4/5/2014

Based on observing the passage of soundwaves through Earth

Methods used in industry

Refraction Seismology

Uses wave arrival times as a function of distance

Based on changes in wave speed/direction with depth

Reflection Seismology

Based on reflection of waves off discontinuities in the subsurface

PROS CONS

Less equipment; cheaper

Less processing

Easier to model results

Distance between source and receiver must be larger

Only works where wave speed increases with depth

Limited to simple subsurface geometry

PROS

CONS Distance between source can be small

Can accommodate any subsurface velocity structure

Can deal with complex subsurface geology

Data set contains more information

Directly image subsurface

Needs more equipment; more expensive

Data processing is complex and computer intensive

Data interpretation requires more sophistication and knowledge

REFRACTION REFLECTION

Used for small scale projects

Used in environmental consulting, geotechnical work

Used by oil industry

Pulses of strain energy that propagate in solids and fluids

Elastic = distortion (deformation) not permanent

Travel at specific velocities

Can be described as waves

Two ways (frames of reference) of looking at waves

In time

Rising and falling of boat on the ocean

In space

Waves on a pond

Space

Time

Space Time

Amplitude (A) height of wave (1/2 trough to peak)

Wavelength (λ) Peak to peak distance (one cycle)

Period (T) Time that it takes to go through on cycle

Frequency Number of cycles in a given period of time 1/period Units of Hertz (Hz) = 1/s

Speed of wave (c) Rate at which wave travels

𝑐 = 𝜆/𝑇

Body waves – move throughout the body of the medium it propagates in

P-wave

S-wave

Surface waves – motion of the surface of the material

Love

Rayleigh

Highest wave speed, arrives first

Consists of train of compression and expansion

Particle motion is parallel to direction of travel

Can travel in both solid and fluid media

Lower wave speed, arrives after P wave

Consists of train of shear motion

Particle motion is perpendicular to direction of travel

Can travel only in solid media

Lower velocity than body waves

Disturbance primarily at surface

Love waves – lateral motion of surface

Rayleigh waves – elliptical particle motion at surface

Amplitude decreases with depth

Raypath – lines that show the direction that the wave is propagating

Wavefront – position of the seismic wave that are doing the same thing at the same time.

The wavefront is always locally perpendicular to the raypath

Reflection

Transmission

Refraction

change in direction of propagation of any wave as a result of its traveling at different speeds at different points along the wave front.

Diffraction

Direction of bending of ray paths depends on

change in wave velocity across interface

Angle between interface and ray path

Going from lower velocity to higher velocity ray path shallows

Going from higher velocity to lower velocity ray path steepens

fast

slow

fast

slow

slow

V1<V2

Wave front (plane wave)

Wave fronts of new waves stimulated at surface

Resulting plane wave front

Described by Snell’s law

𝑠𝑖𝑛 𝑖1𝑣1

=sin 𝑖 2𝑣2

Waves traveling from a single source travel outwards in all directions

Leads to more complex looking wave front

Slower

Faster Direct wave

refracted wave

reflected wave

Depend on physical properties of rock

Density

Elasticity

Each wave type has its own velocity

Depend on physical properties of rock

Density (ρ)

Elasticity

Resistance to compression

Bulk modulus (K)

Resistance to shearing

Shear modulus (μ)

𝑉𝑆 =𝜇

𝜌

𝑉𝑃 =

43𝜇 + 𝐾

𝜌

𝑉𝑃

𝑉𝑆

(Figure is hyper linked)

Refracted wave in lower layer gets ahead of direct wave

Wave front passing along interface sends up “Head wave” aka “critically refracted ray”

At some distance head wave arrives before direct wave

This is basis for seismic refraction technique

Arrival time of direct wave

𝑎𝑟𝑟𝑖𝑣𝑎𝑙 𝑡𝑖𝑚𝑒 =30 𝑚

3 𝑚/𝑚𝑠= 10𝑚𝑠

𝑎𝑟𝑟𝑖𝑣𝑎𝑙 𝑡𝑖𝑚𝑒 =𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒

𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦

Arrival time for head wave

Need ray path of head wave

Need velocity of bottom layer

Path of head wave

(Recall only the critically reflected ray path gives rise to the head wave.)

