Seismic Waves and Inversion

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• Seismic Waves and Inversion
• Vandana Chopra
• Eddie Willett
• Ben Schrooten
• Shawn Borchardt

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Topics

• What are Seismic Waves???????
• History
• Types of Seismic Waves

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What are Seismic Waves ???

• Seismic waves are the vibrations from earthquakes
  that travel through the Earth
• They are the waves of energy suddenly created by
  the breaking up of rock within the earth or an
  explosion .They are the energy that travels
  through the earth and is recorded on seismographs

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History

• Seismology - the Study of Earthquakes and Seismic
  Waves
• 1) Dates back almost 2000 years

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History ?Cont

• Around 132 AD, Chinese scientist Chang Heng
  invented the first seismoscope, an instrument
  that could register the occurrence of an
  earthquake.
• They are recorded on instruments called
  seismographs. Seismographs record a zigzag trace
  that shows the varying amplitude of ground
  oscillations beneath the instrument. Sensitive
  seismographs, which greatly magnify these ground
  motions, can detect strong earthquakes from
  sources anywhere in the world. The time, location
  and magnitude of an earthquake can be determined
  from the data recorded by seismograph stations.

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Seismometers and Seismographs

• Seismometers are instruments for detecting ground
  motions
• Seismographs are instruments for recording
  seismic waves from earthquakes.
• Seismometers are based on the principal of an
  inertial mass
• Seismographs amplify, record, and display the
  seismic waves
• Recordings are called seismograms

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Types of Seismic Waves

• Body waves Travel through the earth's interior
• Surface Waves
• Travel along the earth's surface - similar to
  ocean waves

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P-Wave(Body Wave)

• Primary or compressional (P) waves
• a) The first kind of body wave is the P wave or
  primary wave. This is the fastest kind of seismic
  wave.
• b) The P wave can move through solid rock and
  fluids, like water or the liquid layers of the
  earth.
• c) It pushes and pulls the rock it moves
  through just like sound waves push and pull the
  air.
• d) Highest velocity (6 km/sec in the crust)

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P-Wave
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Secondary Wave (S Wave)

• Secondary or shear (S) waves a)The second type
  of body wave is the S wave or secondary wave,
  which is the second wave you feel in an
  earthquake.
• b) An S wave is slower than a P wave and can only
  move through solid rock. (3.6 km/sec in the
  crust)
• c) This wave moves rock up and down, or
  side-to-side.

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S-Wave
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L-Wave

• Love Waves
• The first kind of surface wave is called a Love
  wave, named after A.E.H. Love, a British
  mathematician who worked out the mathematical
  model for this kind of wave in 1911.
• It's the fastest surface wave and moves the
  ground from side-to-side.

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L-Wave
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Rayleigh Waves

• Rayleigh Waves
• The other kind of surface wave is the Rayleigh
  wave, named for John William Strutt, Lord
  Rayleigh, who mathematically predicted the
  existence of this kind of wave in 1885.
• A Rayleigh wave rolls along the ground just like
  a wave rolls across a lake or an ocean. Because
  it rolls, it moves the ground up and down, and
  side-to-side in the same direction that the wave
  is moving.
• Most of the shaking felt from an earthquake is
  due to the Rayleigh wave, which can be much
  larger than the other waves.

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Rayleigh Waves
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Seismic Wave Equations
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Outline

• Im going to briefly cover three different
  Seismic wave equations
• -Inhomogeneous Constant Density 2-D Wave
  Equation
• -First Order Wave Equation
• -Acoustic Wave Equation and how its
• derived

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Inhomogeneous Constant Density 2-D Wave Equation

• The pressure wave field is ? and the seismic
  source is src(t)
• Media velocity, C(x,z), the sound speed with x
  being the surface coordinate and z being the
  depth coordinate

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Example of 2-D Wave

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First Order Wave Equation
Again the pressure wave field is ?, the sound
speed is c and x is the surface
coordinate Parameter a is determines the
propagation direction of the wave This is the
simplest wave propagation model
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Example of First Order Wave
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Developing the Acoustic Wave Equation
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Wave Equation Variables

• Mass and Momentum are conserved (basis for
  development of wave equation)
• Mass density is ?
• Particle velocity is ?
• Fluid Pressure is P
• Three spatial coordinates xi (i1,2,3) for domain
  O
• Stress matrix is sij (stress within the fluid)

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Conservation of Mass and Momentum
Momentum
Stress matrix
Kronecker delta function (pseudotensor)
Mass
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Some Considerations
Considering small perturbations ? in Particle
velocity Density Pressure
And with Eulers Equation with the viscosity
equal to zero
And realizing P0 is constant and fb is negligible
we have
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Derivations

• The initial medium is at rest so Eulers
  Equation can be changed to
• eliminating the substantial derivatives.
• Then we let the gradient of F be equal to the
  particle velocity
• giving us

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Derivations cont.
Next we assume the derivatives of space and time
can be changed therefore And removing the
gradient operator on both sides gives us Now
the compressibility C and bulk modulus of K are
defined in terms of a unit volume V and ?V
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Derivations cont.

