الرياضيات خلف الزلازل - زلزال المغرب | Les Mathématiques Derrière Les Tremblements de Terre - Maroc

Summary

This video examines the mathematics behind earthquakes, specifically the wave equation governing seismic waves, the Richter scale quantifying earthquake magnitude, Poisson distribution for prediction, and Fourier transforms analyzing quake signals. It aims to demonstrate math's real-world applications, inspiring students to appreciate math not just as abstract formulas but a practical tool that can save lives. The speaker stresses math skills enable engineering earthquake-resistant infrastructure and technology aiding rapid response, while guiding future city planning. They encourage pursuing math regardless of major, as its problem-solving and analytical abilities aid all fields, potentially enabling major discoveries benefitting humanity.

Takeaways

• 😀 Understanding math behind earthquakes helps design earthquake-resistant buildings & save lives
• 🌊 The wave equation is like a GPS predicting how seismic waves will move underground
• 📏 The Richter scale calculates earthquake strength on a logarithmic scale
• 🔢 A 7.0 earthquake is 10 times stronger than a 6.0 earthquake
• 😮 Poisson distribution estimates probability of future earthquakes
• 🕵️‍♂️ Fourier transform analyzes complex seismic waves by breaking them into simpler components
• 👷 Math helps civil engineers build earthquake resistant infrastructure
• 🎓 Math inspires students to become scientists and save lives
• ❤️ Math is a universal language to understand the world and solve problems
• ☪️ Math discoveries can benefit the Islamic nation and humanity

Q & A

What is the wave equation and why is it important for understanding earthquakes?

The wave equation describes how seismic waves propagate during an earthquake. Understanding this helps scientists design earthquake-resistant structures and predict seismic wave patterns to anticipate earthquake damage.

How does the Richter scale quantify earthquake magnitude?

The Richter scale uses a base-10 logarithmic scale to assign a single number to quantify earthquake magnitude. This allows extremely large numbers to be expressed in a short and understandable way.

Why is the Richter scale logarithmic instead of linear?

A linear scale would imply an earthquake of magnitude 7 is only one time stronger than a 6.0 quake. But in reality, each integer increase represents a 10-fold jump in strength, so logarithmic scaling more accurately captures this exponential growth in power.

How do scientists try to statistically predict earthquakes?

Seismologists use the Poisson probability distribution to estimate future earthquake likelihood based on the long-term average rate at which quakes occur in a region. However, this cannot pinpoint exact quake dates and times.

What does the Fourier transform do?

The Fourier transform breaks down a complex seismic signal into its constituent frequencies. This allows scientists to analyze the earthquake's characteristics, such as depth and damage potential, from the signal components.

How can understanding the math behind earthquakes save lives?

Knowing mathematical earthquake models helps engineers build resistant infrastructure. It helps scientists anticipate damage, guide emergency response, and identify at-risk regions for better preparation and land-use planning.

What skills are developed by learning the mathematics presented?

These mathematical concepts build problem decomposition, quantitative reasoning, and critical thinking abilities useful for science, engineering, data analytics, and more.

Why study math if you don't want a STEM career?

Mathematics is a universal language for understanding the world, applicable across disciplines. Learning math enhances one's ability to interpret patterns, analyze information, and make informed decisions.

How can mathematics benefit the Islamic community specifically?

Applying mathematical knowledge to develop life-saving seismic engineering, prediction methods, emergency plans, etc. serves the values of protecting human life and welfare in Islamic communities.

What message does the video try to convey about mathematics?

It aims to show that math is not just abstract concepts but a practical tool to comprehend real world phenomena, identify patterns, and solve impactful problems facing society.

Outlines

00:00

😢 Opening with condolences for earthquake victims

The video opens by offering condolences for the victims of the recent earthquake in Morocco. It expresses sympathy for the dead, injured, and displaced, and prays for God's mercy and relief. The speaker then explains his motivation for making the video is to help people understand earthquakes mathematically in order to design earthquake-resistant infrastructure and anticipate risks.

05:02

📏 Explaining the mathematical Wave Equation behind earthquakes

This section introduces the Wave Equation that models seismic waves. It explains each component of the equation step-by-step. In essence, the equation predicts how seismic waves will propagate based on their speed and shape. This helps engineers design earthquake-resistant buildings and helps predict how different areas will be impacted.

10:04

📈 Breaking down the Richter Scale equation

Here the video analyzes the logarithmic Richter Scale formula used to measure earthquake magnitude or strength. It explains why a logarithmic scale is used and how each unit of increase represents a 10-fold rise in wave amplitude and energy released. This allows easy interpretation of an earthquake's severity and expected impact.

