Predicting Earthquakes: Can it be Done?

The image above is a depiction of the fault zones in the Bay Area, California. The black star indicates where I live in California.
(Source: http://www.ebsinstitute.com/EBS.EQ2_RS_DA.html) 

Life in California often evokes images of palm trees, sunny-blue skies, and sandy beaches. As a resident of California, I can attest that all those stereotypes are often correct. But sometimes, people overlook the idea of California as “Earthquake Country.” Living 0.5 miles away from the Hayward Fault and a few more miles away from the San Andreas Fault, I’ve become used to waking up at odd times during the night to a swaying bed frame or watching pendulums move seemingly on their own.

While most natural disasters - including hurricanes, tornadoes, blizzards, volcanos, and tsunamis - can be predicted ahead of time, earthquakes lack that luxury. They are hard to predict because it’s difficult to tell when exactly the pressure built between two plates will release¹. Prediction is crucial for saving lives because it can give people time to get to a safe place. Several methods have been created to predict earthquakes, including the analysis of the patterns of previous tremors, the use of animal behavior, changes in the concentration of radon gas, and even variations in electromagnetic behavior¹. But these methods all share a common problem - accuracy.

However, we Californians don’t need to fear as much, because there has emerged a new system recently, known as earthquake early warning.

What is earthquake early warning and how do earthquakes work?

In a nutshell, earthquake early warning is a system that sends a warning that an earthquake will strike in a certain area within a few seconds. When an earthquake occurs, one of three main things can happen: two plates may pass each other on a strike-slip fault (one example is the San Andreas Fault), a plate on top of the fault moves down relative to the plate on the bottom on a normal fault, or a plate on the bottom of the fault moves up relative to the plate on the top on a reverse fault². This movement leads pressure to build up between two pieces of land. As this pressure builds up, reaching a point that’s too large to handle by the pieces of land, it’s released in an earthquake. This release of energy transforms into waves that emanate outward from the epicenter of the earthquake. There are two main types of waves: P-waves and S-waves. P waves, which tend not to cause lots of damage, move faster than S-waves, which can cause lots of damage². The variety of waves is useful in detecting earthquakes, because earthquake stations (also known as sensors, placed throughout California) detect P-waves first. P-waves are then used to determine the magnitude and location of the earthquake². These P-waves allow the warning to be sent to people via text messages, computers, radios, and TVs, warning them of the upcoming S-waves, which are dangerous2. This warning normally includes the shaking intensity and estimated time of arrival of the earthquake².

The image above shows how earthquake early warning functions. (Source: https://earthquake.usgs.gov/research/earlywarning/overview.php)

How do you find the warning time and how long is it?

The main factor determining the warning time, the amount of time it takes for the S-waves to reach a specific location, depends on the distance between that location and the earthquake’s epicenter. The farther away the area is from the epicenter, the greater warning time it receives, because the waves take longer to reach that area³. This extended time decreases the intensity of the wave as well. Therefore, a warning may not be useful for people far away from the epicenter. With this in mind, the warning and detection time change based on several factors including the amount of distance between the epicenter and closest station, the absorption of earthquake data by regional networks, and the accurate “diagnosis” of an earthquake’s magnitude and intensity³. Based on this, a warning time can range between 0-60 seconds.

Is it perfect?

0 seconds? This seems pointless. But this is one of the pitfalls of the earthquake early warning system. Around the epicenter of the earthquake, there is a “blind zone,” a radius of places around the earthquake that receive no warning at all. When the earthquake first happens, the P and S-waves start at the same place. Imagine two cars are racing - Car A, which has an average speed of 100 miles per hour, and Car B, which has an average speed of 75 miles per hour. Car A is analogous to P-waves, while Car B is analogous to S-waves. Car A and B start at the same position; for a while, they remain next to each other, until Car A inevitably overtakes Car B permanently. During the time these cars, or waves, remain together, there is no warning, because the S-waves, which can cause damage, arrive at the same time as the harmless P-waves. This is an issue of great magnitude- excuse my pun- because areas closest to the epicenter are the places that have the highest shaking intensity. In other words, these are the areas that need warning!

Although earthquake early warning systems can offer some people fair warning before an earthquake strikes, earthquake prediction still needs work. But at least we can take comfort knowing there are systems being developed to help warn of earthquakes in areas around the world.