• The change in the change of fluid pressure P is
  now
• Now computing the derivative of this equation
  with respect to time is
• showing that the change in pressure is related
  to the change in density.
• Then substitutions with this equation gives us

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Derivations cont.

• Now using the conservation of mass equation with
  the previous equation and time derivative gives
  us
• Then using the time derivative again we get
• And finally

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Derivations Concluded

• We have the Acoustic Wave Equation
• where is the speed of sound
  in the medium

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Example of Acoustic Waves
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Sources

• Seismic Wave Propagation Modeling and Inversion
  www.math.fu-berlin.de/serv/comp/tutorials/csep
• www.llnl.gov/liv_comp/meiko/apps/larsen/larsen3.gi
  f

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History of computing in seismology
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Reasons for Computational methods in Seismology

• Computer development
• More memory
• 64k most accessible for single point
• Early 1970s rule of thumb
• 1k for 1K of computer memory
• Used more in the field
• Size shrank explosively from 1960s 1990s
• Data acquisition, processing, and telemetry
• Processing speed increase

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Seismic Station coverage

• Worldwide coverage by a single network of
  computers
• good azimuthal and fair to good depth control
  for major earthquakes
• Brought about software to analyze the data on
  this network

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Early computer based study

• Dorman Ewing surface-wave data inversion in
  1962
• earthquake location by Bolt, 1960 Flinn,
• 1960 Nordquist, 1962 Eaton, 1969)
• Jerry Eaton first to include source code for his
  program
• Credited with opening up software development to
  others
• Computed travel times and derivatives for a
  source inside multiple layers over a half space.

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Developments in the 80s

• Many groups compiled algorithms
• Methods in Computational Physics
• the two volumes ofComputer Programs in
  Earthquake Seismology
• Other computer code algorithms were also
  published in the engineering and geophysics
  literature

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Developments up until today

• A Working Group on Personal Computers in
  Seismicity Studies was created in 1994
• todays personal computers are taking the place of
  mainframes in this field
• This has been the trend since 1980s
• The publication and distribution of seismological
  software is a major focus

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Software packages available

• Here are a few
• CWP/SU Seismic Unix The Instant Seismic
  Processing and Research Environment
• GeoFEM
• A multi-purpose / multi-physics parallel finite
  element
• solver for the solid earth.

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Earthquakes

• Seismological activity as of 4/4/2002
• 1121 AM

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Software

• Seismic Waves A program for the visualization of
  wave propagation
• By Antonello Trova
• http//www.dicea.unifi.it/gfis/didattica.html

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References and more info

• http//www.iris.washington.edu/DOCS/off_software.h
  tm
• http//orfeus.knmi.nl/other.services/software.link
  s.shtml
• http//www.dicea.unifi.it/gfis/didattica.html
• http//www-gpi.physik.uni-karlsruhe.de/pub/martin/
  MPS/
• http//wwwrses.anu.edu.au/seismology/ar98/swp.html
  
• http//www.nea.fr/abs/html/ests1300.html
• http//www.cwp.mines.edu/software.html
• http//www.iris.washington.edu/seismic/60_2040_1_8
  .html
• http//www.es.ucsc.edu/smf/research.html
• http//nisee.berkeley.edu/
• http//www.seismo.unr.edu/ftp/pub/louie/class/100/
  seismic-waves.html
• http//mvhs1.mbhs.edu/mvhsproj/Earthquake/eq.html
• http//www.riken.go.jp/lab-www/CHIKAKU/index-e.htm
  l(found it interesting, but cannot read Japanese)
• http//www.cs.arizona.edu/japan/www/atip/public/at
  ip.reports.99/atip99.043.html
• http//www.engr.usask.ca/macphed/finite/fe_resour
  ces/node162.html

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Seismic Wave Projects
And Visualizations   Talking Team 2
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Why are seismic waves important?   Some things
seismic waves are good for include       
Mapping the Interior of the Earth       
Monitoring the Compliance of the Comprehensive
Test Ban Treaty        Detection of Contaminated
Aquifers        Finding Prospective Oil and
Natural Gas Locations    
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An Example of a Wave Interacting With a
Boundary        
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      http//www.mines.edu/fs_home/tboyd/GP311/MOD
ULES/SEIS/NOTES/Lmovie.html         We Collect
Information from the waves as they are reflected
back to us and as they propagate to the other
ends of the medium.       What would happen if
there was only 1 medium?  
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The P and S wave velocities of various earth
materials are shown below.
The P and S wave velocities of various earth
materials are shown below.
   