🔮 Using Poisson Distribution to predict earthquakes

This portion discusses using Poisson Distribution in statistics to model earthquake probability over time. It allows seismologists to forecast likelihood of earthquakes by analyzing patterns in historical data. However, it cannot predict exact timing. Still it aids preparedness efforts.

🕵️‍♂️ Breaking down earthquakes signals with Fourier Transforms

Finally, the video introduces Fourier Transforms used to analyze the complex seismic wave signals produced by earthquakes. It allows the waves to be decomposed into more understandable components that reveal insights about the quake itself. This is a core technique in engineering and data science.

Keywords

💡seismic waves

Seismic waves are the waves generated by earthquakes that travel through the earth. Understanding how seismic waves propagate allows scientists to design earthquake-resistant infrastructure and predict the impact of earthquakes. The video discusses the wave equation that describes seismic wave motion.

💡Richter scale

The Richter scale is the standard measurement for assessing the strength or magnitude of earthquakes. It allows earthquakes to be quantitatively compared. The video explains why the Richter scale uses a logarithmic formula rather than a linear scale.

💡Poisson distribution

The Poisson distribution in statistics describes the probability of a number of events happening over a timeframe. Seismologists use it to predict the likelihood of future earthquakes based on past seismic activity.

💡Fourier transform

The Fourier transform is a mathematical technique to break down complex seismic signals into simpler components. This allows scientists to analyze the earthquake signals and understand critical characteristics.

💡wave equation

The wave equation mathematically describes how seismic waves propagate through a medium like the earth. It relates wave speed, shape, and amplitude changes over time and space.

💡earthquake prediction

A major goal of seismology is to be able to reliably predict when and where earthquakes will occur. This remains an imprecise science but statistical techniques like the Poisson distribution provide some earthquake forecast capability.

💡earthquake resilience

Understanding seismic wave propagation enables engineers to design infrastructure and buildings that are resilient against earthquake damage. This can save lives and reduce harm.

💡seismology

Seismology is the scientific study of earthquakes - their causes, effects, and characterization. The video illustrates how mathematics is fundamental to advancing seismology.

💡logarithm

Logarithms allow numbers that range across multiple orders of magnitude to be easily compared. This makes them useful in the context of the Richter scale for quantifying earthquake strength.

💡wave characteristics

Properties like wave amplitude, frequency, speed, shape, and direction of propagation characterize seismic waves and contain information about the earthquake source. Mathematical techniques help decipher these wave characteristics.

Highlights

The wave equation is the DNA of seismic activity and helps design earthquake-resistant buildings.

The Richter scale provides a universal language for discussing earthquake strength.

A 7.0 earthquake is 10 times stronger than a 6.0 due to the logarithmic scale.

The Poisson distribution helps estimate future earthquake probability based on past activity.

Humans still can't predict exact earthquake dates and times.

Log, exponential, and probability functions help understand natural phenomena.

The Fourier transform breaks down complex seismic signals into simpler components.

Identifying waveform components helps assess earthquake damage.

Fourier transforms are used in many fields from sound waves to finance.

Math is a universal language we use to understand the world.

Math helps solve real-world problems even in arts and social sciences.

Math is a useful tool for anyone to understand and participate in the world better.

Great math discoveries can benefit humanity.

Share math videos to show math's importance in daily life.

Math is more than equations - it's understanding phenomena to save lives.

Transcripts

Salam Alaykum

first, my sincere condolences to the victims of the earthquake that occurred yesterday,

may ALLAH have mercy

and may ALLAH grant relief to those who remained alive, and someone from his family died, or lost his home, or suffered harm in his health,

may ALLAH make it a forgiveness of sins

Secondly, why did I make this video?

Because in order to know how to deal with something, you have to understand it,

and to understand it, you have to know how it works.

Mathematics is the codebreaker that our Creator put for us in order to decipher this mysterious world,

starting from the movements of the atom to the rotation of galaxies in their orbits.

Why do you have to watch the video?

This video is very important so that you know why you study mathematics,

starting from high school and above,

and so that you do not feel absurd when you study what you study.

Anything in mathematics has an application on the ground

and can save lives or benefit humanity, ALLAH willing, if you specialize more

in this video, I'm going to talk quickly about the Wave Equation

which is the DNA of seismic activity,

and then I'm going to introduce you to the math behind the Richter Scale that you hear day and night,

which is like a loudspeaker that makes us hear the Earth's words,

and then we'll go through the approximate way that seismologists try to predict earthquakes,

although they have not yet reached a fixed equation,

and finally, how to analyze the fine details of earthquakes using the Fourier transform

Let us begin, with the blessing of ALLAH Almighty

In the name of ALLAH

The first thing to start with when looking into the mathematics behind earthquakes is the wave equation

Why?