References:

1. http://www.bbc.co.uk/guides/zxyd2p3
2. https://www.usgs.gov/faqs/what-a-fault-and-what-are-different-types
3. https://earthquake.usgs.gov/research/earlywarning/background.php

Pareto and Zipf: Distributions, Laws, and Blickets

“An alien spaceship crashes into the Nevada Desert. Eight creatures emerge: a wug, a plit, a blicket, a flark, a warit, a jude, a ralex, and a timon. In at least two-thousand words, describe what happens next.” Go ahead, try it if you want. A curious pattern is likely to emerge. The second most used alien will appear about half as often as the most used alien in your story. The third most used alien will appear about a third as often as the most used alien, and so on, with the eighth most used alien appearing about an eighth as often as the first most used alien.

What word do you think you use the most? Chances are, it is the word “the.” How about the second? Perhaps unsurprisingly, it is the word “be.” In spoken and written English, the word “be” appears about half as often as the word “the.” The third most common word, “to”, appears about one third as often as the word “the.” The 5432nd most common word “grind” appears about 1/5432 times as often as the word “the” in the English language. What accounts for this?

The pattern where the frequency of any word is inversely proportional to its rank is called Zipf’s Law, named after the American linguist George Zipf. Amazingly, Ziph’s Law does not just apply to English. It applies to all languages, from Spanish to Turkish to Zulu to Tamil. Even languages we haven’t translated yet, like Meroitic, have been shown to obey Zipf. When you plot word rank versus frequency, you get a distribution that looks like this, with word rank on the x-axis and relative frequency on the y axis :

This curve, or probability density function, is called the Pareto distribution. Natural language follows a discrete form of the continuous Pareto distribution. When the data are graphed on a log-log scale, you get a straight line. For natural language, it looks something like this:

It’s not just language that is distributed in this way however. City populations roughly follow the Pareto distribution.  Last names, ingredients found in cookbooks and recipes, and earthquake intensities all follow the Pareto distribution. Even the rate at which we forget, the famous Ebbinghaus curve, follows a Pareto distribution.

An interesting outcome from the Pareto distribution is the famous Pareto Principle, which states that in a general situation, 20 percent of the causes are responsible for eighty percent of the outcomes. This idea is everywhere.  Microsoft reported that 80% of the errors in their products came from 20% of the bugs detected. The richest 20% of people have about 80% of the world’s wealth. In a house, about 20% of the carpet receives 80% of the wear. And of course, as we’ve seen, language follows a similar pattern.

How can something as creative and personal as language be described by the strict rules of mathematics? It’s hard to know. Some believe that distribution of words in a language is a compromise between speakers wanting to be as concise as possible and listeners wanting to have as much detail as possible. Beyond language, this curious curve has implications for our understanding of processes as disparate as wealth distribution and memory loss. Why is this? It is fun to hypothesize, but until we know for sure, we can continue to marvel at the strange little function that models so much of our world: the Pareto distribution.

And just for fun:

Sources:

• Power laws, Pareto distributions and Zipf’s law. M. E. J. Newman, Department of Physics and Center for the Study of Complex Systems, University of Michigan, Ann Arbor. https://arxiv.org/pdf/cond-mat/0412004.pdf
• Zipf’s word frequency law in natural language: a critical review and future directions Steven T. Piantadosi. University of Rochester. https://colala.bcs.rochester.edu/papers/piantadosi2014zipfs.pdf
• The Zipf Mystery. Michael Stevens. Vsauce. https://www.youtube.com/watch?v=fCn8zs912OE

Wave to the New Age of Astronomy

The LIGO (Laser Interferometer Gravitational-Wave Observatory) (image courtesy: LIGO)

Ever since their discovery in February 2016, gravitational waves have been making huge ripples in the physics community. These waves are essentially ripples in the fabric of spacetime, caused by intense gravitational interactions. An example is the merging of two black holes, which is actually the event that generated the waves we detected back in February 2016. After the detection of that first black whole merger, three other occurrences have been identified and confirmed in the past two years. You might have also heard that the Nobel Prize in Physics was awarded to three scientists who were tremendously involved in developing the interferometers^I to detect gravitational waves. What used to be uncharted territory, theorized by Einstein over a hundred years ago, is now being heavily explored.