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Visualizations Done With Seismic Wave Data in
Supercomputing   3-D Seismic Wave Propagation on
a Global and Regional Scale Earthquakes, Fault
Zones, Volcanoes   Information and Images Source
Prof. Dr. Heiner Igel Institute of Geophysics,
Ludwig-Maximilians-University, Germany   Whats
the purpose of the accurate simulation of seismic
wave propagation through realistic 3-D Earth
Models?          Further understanding of the
dynamic behavior of our planet
       Deterministic earthquake fore-casting,
assessing risks for various zones (i.e. San
Francisco Bay Area)        Understanding active
volcanic areas for risk assessment  
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Goals of the project   1.   Parallelization and
implementation of algorithms for numerical wave
propagation on the Hitachi SR8000-F1   2.  
Verification of the codes and analysis of their
efficiency   3.   First applications to realistic
problems   Before moving into 3-D the base
numerical solutions had to be compared to
analytical solutions for simple (layered) model
geometries.        
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The System used for Simulation     Hitachi
SR-8000 F1     Typical Speed 750Mflops per
node     Internode Transfer Speed
1GB/s       Technical Methods          Numerical
solutions to the elastic wave equations in
Cartesian and spherical coordinates.        Time
dependent partial differential equations are
solved numerically using high-order finite
difference methods        Space-dependent fields
are defined on a 3-D grid and the time
extrapolation is carried out using a Taylor
expansion        Space derivatives are
calculated by explicit high-order
finite-difference schemes that do not necessitate
the use of matrix inversion techniques  
Languages Used          Fortran 90 coupled with
the Message Passing Interface (MPI)    
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Performance   The parallel performance was tested
with a code where all I/O was as in production
runs carried out. An FD algorithm was run for
10 time steps on varying number of nodes.
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Experiments Implemented   Volcano topography in
3-D seismic wave propagation   1.    The seismic
signature of pyroclastic flows   2.    Seismic
sources inside magma chambers and volcanic
dykes   3.       Scattering vs. topographic
effects as observed on Merapi  
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Site effects of the Cologne Basin   -In this
project the first 3D calculation for the area in
Germany with the highest seismic risk the
Cologne Basin were carried out. The simulations
show remarkably good agreement with observed data
as far as the amplitudes for the ground motion is
concerned which tells us that we are on the right
way to be able to predict the possible ground
motion amplification due to 3D structure for this
(and other) areas.  
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The seismic signature of subduction zones     -
Subduction zones contain the largest earthquakes
on Earth. Knowledge of there structural details
not only is important for hazard assessment but
also to understand the dynamics of subduction and
mantle convection. In this project a 3D algorithm
in spherical coordinates was implemented and
earthquakes in subduction zones simulated. We
were able to simulate particular wave effects
observed in nature which in the future can be
used to further constrain the structure of
subduction zones.    
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Fault zone wave propagation   - Fault zones (FZ)
are though to consist of a highly
localized damage zone with low seismic velocity
and high attenuation. The structure of FZs at
depth has important implications for the size of
(future) earthquakes and the dynamic behaviour of
the rupture. Only recently it was observed that
right above FZs a particular wave type (guided
waves) can be observed which may allow imaging
FZs at depth. Numerical simulations play an
important role in developing imaging schemes and
assess their reliability.          
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Future of this Project   a. Wave Propagation in a
heterogeneous spherical Earth (DFG, 2000-2002) b.
The seismic signature of plumes (DFG,
2001-2003) c. The simulation and interpretation
of rotational motions after earthquakes (BMBF,
2002-2005) d. Numerical wave propagation in
seismically active regions (KONWIHR, initially
until 2002, may be further extended). e.
International Quality Network Georisk
(www.iqn-georisk.de) funded by the DAAD,
2001-2003. Will allow students, post-docs,
professors from other countries to visit our
Institute and take part in research projects. In
combination with our simulation algorithms this
may allow us to combine the numerical aspects
with data from regions at risk. Involved
countries USA, Indonesia, China, New Zealand,
Japan. The core of this network is a research
group (1 post-doc, 3 PhD students) residing in
Munich working of risk and hazard related
problems in seismology and volcanology.  
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REGIONAL OBSERVATIONS OF MINING BLASTS BY THE
GSETT-3 SEISMIC MONITORING SYSTEM Brian W. Stump
and D. Craig Pearson EES-3, MS-C335 Los Alamos,
NM 87545     Background   The cessation of
testing of any nuclear explosive devices in all
environments is the goal of the Comprehensive
Test Ban Treaty. In order to assure compliance
with such a treaty, an international monitoring
system has been proposed. This system will