Because seismic waves are what make an earthquake an earthquake.

Understanding this equation and delving into it helps us to design and build anti-seismic buildings that do not fall.

At the same time, it helps us to know how people felt the earthquake from their different places.

The wave equation is like a guide for seismic waves

especially those that occur after the earthquake. The first, which is called a back wave

is as if you were throwing a stone into a pond, and just like that...

The equation is something like this

do not panic, we will decompose it part by part.

This symbol is called the partial derivation

which is, in short, if there is a function with two variables

that means not only f (x) but f (x, y), and you want to derive it,

then here the function derives either with respect to x or with respect to y

if you derive it with respect to x, then you consider y as a fixed number,

and if it is by itself, then its derivation is 0, just like any constant,

and if you derive it with respect to y, then you consider x as a fixed number,

and also if it is by itself, then its derivation is 0

so we call this process partial derivation, and we denote it with delta, which is diminutive of the letter D

As for the "square exponent" located above and below, it means that we derive the function u twice for the variable t

This part is basically as if you are asking: How does the height of the seismic wave change over time?

The value c is the speed of the wave raised to the square power

and it tells us the speed at which the seismic wave travels underground

and this means that it travels c times faster

and finally, this part is similar to the first part, the difference here is that we derive the function twice with respect to the variable x

this part tells us about the height of the waves in Different regions of the Earth

after decoding this equation, what does it tell us?

Simply the equation tells you: based on the shape of the wave and its speed, this is what will happen later.

Imagine that this equation is like GPS.

The GPS is trying to predict the time you will reach your destination based on the speed you are traveling and the distance that you will travel

This equation also helps seismologists predict how seismic waves will move based on the speed and shape of the wave

Why is this equation important? Imagine that you live in an area prone to earthquakes.

If seismologists can use this equation to predict how seismic waves will move,

then engineers will be able to design earthquake-resistant homes and buildings

It is as if you knew the storm was coming so you quickly closed the windows

meaning you anticipate events

As for young people who are studying

perhaps you are asking yourselves: “What do I do with all this?”

But you have to understand the basics like this equation will help you to actually understand the world around you

and who knows? May all this inspire you to become a seismologist who anticipates their occurrence and saves people's lives,

ALLAH willing...

He said that the epicenter of the earthquake is located in the southwest region of Marrakesh,

and according to the National Institute, the strength of the earthquake reached 7 degrees and two-tenth of a degree on the Richter scale.

What does this number mean?

and why is a magnitude 7.0 earthquake 10 times stronger than a magnitude 6.0 earthquake? Let's find out

why the Richter scale is so important?

First, this scale - which was invented by the American seismologist Charles Francis Richter -

is a way to calculate the strength of earthquakes.

This scale provides us with a universal language for discussing and understanding the strength of earthquakes.

You can consider it like the scale by which we measure the heartbeat

The formula that Richter used in his book Elementary Seismology was this:

where M is the magnitude or level of the earthquake’s magnitude

which is what we are looking for, that number you always hear about in the news.

A is the amplitude of the wave

meaning it is the height of the waves that arose due to the earthquake,

The longer the wave, the more energy it contains.

T is the wave period,

means the time it takes for one wave to pass through one specific point.

Finally, the logarithm with base 10

which helps us a lot to deal with very large or very small numbers easily

because if you have a Log of a large number, for example, the log of base 10 for the number one million, for example... the result will be 6

and thus gives us a scale that we can read even though the numbers are very large

now, why is this formula for Richter’s scale logarithmic and not linear?

Because if it is linear... in order to go from 1 to 2 to 3, it must increase by the same amount each time.

This means that an earthquake with a magnitude of 7 will be only one time stronger than an earthquake with a magnitude of 6.

But this is not the reality on the ground.

On the Richter scale, when you go from scale 6 to scale 7

it means that an earthquake with a magnitude of 7 is about 10 times stronger than an earthquake with a magnitude of 6

This is why the logarithm helps us.

If you understand the Richter scale, you will be able to assess the severity of the earthquake

An earthquake with a magnitude of 4.0 can move the dishes in the kitchen,

but a 7.0-magnitude earthquake can bring down the whole house on you

Thank ALLAH that the earthquake that hit Morocco did not strike in an urban area As big as Marrakesh or Agadir

Although it struck in a rural area, and look how many victims have died,

more than 2,100 have died so far.