Just a couple weeks ago, another bombshell dropped. After extensive calculations, LIGO and Virgo (two gravitational wave detectors) confirmed that the fifth and most recent blip in their readings, one that did not match the profile of a black whole merger, was actually from the cataclysmic collision of two neutron stars^II. Why is this such a big deal, you ask? For starters, this is the first time gravitational waves have been detected from a source other than a black hole merger. By getting a glimpse at new interactions that have long been shrouded in mystery, we’re standing the very frontiers of current scientific knowledge! Second, this observation has given us great insight into two longstanding hypotheses in astrophysics. It has long been hypothesized that the collision of neutron stars is the cause of high-intensity gamma-ray bursts, an event that unleashes “more energy in a fraction of a second than the sun will pump out in ten billion years.” A mere 1.7 seconds after the gravitational waves were detected, NASA’s Fermi satellite observed gamma rays from the same general area in space, making the relationship between the two events crystal clear. For the following weeks, an arsenal of telescopes were aimed at the patch of the sky from which the gamma-ray burst was observed. By analyzing the spectral linesIII of the embers of the explosion, it was found that heavy radioactive elements were formed, which then decayed into a superabundance of precious metals like gold, silver and platinum. In fact, the gamma-ray burst “could have produced as much gold as the entire mass of the Earth,” upturning the previously popular theory that the majority of the universe’s gold is forged in supernovas. So when you exchange gold rings with your significant other during your wedding ceremony, remember that it was made in the glowing remnants of a catastrophic neutron star collision. Now isn't that romantic?

An artist’s depiction of the aftermath of two neutron stars colliding (image courtesy: NASA)

This gamma-ray burst, given the rather lovely name of GW170817, has given us answers to two prevailing mysteries in astrophysics, made possible only at the intersection of gravitational wave and electromagnetic astronomy.

Gravitational wave astronomy has also given us a richer understanding of the expansion of space. Traditionally, the expansion of the universe has been calculated by measuring the redshift^IV of cosmic objects moving away from us. However, to measure this expansion we need to know the distance between the object and the Earth. Now, this is much easier said than done, requiring extensive distance calibrations with the use of techniques such as ‘standard candle’V observation. However, gravitational waves make things a whole lot easier - the amplitude of the waves received at Earth contain a built-in indication of distance. The arriving waves from GW170817 signified that the event was 130 million lightyears away. Compounding this with redshift measurements allowed astronomers to calculate the Hubble constant, a measure of rate of expansion of the universe, to a greater degree of precision. Electromagnetic measurements calculated Hubble’s constant to be somewhere between 67 and 72 kilometers per second per megaparsec. Gravitational wave astronomers placed this constant right in the middle, at 70 kilometers per second per megaparsec. This value is in full agreement with our existing measurements, while being totally independent of them. This is amazing! Not only does this give us more confidence in our existing astronomic techniques, but also shows the power of gravitational waves - we attained a more precise measurement of the expansion of space through an inherently simpler method. This is the very epitome of scientific advancement.

Gravitational wave astronomy is shedding light (excuse the pun) on the most violent, mysterious high-energy phenomena that traditional electromagnetic techniques have not been able to fully comprehend. It’s giving us a new way to look at interactions in the universe, which in turn gives us new insight. Not only does it give us confirmation of existing observations, but also gives us surprising new knowledge of the universe: black holes are colliding with a greater frequency than we thought; neutron star collisions are the primary causes of gamma-ray bursts and formation of precious metals.

This is only the beginning though. Get wavy - we’re entering a new age in astronomy!

Glossary:

I.           Interferometer: an instrument that measures the interference between two parallel beams of light - the difference in phase indicates how much space has been stretched by gravitational waves.

II.        Neutron stars: these are extremely dense remnants of supernova explosions which are made up entirely of neutrons. The density of a neutron star is comparable to the entire mass of the Earth squeezed into a stack of 10 pennies.

III.     Spectral lines: every element releases characteristic wavelengths of light. By analyzing the light from cosmic objects, we can identify what elements are present.

IV.    Redshift: a process in which light gets stretched as a result of the source moving away from us. This is similar to how an ambulance siren sounds lower-pitched as it moves away from you.

V.       Standard candles: these are certain cosmic objects that always emit light at a specific rate.

References:

1. Hendry, M. (2017). How we discovered gravitational waves from ‘neutron stars’ – and why it’s such a huge deal. [online] The News Minute. Available at: http://www.thenewsminute.com/ article/how-we-discovered-gravitational-waves-neutron-stars-and-why-it-s-such-huge- deal-70324 [Accessed 23 Oct. 2017]. 
2. Drake, N. (2017). Strange Stars Caught Wrinkling Spacetime? Get the Facts. [online] Available at: https://news.nationalgeographic.com/2017/08/new-gravitational-waves-neutron-stars- ligo-space-science/ [Accessed 23 Oct. 2017]. 
3. Scharping, N. (2017). Gravitational Waves Show How Fast The Universe is Expanding. [online] Available at: http://www.astronomy.com/news/2017/10/gravitational-waves-show-how-fast- the-universe-is-expanding [Accessed 23 Oct. 2017]. 
4. Abbot, B. P., et al. (2017). A gravitational-wave standard siren measurement of the Hubble constant. Nature, 551 (7678), pp.85-88.