include seismic, infrasound, hydroacoustic and
radionucleide monitors located throughout the
world. The goal of this system is the detection
of any nuclear test.   The monitoring
technologies that are included in the treaty are
designed to detect a nuclear explosion in any
environment and include seismic (50 primary and
120 auxiliary stations), infrasonic (60
stations), hydroacoustic (6 hydrophone and 5
T-phase) and radionuclide (80 stations) sensors
distributed throughout the world
(CD/NTB/WP.330/Rev.2, 14 August 1996). These
sensors and the accompanying data would then
become a part of the International Monitoring
System (IMS) with the collation, analysis and
dispersal of the resulting data and data products
by an International Data Center
(IDC).                
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Purpose of this Project   Mining explosions
generate both ground motion and acoustic energy
that have some characteristics similar to small
nuclear explosions, thus the proposed monitoring
system may detect, locate and characterize some
mining explosions.   In order to gain practical
experience with the seismic component of
worldwide monitoring, a series of empirical tests
in the gathering, exchange and analysis of
seismic data have been conducted under the
auspices of the Conference on Disarmament in
Geneva.   These tests have been titled the Group
of Scientific Experts Technical Tests (GSETT)
with the most extensive and recent test, GSETT-3.
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          An example of a set of seismic stations
that could be used for international monitoring
of a CTBT. Primary stations are represented as
circles and Auxiliary stations are represented as
triangles.
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  Teleseismic Events and Regional
Events   Seismic waves that travel hundreds to
over a thousand kilometers are classified as
regional seismograms because they travel
primarily in the earth's crust. Events that are
only observed regionally are generally smaller
than those observed teleseismically since the
amplitude of the seismic disturbance decays as it
propagates. The right part of Figure 2
illustrates the regional GSETT-2 triggers at
Lajitas. It is interesting to note that these
smaller regional events occur primarily Monday
through Friday and during working hours,
suggesting that they are man made. This data
suggests that a number of these regional signals
may be associated with mining operations, in this
case near surface coal extraction in Northern
Mexico.    
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GSETT-3 included a greater number of seismic
stations, continuous transmission of data and
more detailed analysis of the data than GSETT-2.
This experiment and the resulting data products
allow further insight into the numbers and types
of mining explosions that might be detected by
regional seismic stations.  The fifteen months of
activity represented in Figure 3 suggests that in
an active mining region such as the Powder River
Basin, as many as several events per month might
be expected.    
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Event location is very important in the
assessment of the seismic data. Utilization of
the arrival times of multiple seismic phases at a
single seismic station, relative arrival times at
an array of closely spaced seismometers, and
observations at multiple stations are used to
determine the origin of the events in space and
time as well as some assessment of error in the
estimates.      
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    Figure 4 GSETT-3 events located in the
Southern Powder River Basin compared to SPOT
imagery and known locations of the events in coal
mines in the region.          5 Active mines
outlined in Green Boxes        Ellipses show
GSETT-3 Detections        Detections in many
cases will associate with a region and not a
specific mine with the GSETT-3      
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Conclusions of the Project   Large scale mining
explosions, with the detonation of a large amount
of explosives simultaneously, are observed at
regional (100-2000km) and occasionally
teleseismic (2000-10000 km) distances with
seismic sensors.   As a result of the CTBT
verification system, the largest of these events
will have to be associated with standard mining
operations to avoid the conclusion that the
signal was created by a small nuclear
explosion.   There is a need to implement
techniques designed to reduce seismic amplitudes
to reduce problems with the CTBT detection
system.   Improved understanding of blasting
practices and their effects on regional
seismograms provides the opportunity for improved
monitoring of a CTBT. Similarly, blasting
practices designed to maximize explosive
efficiency while minimizing ground motion within
the mine are exactly those practices best for
reducing both the size and ambiguity of regional
seismic signals.
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Sources   Wave Pictures and Movie
Source http//www.mines.edu/fs_home/tboyd/GP311/MO
DULES/SEIS/NOTES/Lmovie.html  
The GSETT3 Project http//www.geology.smu.edu/dp
a-www/papers/pdf/gsett3.pdf   The 3D Seismic Wave
Propagation Simulation Project http//www.lrz-muen
chen.de/projekte/hlrb-projects/reports/h019z_r1.pd
f     Addition Reading Recommended on mine
blasting detection, monitoring of seismic waves
caused by Blasting.   Black Thunder mine research
with Los Alamos National Labs   http//www.geology
.smu.edu/dpa-www/papers/pdf/blackt.pdf    
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THE END