seismic rays and the interior of the earth
DESCRIPTION
Seismic Rays and The Interior of the Earth. Dusty Wilson Tina Ostrander Eric Baer With lots of great help from Logan Wallace and Tim Minalia. The Problem:. How do we know what is beneath our feet?. How can we find out about the Interior of the Earth?. The deepest a human has ever gone: - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/1.jpg)
Seismic Rays and The Seismic Rays and The Interior of the EarthInterior of the Earth
Dusty WilsonDusty WilsonTina OstranderTina Ostrander
Eric BaerEric BaerWith lots of great help fromWith lots of great help from
Logan Wallace and Tim MinaliaLogan Wallace and Tim Minalia
![Page 2: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/2.jpg)
The Problem:The Problem:
How do we know what is beneath our feet?
![Page 3: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/3.jpg)
How can we find out about the How can we find out about the Interior of the Earth?Interior of the Earth?
• The deepest a human has ever gone:• The deepest well ever drilled:• The deepest a rock has ever been
retrieved from:• The center of the Earth:
10 km
250 km6370 km
3 km
![Page 4: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/4.jpg)
Seismic WavesSeismic Waves
• Formed when earthquakes occur
![Page 5: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/5.jpg)
Seismic compression wave velocitySeismic compression wave velocity
In air 0.344 km/secIn water 1.5 km/secIn Jello 4 km/secIn glass 4.5 km/secIn rocks 7-15 km/sec
![Page 6: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/6.jpg)
We can measure the arrival timesWe can measure the arrival times
![Page 7: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/7.jpg)
So, lets use this information… So, lets use this information…
• Could the Earth be entirely made of blue cheese?
• Seismic velocity through blue cheese is 5 km/sec
![Page 8: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/8.jpg)
An Earth made of cheeseAn Earth made of cheese
40
80
120
150180
0Geocentric
Angle (degrees)
raypath length
(km)
TravelTime(s)
TravelTime(min)
0
40
80
120
150
180
12760 km
![Page 9: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/9.jpg)
An Earth made of cheeseAn Earth made of cheese
40
80
120
150180
0Geocentri
cAngle
(degrees)
raypath length(km)
TravelTime(s)
TravelTime(min)
0 0 0 040 4357 871 14.5
80 8189 1638 27.29 120 11050 2210 36.8 150 12305 2461 41180 12760 2552 42.5
![Page 10: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/10.jpg)
Remember, it has to match what Remember, it has to match what we measure!we measure!
![Page 11: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/11.jpg)
Does it work?Does it work?Geocentri
cAngle
(degrees)
raypath length(km)
TravelTime(s)
TravelTime(min)
0 0 0 040 4357 871 14.5 80 8189 1638 27.29
120 11050 2210 36.8 150 12305 2461 41180 12760 2552 42.5
![Page 12: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/12.jpg)
Can any work? Can any work?
• No single velocity• Upper Earth is
slower than deep Earth
15 1212 10 8
5
![Page 13: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/13.jpg)
So what about an Earth with 2 So what about an Earth with 2 layers?layers?
??
![Page 14: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/14.jpg)
RefractionRefraction• When a wave
changes speed it bends
• The amount of bending is given by Snell’s law
A V1
V2B
Sin (A) V1
V2Sin (B)
=
![Page 15: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/15.jpg)
So what about an Earth with 2 So what about an Earth with 2 layers?layers?
![Page 16: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/16.jpg)
Unfortunately, that does not Unfortunately, that does not work either…..work either…..
We need more layers!
Call in the mathematician!
![Page 17: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/17.jpg)
Mathematical OverviewMathematical Overview
• A description of the problem• The mathematics of the solution• Examples of two models • Lessons learned for next time
![Page 18: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/18.jpg)
A Description of the ProblemA Description of the Problem
• Create an algorithm to model the path of a seismic ray through a planetary body.– Assume an arbitrary number of layers (or
shells) in the planetary model.– Assume rays travel at a constant velocity
through each layer.– Assume the trajectory of each ray changes as
the ray changes layers, subject to Snell’s law.
![Page 19: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/19.jpg)
The MathematicsThe Mathematics
• The mathematics of this project required topics found at pre calculus level.– The Law of Cosines– The Quadratic Formula– Rotation of Axes
![Page 20: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/20.jpg)
Law of CosinesLaw of Cosines
• Law of Cosines
• Solve for C by sub-tracting A2 from both sides of the equation
2 2 2 2 cosA B BC C a
2 2 20 2 cosB aC C B A
![Page 21: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/21.jpg)
The Quadratic FormulaThe Quadratic Formula
• This equation (below) is quadratic in C:
• Which can be solved using the quadratic formula:
• Do I choose “+” or “–”?
