Seismic Waves and Inversion

Vandana ChopraEddie WillettBen SchrootenShawn Borchardt

Topics Topics

What are Seismic Waves???????

History

Types of Seismic Waves

What are Seismic Waves ???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

HistoryHistory Seismology - the Study of Earthquakes and

Seismic Waves 1) Dates back almost 2000 years

History History ContCont

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.

Seismometers and Seismometers and SeismographsSeismographs

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

Types of Seismic WavesTypes of Seismic Waves

Body waves Travel through the earth's interior

Surface Waves Travel along the earth's surface - similar to

ocean waves

P-Wave(Body Wave)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)

P-Wave P-Wave

Secondary Wave (S Wave) 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.

S-WaveS-Wave

L-WaveL-Wave

Love WavesThe 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.

L-WaveL-Wave

Rayleigh WavesRayleigh 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.

Rayleigh WavesRayleigh Waves

Seismic Wave EquationsSeismic Wave Equations

OutlineOutline

I’m 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 it’s

derived

Inhomogeneous Constant Inhomogeneous Constant Density 2-D Wave EquationDensity 2-D Wave Equation

The pressure wave field is ψ 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

Example of 2-D WaveExample of 2-D Wave

First Order Wave EquationFirst Order Wave Equation

Again the pressure wave field is ψ, the sound speed is c and x is the surface coordinate

Parameter α is determines the propagation direction of the wave

This is the simplest wave propagation model

Example of First Order WaveExample of First Order Wave

Developing the Acoustic Developing the Acoustic Wave EquationWave Equation

Wave Equation VariablesWave Equation Variables

Mass and Momentum are conserved (basis for development of wave equation)

Mass density is ρParticle velocity is ψFluid Pressure is PThree spatial coordinates xi (i=1,2,3) for

domain ΩStress matrix is σij (stress within the fluid)

Conservation of Mass and Conservation of Mass and MomentumMomentum

Momentum

Mass

Stress matrix

Kronecker delta function(pseudotensor)

Some ConsiderationsSome ConsiderationsConsidering small perturbations Δ inParticle velocityDensityPressure

And with Euler’s Equation with the viscosity equal to zero

And realizing P0 is constant and fb is negligible we have

DerivationsDerivationsThe initial medium is at rest so Euler’s Equation can be changed to

eliminating the substantial derivatives.

Then we let the gradient of Φ be equal to the particle velocity

giving us

Derivations cont.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 ΔV

Derivations cont.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

Derivations cont.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…

Derivations ConcludedDerivations Concluded

We have the Acoustic Wave Equation

where is the speed of sound in the medium

Example of Acoustic WavesExample of Acoustic Waves

SourcesSources

Seismic Wave Propagation Modeling and Inversion www.math.fu-berlin.de/serv/comp/tutorials/csep

www.llnl.gov/liv_comp/meiko/apps/larsen/larsen3.gif

History of computing in History of computing in seismologyseismology

Reasons for Computational Reasons for Computational methods in Seismologymethods in Seismology

Computer developmentMore memory

64k most accessible for single point Early 1970’s rule of thumb

1k for 1K of computer memory

Used more in the field Size shrank explosively from 1960’s – 1990’s Data acquisition, processing, and telemetry

Processing speed increase

Seismic Station coverageSeismic Station coverage

Worldwide coverage by a single network of computers good azimuthal and fair to good depth

control for major earthquakesBrought about software to analyze the data on

this network

Early computer based studyEarly 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.

Developments in the 80’sDevelopments in the 80’s

Many groups compiled algorithmsMethods in Computational Physicsthe two volumes of“Computer

Programs in Earthquake Seismology”Other computer code algorithms were

also published in the engineering and geophysics literature

Developments up until todayDevelopments up until today

A Working Group on Personal Computers in Seismicity Studies was created in 1994todays personal computers are taking

the place of mainframes in this fieldThis has been the trend since 1980’sThe publication and distribution of

seismological software is a major focus

Software packages availableSoftware packages available

Here are a fewCWP/SU: Seismic Unix: The Instant Seismic

Processing and Research Environment

GeoFEM A multi-purpose / multi-

physics parallel finite element

solver for the solid earth.

EarthquakesEarthquakes

Seismological activity as of 4/4/2002

11:21 AM

SoftwareSoftware

Seismic Waves: A program for the visualization of wave propagationBy Antonello Trovahttp://www.dicea.unifi.it/gfis/didattica.html

References and more infoReferences and more info http://www.iris.washington.edu/DOCS/off_software.htm http://orfeus.knmi.nl/other.services/software.links.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.html(found it interesting, but cannot read

Japanese) http://www.cs.arizona.edu/japan/www/atip/public/atip.reports.99/atip99.043.html http://www.engr.usask.ca/~macphed/finite/fe_resources/node162.html

 

Seismic Wave Projects

And Visualizations

 Talking Team #2

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  

An Example of a Wave Interacting With a Boundary    

 

  

http://www.mines.edu/fs_home/tboyd/GP311/MODULES/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? 

Material P wave Velocity (m/s) S wave Velocity (m/s)

Air 332  

Water 1400-1500  

Petroleum 1300-1400  

Steel 6100 3500

Concrete 3600 2000

Granite 5500-5900 2800-3000

Basalt 6400 3200

Sandstone 1400-4300 700-2800

Limestone 5900-6100 2800-3000

Sand (Unsaturated) 200-1000 80-400

Sand (Saturated) 800-2200 320-880

Clay 1000-2500 400-1000

Glacial Till (Saturated) 1500-2500 600-1000

     

The P and S wave velocities of various earth materials are shown below.

Visualizations Done With Seismic Wave Data in Supercomputing 

3-D Seismic Wave Propagation on a Global and RegionalScale: Earthquakes, Fault Zones, Volcanoes Information and Images Source: Prof. Dr. Heiner IgelInstitute 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  

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.

    

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)  

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.

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 

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. 

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.

  

Fault zone wave propagation

 - Fault zones (FZ) are though to consist of a highly localizeddamage 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.

     

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. 

REGIONAL OBSERVATIONS OF MINING BLASTS BY THE GSETT-3 SEISMICMONITORING SYSTEM

Brian W. Stump and D. Craig PearsonEES-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).     

  

 

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.

    

 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.

 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.  

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.

  

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.

   

  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   

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.

Sources: Wave Pictures and Movie Sourcehttp://www.mines.edu/fs_home/tboyd/GP311/MODULES/SEIS/NOTES/Lmovie.html 

The GSETT3 Projecthttp://www.geology.smu.edu/~dpa-www/papers/pdf/gsett3.pdf The 3D Seismic Wave Propagation Simulation Projecthttp://www.lrz-muenchen.de/projekte/hlrb-projects/reports/h019z_r1.pdf  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  

 THE END