakes in time period is: 288.514 , Number of days in period = 10957.3
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It would be useful to post the source of the raw data, as other people may like to delve into it too (eg some part of the USGS website (https://earthquake.usgs.gov/)?).
Would you like to make some observation about the trends?
- Generally, earthquakes are thought to be a fractal-type phenomenon, with a negative exponential behavior.
- See: https://en.wikipedia.org/wiki/Gutenberg%E2%80%93Richter_law
Two areas that seem suspicious in the first line of data is where it says:
- count = 1.0302: You can't count "1.0302 earthquakes > 5 on the Richter scale". I assume that this is meant to be 1?
- sd = 0.856922: With a count of 1 (or even 1.0302), the standard deviation is infinite, not 0.856922. You need a count of at least 2 to get a defined sd.
Please clarify.
PS: I recently visited a volcanic island in Greece. The guide said that a few km away there was an undersea volcanic mountain that was suffering earthquakes about every 2 minutes, on average. But they must be pretty low on the Richter scale, because they didn't wake me up at night.