If it struck in a large urban area, it would have been tens of thousands of dead victims and millions of homeless

may ALLAH Almighty protect us

Can we predict when earthquakes will occur?

We all ask ourselves this question

because if we could, we could avoid a lot of misfortunes that could happen.

What does mathematics say about this matter?

Seismologists use what's called the Poisson Distribution

to try to estimate when an earthquake might occur

The formula for the Poisson Distribution is like this:

Complicated, isn't it? Don't worry... P(x, lambda) tells us the probability of x number of events occurring in a given time frame

which is the probability of x number of earthquakes occurring in a given time frame

Lambda is the average event rate

for earthquakes, the average is the number of times earthquakes occur somewhere during a given period,

such as a year, a decade, or a century

x! It is an arithmetic operation

For example, for a factorial number 3, it is equal to 3 times 2 times 1.

i.e. a factorial number is that you multiply that number by the number before it and you multiply until you reach 1

Finally, e, which is a constant in mathematics, equals approximately 2.718,

and is found everywhere in nature, from population growth to radioactive decay

Simply put, this formula helps seismologists predict the possibility of earthquakes in the future based on the activity of earthquakes in the past

Imagine it like weather forecasters

using weather data for the past years to guess whether this or that day in the next month, for example, will rain or not...

Likewise, seismologists use data from past earthquakes to predict earthquakes in the future.

The problem is that this Poisson distribution cannot predict the exact day and time of an earthquake.

This level is still beyond the reach of humans

but it gives you an approximate bird's-eye view

if seismologists knew that maybe in the next 10 years, a big earthquake might strike somewhere

the concerned country will try to avoid building in the vicinity of that place,

and they will be more prepared and will carry out more awareness campaigns.

As for the pupils and students... Here you see how the logarithmic, exponential, and probability functions are very important

because they make us understand many of the natural phenomena surrounding us

which we can benefit the nation with, ALLAH willing...

We have now come to the last piece of our puzzle, and the most difficult of all

the Fourier Transformation

This transformation makes you become like Detective Conan, but for earthquakes... How so?

An earthquake is not a simple thing.

When an earthquake occurs in a specific focus,

imagine the number of complex vibrations that cause the Earth to move up, down, forward, and backward

Literally, it is very complicated... And here comes the role of the Fourier transform investigator,

because it takes all this chaos and he breaks it down into individual pieces that we can understand...

as if you were taking apart an intertwined puzzle in order to see each piece clearly...

The Fourier transform equation is a little complicated

It is very complex... But be patient and let's break it down one by one

F(k) is the answer we're trying to find

That's where the components of frequency are, which are the individual pieces of the puzzle

f(x) is the original complex signal from the earthquake... and it's the whole puzzle...

This part makes us look at each frequency separately, meaning each individual piece we can see alone, isolated from the rest of the pieces...

and finally, this integration, which simply means we add up all the little pieces to get the whole picture.

The equation simply says:

If you give me this complex sign f(x), I can decompose it into its individual blocks and pieces, which is F(k)

Imagine it as if I gave you a sentence and you broke it down into individual words to try to understand it word by word...

this is exactly what the Fourier transform does, breaking down complex seismic waves into simpler components.

Identifying those components helps scientists understand the type of earthquake that occurred, its depth, and the type of damage it might have caused.

It's like forensics, but for earthquakes,

and this information can be very important for rapid response and future planning.

This Fourier transform is taught by post-secondary students

and it helps a lot if you want to become an engineer, a scientist, or even a data analyst

because you always have to decompose a big problem into simpler parts, and this is a skill that you will use in your entire life

whether you're dealing with earthquakes, sound waves, or finance

Finally

I ask Almighty ALLAH to have mercy on our deaths and the deaths of all Muslims

and if you enjoyed this video, please share it so that people realize the importance of mathematics

in our daily life and our practical life

and how we can save lives with it

instead of following calamities and wasting our time

mathematics is not only about numbers and equations

but a universal language that we use to understand the world around us

and you don't have to be very smart

to understand how it can help us solve real-world problems.

and even if you were planning to pursue science

technology and engineering or even arts and social sciences

math is always a tool that helps to understand the world and participate in it in a much better way

Before I finish

I would like to remind everyone that the mathematical notions we have been discussing are just tools

and like any tool… they are most useful in the hands of those who understand and respect their potential

so whether you are a freshman in high school or advanced in your career

it is never too late to start learning

who knows?

You may be the one who will make a great discovery that will benefit the Islamic nation and all of humanity.

This is all there is to it.