Environmental and Exploration Geophysics II

Environmental and Exploration Geophysics II Energy Loss and Partitioning tom.h.wilson tom.wilson@mail.wvu.edu Department of Geology and Geography West Virginia University Morgantown, WV Tom Wilson, Department of Geology and Geography

Can you name the events? Miller et al. 1995 Tom Wilson, Department of Geology and Geography

Ground roll = noise to the exploration geophysicist Tom Wilson, Department of Geology and Geography

We start off with these noisy looking field records and with some effort get a more geological look at the subsurface Tom Wilson, Department of Geology and Geography

Velocities > VA, VB VC, Vairwave Tom Wilson, Department of Geology and Geography

The seismic diffraction event may seem different than it’s optical cousin This hyperbolic event is an acoustic diffraction But it all boils down to a point Skip to 48 Tom Wilson, Department of Geology and Geography

A conventional look: the optical diffraction http://www.math.ubc.ca/~cass/courses/m309-03a/m309-projects/krzak/index.html Tom Wilson, Department of Geology and Geography

Diffraction (point source) Events Tom Wilson, Department of Geology and Geography

Diffractions, like reflections are hyperbolic in a time-distance plot. They are usually symmetrical about the apex. Diffractions usually arise from point-like discontinuities and edges ( for example the truncated edges of stratigraphic horizons across a fault). Tom Wilson, Department of Geology and Geography

Note that the apex of the diffraction event is not located at X=0. The apex will be located over the location of the discontinuity. Tom Wilson, Department of Geology and Geography

Ray_trace Questions? Tom Wilson, Department of Geology and Geography

Be sure to do the following for all exercises 1) label all plotted curves, 2) label all relevant points and …. Tom Wilson, Department of Geology and Geography

3) Where appropriate, provide a paragraph or so of discussion regarding the significance and origins of the interrelationships portrayed in the resultant time-distance plots. In exercise II for example, how do you account for the differences in the two reflection hyperbola? How is their appearance explained by the equations derived in class for the reflection time-distance relationship. Tom Wilson, Department of Geology and Geography

Re: 3) Discussion - In Exercise III, explain the differences observed in the arrival times of the reflection and diffraction observed in the shot record. Why does the diffraction event drop below the reflection? Tom Wilson, Department of Geology and Geography

As noted earlier - accurately portray the arrival times at different offsets or surface locations. Your plots should serve as an accurate representation of the phenomena in question. Tom Wilson, Department of Geology and Geography

Let’s come back to ray-tracing concepts for a minute and consider the diffraction problem in a little more detail. How would you set up the mathematical representation of diffraction travel time as a function of source receiver distance? Tom Wilson, Department of Geology and Geography

Tom Wilson, Department of Geology and Geography

We’ve taken a few shortcuts here, but we need go no further. We have defined the basic features of the diffraction and we can see how in subtle ways it will differ from that of the reflection. Tom Wilson, Department of Geology and Geography

Questions? Tom Wilson, Department of Geology and Geography

Review - Questions? Tom Wilson, Department of Geology and Geography

Although the time intercept remains the same - how do the shapes of the reflection hyperbola differ in these two cases? Tom Wilson, Department of Geology and Geography

Can you pick out the direct arrival? Can you pick out the refraction arrivals? How many critical refractions are there? How would you determine the refraction velocity? How would you determine the air wave or direct arrival velocity? Tom Wilson, Department of Geology and Geography To calculate the speed of sound go to http://www.measure.demon.co.uk/Acoustics_Software/speed.html

Discussion of Chapter 3: What happens to the seismic energy generated by the source as it propagates through the subsurface? Basic Concepts- Energy - The ability to do work. It comes in two forms - potential and kinetic Work expended (W) equals the applied force times the distance over which an object is moved. Power is the rate at which work is performed. As a mechanical disturbance or wavefield propagates through the subsurface it moves tiny particles back and forth along it path. Particle displacements are continually changing. Hence, it is more appropriate for us to consider the power, or the rate at which energy is being consumed at any one point along the propagating wavefront. Tom Wilson, Department of Geology and Geography

The rate of change of work in unit time. This force is the force exerted by the seismic wave at specific points along the propagating wavefront. Tom Wilson, Department of Geology and Geography

and since force is pressure (p) x area (A), we have The power generated by the source is PS. This power is distributed over the total area of the wavefront A so that We are more interested to find out what is going on in a local or small part of the wavefield and so we would like to know - * Note we are trying to quantify the effect of wavefront spreading at this point and are ignoring heat losses. Tom Wilson, Department of Geology and Geography

Over what surface area is the energy generated by the source distributed? Tom Wilson, Department of Geology and Geography

Area of a hemisphere is 2R2 - hence - This is the power per unit area being dissipated along the wavefront at a distance R from the source. (Recall p is pressure, v is the particle velocity, PS magnitude of the pressure disturbance generated at the source and R is the radius of the wavefront at any given time. Tom Wilson, Department of Geology and Geography

