Sunday, April 26, 2015

A mathematician's analysis of the Kathmandu earthquake - Painting by numbers

Good Morning, Kathmandu! It is noon on April 27th, 2 days post the 7.8 scale quake that has since set off almost 50 aftershocks, or one every 50 minutes, on average. 

I hope tonight will be much better for you than the last two. The numbers below strongly suggest they will. To start, as of right now (10:45 AM), you have gone for four hours without an aftershock, two times longer than at any time in the last 2 days. I hope this continues for many more hours. 

[(Update at 7pm) - Good evening Kathmandu - you have had NO aftershocks in the last 12 hours! There was a 5 scale on the Nepal/India border. We are praying that these are the final ones, and there are very few ahead. Sleep tight - you must be so tired. Sweetdreams!] 

In the last 12 hours, you were hit by 8 shocks averaging 4.5 on the intensity scale. You received an aftershock twice every three hours, which is similar to the 12 hours before that. 

Compare this with the first 18 hours, when you were hit by 34 shocks, at the rate of one every thirty minutes! They averaged 5.0. Remember that 5.0 is 5 times stronger than 4.5 on the logarithmic earthquake scale. The intensity of the shocks is declining...  

The picture below (click to enlarge) has every shock you received in the last 42 hours, 49 in total. In the last 10 hours, its fallen to 4. Things continue to normalize, and I hope your lives will too.

Thinking of you as we go to bed across the globe. God bless you all and look after you this day.

Last 48 hours in Kathmandu - attempt at some words of calm through a Mathematician's analysis of the earthquakes

My Dearest Kathmandu.

This will all come to pass. Soon. Very soon. Be brave, you may only have one more night of this ahead of you. The entire Nepali diaspora is constantly thinking of you and your well being. We will overcome this tragedy.

Below is some analysis that attempts to put your tired minds at ease as your rest this rainy night.  I am writing this in response to speaking to my family, my wife's family, and extended family members and friends that are panicky because "NASA / BBC / America is forecasting a 8 to 10 Richter Scale quake will go off soon."

First, nobody can forecast an earthquake. That is why its so devastating. Second, a 10 scale quake has never happened. Third, an Asian quake has never been larger than approximately 9. Fourth, a Himalayan belt quake has never been greater than the one you just experienced. Lastly, a larger quake following a smaller, first event is extremely rare.These are geologic precedents. You've borne the worst, in my opinion.See below's chart (courtesey of Pravin Tripathi) as to how extremely rare a 8-scale event is. You have been through one of the worst earthquakes in modern history.

Since the major earthquake on 04.25.2015, a staggering 41 earthquakes have gone off in and around the Kathmandu Valley. However, only three have been greater than 6, and the lone 7.8 that precipitated this chaos. The intensity of the earthquakes are falling rapidly.

Total Earthquakes 41 100%
Earthquakes Greater than 5 14 34%
Earthquakes Greater than 6  3 7%

In this bleak moment, it is extremely important to understand that earthquake intensities are measured on a logarithmic scale. The Richter scale is misleading. A scale 8 quake is one thousand times more intense than a scale 5.  The majority of the aftershocks at 4-5 scales are actually a fraction of the intensity of the original one. To be precise, one thousand to ten thousand times less intense. The strongest aftershock of 6.7 was 30-50 times less intense than the original one. Things will improve, the law of math promises it. 

Earthquake Intensities - Relative Measure 

Versus 4  Versus 6 Versus 8
Scale 4 1 0.01 0.0001
Scale 5 10 0.1 0.001
Scale 6 100 1 0.01
Scale 7 1,000 10 0.10
Scale 8 10,000 100 1.0

Lastly, a total of 22 earthquakes went off in the first 6 hours of the first one. However, that intensity is falling rapidly. In the next 12 hours, only 10 went off, and in the last 12, only 7. At this rate, mathematically, the aftershocks will likely fall to unnoticeable levels by tomorrow (Monday) night. Hang in there. This will come to pass. Soon. Very soon.

12 PM Sat to 6 PM Sat (6 hours)  22
6 PM Sat to 6 AM Sun (12 hours)  10
6 AM Sun to 6 PM Sun (12 hours) 7
Total 41

Below's chart, courtesy of the facebook disapora shows how the tremors are getting less frequent daily, a pictoral description of the above.

Lastly, I can imagine your exhaustion with the aftershocks. The seismic event picture below complied from USGS, the only authoritative data repository, shows that every single earthquake in the last 2 days except the first 2 major events has gone off in the Bagmati Zone around Kathmandu valley. It must truly be exhausting.

Be bold, Stay strong, squash rumours, and be Nepali. We've lost our Durbar Squares, but Pashupati and Swayambhu are still standing, tall and proud, like each and every one of you. God bless you all, and to quote my childhood school - "Karod diyo ko gham banera desh ujyalo paarne chhau" 

[Update on 7 pm 4.27.15 - There were zero aftershocks in the last 12 hours in the Kathmandu Valley and surrounding areas. The lone one in the region was far on the eastern border with India. I hope this trend continues. Goodnight my tired and weary countrymen. I hope this restful sleep tonight rejuvenates your spirit and your soul. Do not forget your perseverance and courage and above all, your charity and kindness to others, when you wake up.]