2 2 2 21 2 cos 4 cos 42
B a B a B AC
2 2 20 2 cosB aC C B A
![Page 22: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/22.jpg)
Rotation of AxesRotation of Axes
• After the ray travels through the outer layer, all subsequent paths are determined by an angle made with a tangent.
• This requires a rotation of axes by the angle Ө., cos sin , sin cosx y x y x y
![Page 23: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/23.jpg)
ExamplesExamples
• Example 1: A model using two layers.
• Example 2: The PREM model which uses 74 layers to model the Earth.
![Page 24: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/24.jpg)
Example 1: A Two Layer ModelExample 1: A Two Layer Model
• The earthquake takes place at the N. Pole.
• Waves are sent out in all directs at once.
• The model shows individual ray paths – but all begin at the same time.
• The waves bend subject to Snell’s Law
![Page 25: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/25.jpg)
Example 1: Angle vs. TimeExample 1: Angle vs. Time
• The graph shows angle (around the globe) from the rays start to finish versus the time for the way to travel through the model.
• The “discontinuity” correlates to the layer change.
![Page 26: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/26.jpg)
Example 2: The PREM ModelExample 2: The PREM Model
• The Preliminary Reference Earth Model (PREM) is a current model used by geologists to understand the interior of the Earth
• It uses 74 layers to model the physical results of seismographs.
![Page 27: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/27.jpg)
Example 2: Angle vs. TimeExample 2: Angle vs. Time
• This output from seismic algorithm models the actual output of seismographs around the world.
![Page 28: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/28.jpg)
Lessons LearnedLessons Learned
• Mathematics is difficult when “the answer is not in the back of the book”
• Documentation and prep work is well worth the time
• Mathematics doesn’t need to be sophisticated to pose a serious challenge
• Mathematica – beautiful yet aggravating• Challenges lead to excitement (and …)
![Page 29: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/29.jpg)
That’s all fine and good, but That’s all fine and good, but we need something a student we need something a student
can use!can use!
![Page 30: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/30.jpg)
Why We Used JavaWhy We Used Java
• Graphical User Interface (GUI)• Web based Applets
– Runs in a browser– Platform Independent– Can be accessed from anywhere
MyProgram.jaMyProgram.javava
MyProgram.clMyProgram.classass
compile
![Page 31: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/31.jpg)
Program DevelopmentProgram Development
AnalyzeDocument
Debug
Test Code
Design
![Page 32: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/32.jpg)
RealData
ConverterLine
Graph
InputPanel
LineManager
Display
ProgramDesign
![Page 33: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/33.jpg)
Code TranslationCode TranslationNextj_,n_: Module0,1,v0,v1,
0 THETAj;Known angle within layer nearer the surfacev0 VelocityWInLayernj;Layer neared the surfacev1 VelocityWInLayernj1;Layer nearer the center1 ArcSinv1Sin
2 0
v0;Angle found with Snell's Law near the center
AppendToALPHA,1public static void nextSymAlpha() {
double symTheta0 = theta[j-1];
double v0 = velocityWInLayer[nLayers-j-1];
double v1 = velocityWInLayer[nLayers-j];
double symAlpha1 = Math.asin((v1*Math.sin((Math.PI/2)-symTheta0))/v0);
alpha = appendTo1D(++alphaIndex, symAlpha1, alpha); }
Java
Mathematica
![Page 36: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/36.jpg)
Some final notes…Some final notes…• This project required all of our expertise• The only place a project like this could
happen is at a community college• Many times we face problems that require
knowledge and expertise from outside of our field
• The result is an amazing learning opportunity for students!
![Page 37: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/37.jpg)
Questions?Questions?
• Afterwards you are welcome to try the Java program
![Page 38: Seismic Rays and The Interior of the Earth](https://reader036.vdocuments.us/reader036/viewer/2022081502/56815ded550346895dcc177d/html5/thumbnails/38.jpg)
How to use the programHow to use the program
• Turn on a laptop• Press cntrl-alt-del• Log on as FRCuser • No Password• Log on to : (this computer) • Start seismicGraph document on the
desktop (not the folder)