In the derivation of the acoustic wave equation (we’ll spare you that) we obtain a quantity Z which is called the acoustic impedance. Z = V, where  is the density of the medium and V is the interval velocity or velocity of the seismic wave in that medium. Z is a fundamental quantity that describes reflective properties of the medium. We also find that the pressure exerted at a point along the wavefront equals Zv or Vv, where v is the particle velocity - the velocity that individual particles in the disturbed medium move back and forth about their equilibrium position. Tom Wilson, Department of Geology and Geography

Combining some of these ideas, we find that v, the particle displacements vary inversely with the distance traveled by the wavefield R. Tom Wilson, Department of Geology and Geography

We are interested in the particle velocity variation with distance since the response of the geophone is proportional to particle (or in this case) ground displacement. So we have basically characterized how the geophone response will vary as a function of distance from the source. • The energy created by the source is distributed over an ever expanding wavefront, so that the amount of energy available at any one point continually decreases with distance traveled. • This effect is referred to as spherical divergence. But in fact, the divergence is geometrical rather than spherical since the wavefront will be refracted along its path and its overall geometry at great distances will not be spherical in shape. Tom Wilson, Department of Geology and Geography

The effect can differ with wave type. For example, a refracted wave will be confined largely to a cylindrical volume as the energy spreads out in all directions along the interface between two intervals. z R The surface area along the leading edge of the wavefront is just 2Rz. Tom Wilson, Department of Geology and Geography

Hence (see earlier discussion for the hemisphere) the rate at which source energy is being expended (power) per unit area on the wavefront is Remember Zv2 is just Following similar lines of reasoning as before, we see that particle velocity Tom Wilson, Department of Geology and Geography

The dissipation of energy in the wavefront decreases much less rapidly with distance traveled than does the hemispherical wavefront. This effect is relevant to the propagation of waves in coal seams and other relatively low-velocity intervals where the waves are trapped or confined. This effect also helps answer the question of why whales are able to communicate over such large distances using trapped waves in the ocean SOFAR channel. Visit http://www.beyonddiscovery.org/content/view.page.asp?I=224 for some info on the SOFAR channel. Tom Wilson, Department of Geology and Geography

See also - http://www.womenoceanographers.org/doc/MTolstoy/Lesson/MayaLesson.htm Tom Wilson, Department of Geology and Geography

To orient ourselves, you can think of the particle velocity as the amplitude of a seismic wave recorded by the geophone - i.e. the amplitude of one of the wiggles observed in our seismic records. The amplitude of the seismic wave will decrease, and unless we correct for it, it will quickly disappear from our records. Tom Wilson, Department of Geology and Geography

Since amplitude (geophone response) is proportional to the square root of the pressure, we can rewrite our divergence expression as Geophone Output Thus the amplitude at distance r from the source (Ar) equals the amplitude at the source (AS) divided by the distance travelled (r). This is not the only process that acts to decrease the amplitude of the seismic wave. Tom Wilson, Department of Geology and Geography

Absorption When we set a spring in motion, the spring oscillations gradually diminish over time and the weight will cease to move. In the same manner, we expect that as s seismic wave propagates through the subsurface, energy will be consumed through the process of friction and there will be conversion of mechanical energy to heat energy. We guess the following - there will be a certain loss of amplitude dA as the wave travels a distance dr and that loss will be proportional to the initial amplitude A. i.e. How many of you remember how to solve such an equation? Tom Wilson, Department of Geology and Geography

 is a constant referred to as the attenuation factor In order to solve for A as a function of distance traveled (r) we will have to integrate this expression - In the following discussion,let Tom Wilson, Department of Geology and Geography

Mathematical Relationship Graphical Representation Tom Wilson, Department of Geology and Geography

 - the attenuation factor is also a function of additional terms -  is wavelength, and Q is the absorption constant 1/Q is the amount of energy dissipated in one wavelength () - that is the amount of mechanical energy lost to friction or heat. Tom Wilson, Department of Geology and Geography

 is also a function of interval velocity, period and frequency Tom Wilson, Department of Geology and Geography

 is just the reciprocal of the frequency so we can also write this relationship as Tom Wilson, Department of Geology and Geography

Smaller Q translates into higher energy loss or amplitude decay. Tom Wilson, Department of Geology and Geography

increase f and decrease A Higher frequencies are attenuated to a much greater degree than are lower frequencies. Tom Wilson, Department of Geology and Geography

When we combine divergence and absorption we get the following amplitude decay relationship The combined effect is rapid amplitude decay as the seismic wavefront propagates into the surrounding medium. We begin to appreciate the requirement for high source amplitude and good source-ground coupling to successfully image distant reflective intervals. Tom Wilson, Department of Geology and Geography

But we are not through - energy continues to be dissipated through partitioning - i.e. only some of the energy (or amplitude) incident on a reflecting surface will be reflected back to the surface, the rest of it continues downward is search of other reflectors. The fraction of the incident amplitude of the seismic waves that is reflected back to the surface from any given interface is defined by the reflection coefficient (R) across the boundary between layers of differing velocity and density. Tom Wilson, Department of Geology and Geography

Environmental and Exploration Geophysics II