Use Snell’s law

𝑠𝑖𝑛 𝑖1𝑣1

=𝑠𝑖𝑛 𝑖2𝑣2

;

𝑖2 = 90°

𝑠𝑖𝑛 𝑖2 = 1

∴ sin 𝑖1𝑐 =𝑣1𝑣2

Critical angle = 𝑖1𝑐

𝑇𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑 𝑏𝑦 ℎ𝑒𝑎𝑑 𝑤𝑎𝑣𝑒 𝑑𝑇 = 𝑑1 + 𝑑2 + (𝑥 − 2𝛿)

𝑑1 = 𝑑2 = ℎ (𝑐𝑜𝑠𝑖1𝑐) 𝛿 = ℎ(𝑡𝑎𝑛𝑖1𝑐)

𝑑𝑇 = 2ℎ 𝑐𝑜𝑠𝑖1𝑐 + (𝑥 − 2ℎ 𝑡𝑎𝑛𝑖1𝑐 )

sin 𝑖1𝑐 =𝑣1𝑣2

𝑎𝑟𝑟𝑖𝑣𝑎𝑙 𝑡𝑖𝑚𝑒 = 2ℎ 𝑐𝑜𝑠𝑖1𝑐

𝑣1 +

(𝑥 − 2ℎ 𝑡𝑎𝑛𝑖1𝑐 )𝑣2

Measured with a geophone or seismograph

Offset = distance from wave’s origin

Time is time elapsed

Seismogram

Multiple seismograms as a function of distance

Multiple seismograms as a function of distance

Direct wave

𝑎𝑟𝑟𝑖𝑣𝑎𝑙 𝑡𝑖𝑚𝑒 =𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒

𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦

Equation for a straight line

Reflected wave

𝑎𝑟𝑟𝑖𝑣𝑎𝑙 𝑡𝑖𝑚𝑒 =𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒

𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦

𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 𝑑1 + 𝑑2 = 2 ℎ2 +𝑥

2

2

Travel time for reflected wave

Refracted wave Arrives first at a

distance Much smaller in

amplitude

Refracted wave arrival time

From before:

Therefore, will also form a line

𝑎𝑟𝑟𝑖𝑣𝑎𝑙 𝑡𝑖𝑚𝑒 = 2ℎ 𝑐𝑜𝑠𝑖1𝑐

𝑣1 +

(𝑥 − 2ℎ 𝑡𝑎𝑛𝑖1𝑐 )𝑣2

𝑎𝑟𝑟𝑖𝑣𝑎𝑙 𝑡𝑖𝑚𝑒 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡1 +(𝑥 − 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡2)

𝑣2

𝑎𝑟𝑟𝑖𝑣𝑎𝑙 𝑡𝑖𝑚𝑒 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡1 +𝑥

𝑣2 −

𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡2𝑣2

Reflection convention Refraction convention

Cross over distance

𝑎𝑟𝑟𝑖𝑣𝑎𝑙 𝑡𝑖𝑚𝑒 =𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒

𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦1

Direct wave arrival time

Refracted wave arrival time

𝑎𝑟𝑟𝑖𝑣𝑎𝑙 𝑡𝑖𝑚𝑒 =

𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡1 +𝑥

𝑣2 −

𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡2𝑣2

Cross over distance (xc) ℎ =

Zero-offset time (t0)

First arrival time is first sign of ground motion

Can be hard to spot

Can use time of first peak time instead

No head wave forms The boundary will be invisible in a

refraction survey

Sound source

Listening device – Geophones

Recording equipment

Source needs to be reproducible

Best if you can control when the source sound happens

E.g. not an earthquake

Timing of source needs to be precisely measured relative to arrival times

Examples

Hammer and plate

Explosives

Device which converts motion to an electrical signal

Need to be inexpensive and rugged

Used in groups (12 – hundreds)

http://www.kgs.ku.edu/Publications/PIC/pic37.html

Distributed

Satellite recording systems connect to central brain

Allows for more geophones

Cuts down on the number of wires

Some new systems are wireless

Converts signal to digital information

Stores seismograms

Traditional

All geophones connected to one recording system