environmental and exploration geophysics iipages.geo.wvu.edu/~wilson/geol554/lect2/lec2.pdf20% expl...

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Tom Wilson, Department of Geology and Geography

Environmental and Exploration Geophysics II

[email protected]

Department of Geology and GeographyWest Virginia University

Morgantown, WV

TimeTime--distance relationshipsdistance relationshipsRayRay--tracingtracing

Don’t forget to visit the web site for slides and other info -http://www.geo.wvu.edu/~wilson/geol554/lect2/lec2.pdf


I’m often in my office, so feel free to drop by. To be sure I’m not tied up with

something send me an e-mail in advance.

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Grading25% on computer labs,

30% problem sets,

10% mid term exam,

20% Expl project/term report and class presentation,

15% final exam.

Questions about class content and grading? The exploration project?

Have you tried using your class accounts? Go ahead and give that a try now if you already haven’t.


Different kinds of waves … Body Waves

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Surface Waves


Body vs. “Surface” Waves

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In general VR <VL <VS <VP

But this is not strictly true. The Love wave is a surface wave and its velocity will be equal to the shear wave velocity in the upper medium. The Love wave like the Rayleigh wave is also a dispersive wave. That means that deeper Love wave motion usually propagates more rapidly since velocity increases with depth.

Shear waves beneath the surface layers are generally much faster than those in the surface, so in application, the shear waves that we are concerned with generally have higher velocity than the Love waves.


Love waves tend not to be recorded in the conventional seismic survey where the interest is primarily in the recording of P-waves. The geophones used in such surveys respond to vertical ground motion and thus do not respond to the side-to-side vibrations produced by Love waves.

Rayleigh waves produce large vertical displacements and are a significant source of “noise” in the conventional P-wave reflection seismic survey.

Single component vertical motion detectors

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Breaking seismic disturbances down into their component parts

Some nomenclature


time and frequency

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wavelength and wavenumber


Sinusoid arguments

2 2Amplitude = sin or sin

through substitution for or =v , we get two additional forms

2 2Amplitude = sin or sin

x t

x vtvt x

v

π πλ τ

λ τπ πλ τ

=

Temporal

form

Spatial

form

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Some examples of the seismic source


The seismic wavelet

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The wavelet or pulse is a transient disturbance – it comes and goes


Spatial view

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A Wave Packet or Wavelet

Time domain and frequency domain a different way of viewing the time series


Creating a wavelet using a sum of sinusoids

See http://www.geo.wvu.edu/~wilson/geol554/SumofCosines.xls

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The wavelet

Any time series can be represented as a sum of sinusoids


How do mechanical waves get from point A to B

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You can go straight there or …


The reflection events we see in a seismic section don’t start off looking like this

The geologist usually immediately starts to see layers, stratigraphy, depositional history, structure…

Fruitland coals-

San Juan Basin, NM

The

migrated

stack

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When we bang on the ground, the reflection events are mixed together with a variety of other events

This time-distance record shows everything coming in with different shapes, sometimes almost at the same time and sometimes earlier,

sometimes later. A real mess!


Our initial goal is to develop an understanding of the different types of events that appear in a shot record and how to extract information from these observations

and to understand how their travel times (t) vary with source receiver offset (x).

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Some shallow high res data from Marshall Co. WV

Pentolite charges


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Another record from the Marshall Co. site


Migrated stack display-The “geological” display

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Routine logs (ρ, γ, resistivity, July, 07). Sonic Scanner for Acoustic and

Mechanical Properties (March, 08)

Geophysical CharacterizationLogging Effort


Schematic Schlumberger Sonic Scanner

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Pittsburgh Coal

Geophysical CharacterizationMechanical Properties


For the seismic work we take information from sonic and density logs and create a synthetic seismogram

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Migrated stack display-The “geological” display


A shot record is a recording of ground movements produced by a single shot (mechanical disturbance created at some point on or near the earth’s surface).

The recording is made at several locations ideally along a straight line extending in either or both directions away from the source.

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How will the travel times of the direct arrival vary with offset? What will a direct arrival look like in a time distance plot?


Direct Arrival

shot record

Also need to consider the type of direct arrival ...

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Time Distance Plot

Direct Arrival


The reflection event and its time distance relationships-The reflection law

These chalk board slides are just for reference. I’ll set this up independently in class and you’ll find prettier notes in the text.

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The image point


V1

The image point

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( ) ( )212 2hxd +=

Triangles come in quite handy in geophysics


Seismic reflections have a hyperbolic shape in their time-distance representation.

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Reflection time distance curve in basic hyperbolic form


Some basic math probably worth seeing again

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Location of the apex in time


As time goes by reflection events approach start to come in linearly with time. They approach the asymtotes of the hyperbola

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The direct arrival has the relationship of an asymptote to the arrival times of the reflection event.


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21

21

22 4

Vh

Vxt +=From the basic time-distance relationship

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21

212 2or 4

Vht

Vht ==When x = 0, which is the time intercept.

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121

22 or

Vxt

Vxt ≈≈

When x becomes very large with respect to the thickness of the reflecting layer, the x2/V2 term

becomes much larger than the 4h2/V2 term so that


The single layer refraction time-distance relationship - but first -

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The c’s cancel out and we have ...

1 1 2 2 1 21 2

sin sin ; sin sinc cn nV V

θ θ θ θ= =


One of our assumptions -

Assume V1 < V2 < V3

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because sin(π/2) = 1

11 2

2

sin sinVV

θ θ=

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For next time

• Hand in problems 2.1 and 2.2

• Continue your reading of Chapter 2

• Review background on the refraction time-distance relationship

• Look over problems 2.3 and 2.6 for next Monday. These problems will be due next Wednesday,

January 20th.

environmental and exploration geophysics iipages.geo.wvu.edu/~wilson/geol554/lect2/lec2.pdf20% expl...

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