Seismic Waves and Inversion
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Seismic Waves and Inversion Vandana Chopra Eddie Willett Ben Schrooten Shawn Borchardt. Topics. What are Seismic Waves??????? History Types of Seismic Waves. What are Seismic Waves ???. Seismic waves are the vibrations from earthquakes that travel through the Earth

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  • 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


  • Seismology - the Study of Earthquakes and Seismic Waves

  • 1) Dates back almost 2000 years

History cont
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.

Seismometers and seismographs
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

Types of seismic waves
Types of Seismic Waves

  • Body wavesTravel 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)

Secondary wave s wave
Secondary Wave (S Wave)

  • Secondary or shear (S) wavesa)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.

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.

Rayleigh waves
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.


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


Inhomogeneous constant density 2 d wave equation
Inhomogeneous Constant Density 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

First order wave equation
First 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

Wave equation variables
Wave Equation Variables

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

  • Mass density is ρ

  • Particle velocity is ψ

  • Fluid Pressure is P

  • Three spatial coordinates xi (i=1,2,3) for domain Ω

  • Stress matrix is σij (stress within the fluid)

Conservation of mass and momentum
Conservation of Mass and Momentum


Stress matrix

Kronecker delta function



Some considerations
Some Considerations

Considering small perturbations Δ in

Particle velocity



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

And realizing P0 is constant and fb is negligible we have


The 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 cont1
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 cont2
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 concluded
Derivations Concluded

We have the Acoustic Wave Equation

where is the speed of sound in the medium


  • Seismic Wave Propagation Modeling and Inversion


Reasons for computational methods in seismology
Reasons for Computational methods in Seismology

  • Computer development

    • More 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 coverage
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

Early computer based study
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.

Developments in the 80 s
Developments in the 80’s

  • Many groups compiled algorithms

    • Methods in Computational Physics

    • the two volumes of“Computer Programs in Earthquake Seismology”

    • Other computer code algorithms were also published in the engineering and geophysics literature

Developments up until today
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 1980’s

    • The publication and distribution of seismological software is a major focus

Software packages available
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.


Seismological activity as of 4/4/2002

11:21 AM


  • Seismic Waves: A program for the visualization of wave propagation

    • By Antonello Trova


References and more info
References and more info













  • it interesting, but cannot read Japanese)



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

·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?

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


P wave Velocity (m/s)

S wave Velocity (m/s)

























Sand (Unsaturated)



Sand (Saturated)






Glacial Till (Saturated)



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

Visualizations Done With Seismic Wave Data in Supercomputing shown below.

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

Goals of the project: shown below.

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 shown below.

·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 shown below.

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 shown below.

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 shown below. 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 shown below.

- 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 shown below.

- 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.

Future of this Project shown below.

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 ( 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.



Brian W. Stump and D. Craig Pearson

EES-3, MS-C335

Los Alamos, NM 87545


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: SEISMIC

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,


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 for international monitoring of a CTBT. Primary stations are represented as circles and Auxiliary stations are represented as triangles.

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


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: River Basin compared to SPOT imagery and known locations of the events in coal mines in the region.

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: River Basin compared to SPOT imagery and known locations of the events in coal mines in the region.

Wave Pictures and Movie Source

The GSETT3 Project

The 3D Seismic Wave Propagation Simulation Project

Addition Reading Recommended on mine blasting detection, monitoring of seismic waves caused by Blasting.

Black Thunder mine research with Los Alamos National Labs

THE END River Basin compared to SPOT imagery and known locations of the events in coal mines in the region.