Refraction: What happens when V changesRefraction: What happens when V changes

In addition to being In addition to being reflected at an interface, reflected at an interface, sound can be refracted, = sound can be refracted, = change directionchange direction

This refraction will be This refraction will be described by Snell’s Law:described by Snell’s Law:

sin i1 sin i2 V1 V2

sound is always 'bent' sound is always 'bent' toward the slower layertoward the slower layer

=

i2

i1

V1

V2

i1 = “angle of incidence”i2 = “angle of refractin”

Okay, so Okay, so this is a bit this is a bit juvenilejuvenile

still, I like still, I like pictures!pictures!

Sound Velocity in waterSound Velocity in water

Velocity increases Velocity increases with:with: ININcreasing pressurecreasing pressure ININcreasing creasing

temperaturetemperature

Velocity minimum at Velocity minimum at around 1,000maround 1,000m

The SOFAR The SOFAR ChannelChannel

Sound is bent Sound is bent toward the toward the slower layerslower layer

this is always this is always the center of the the center of the channelchannel

sound is sound is trappedtrapped

Acoustic TomographyAcoustic Tomography

Shallow water acousticsShallow water acoustics

This only works if the water column is just right!This only works if the water column is just right!

Example Acoustic VelocitiesExample Acoustic Velocities

Material P wave Velocity (m/s) S wave Velocity (m/s)Air 332

Water 1400-1500

Petroleum 1300-1400Steel 6100 3500

Concrete 3600 2000Granite 5500-5900 2800-3000

Basalt 6400 3200Sandstone 1400-4300 700-2800

Limestone 5900-6100 2800-3000

Sand (Unsaturated) 200-1000 80-400Sand (Saturated) 800-2200 320-880

Clay 1000-2500 400-1000Glacial Till (Saturated) 1500-2500 600-1000

Refraction in SedimentsRefraction in Sediments Sound is reflected from layers where acoustic Sound is reflected from layers where acoustic

impedence changesimpedence changes Sound is refracted where velocity changesSound is refracted where velocity changes These almost always co-occurThese almost always co-occur

RefractionRefraction This effect is of no This effect is of no consequence if the consequence if the source and receiver source and receiver are co-locatedare co-located

in order to ever in order to ever receive the refracted receive the refracted signal, they have to signal, they have to be widely separatedbe widely separated

i2

i1

V1

V2

Critical RefractionCritical Refraction

If If i1 shallow enough, a neat thing happens: ii22 becomes 90 becomes 90oo

this means that the sound this means that the sound arriving at this angle does arriving at this angle does not penetratenot penetrate

instead it travels ALONG instead it travels ALONG the interfacethe interface

Snell’s lawSnell’s law

sin i1 sin 90o

V1 V2

i2=90o

i1

V1

V2

=

Critical RefractionCritical Refraction

sin i1 sin 90o

V1 V2

i1 =sin-1 (V1 / V2)

We call the angle at which is occurs the “critical angle”

ic=sin-1 (V1 / V2)

i2=90o

i1

V1

V2

=

An example*An example*

Start with a layered bottom; discontinuity at 100mStart with a layered bottom; discontinuity at 100m

*Thanks to http://www.mines.edu

Watch the wave propagate:Watch the wave propagate: both reflected and refracted returnsboth reflected and refracted returns

Resulting T vs. X DiagramResulting T vs. X Diagram

Refracted

Distance (x)T

ime

Distance

slope=1/vslope=1/voo

VVoo

VV11

slope=1/vslope=1/v11

xc

Refraction survey: T vs X plotRefraction survey: T vs X plot

Must achieve xMust achieve xcc

slopes of arrivals slopes of arrivals defined by defined by in situ in situ sound velocitiessound velocities

advantages:advantages: velocity velocity

determinationdetermination deep penetrationdeep penetration

disadvantages:disadvantages: requires extra requires extra

hardwarehardware often two shipsoften two ships need loud, low f need loud, low f

sound sourcesound source

Real World Real World ExampleExample

with several with several layers, it layers, it gets more gets more complicatedcomplicated

these are these are lines drawn lines drawn by by interpreterinterpreter

actual actual arrival arrival signals are signals are far messier.far messier.

to be more to be more accurate, we need accurate, we need to show the to show the curvature of these curvature of these lineslines

note that a note that a reflected arrival in reflected arrival in one layer arrives one layer arrives at nearly the same at nearly the same time as the time as the refracted from the refracted from the next deeper layer next deeper layer (R(R22/F/F11))

X

T

direct water arrival

reflected arrival

refracted arrival

R2

F1

A real-world A real-world exampleexample

VERY large VERY large scalescale

GRAVITYGRAVITY

gravity is used to determine:gravity is used to determine: Subsurface structuresSubsurface structures Active tectonismActive tectonism

= another technique to determine subsurface = another technique to determine subsurface featuresfeatures a. local mass distributionsa. local mass distributions b. isostatic balance of an area.b. isostatic balance of an area.

gravimeter: mass on a series of springsgravimeter: mass on a series of springs data are normally used in conjunction with other data are normally used in conjunction with other

geophysical data geophysical data they are difficult (or impossible) to interpret they are difficult (or impossible) to interpret

alone and require several corrections:alone and require several corrections:

GravityGravity Gravity: Newton's law: Gravity: Newton's law:

F =F = G(mG(m11mm22))

rr22

where G=gravitational constant which is 6.67 x 10 dynes*cm /gwhere G=gravitational constant which is 6.67 x 10 dynes*cm /g F = M x A (A is acceleration)F = M x A (A is acceleration)

= M= M11 x A x A

MM11 x A = x A = G(mG(m11mm22)) (m (m11’s cancel)’s cancel)

rr22

g = A = g = A = G x M G x Mee

rr22

on earth, the acceleration is g=981mgals,on earth, the acceleration is g=981mgals, different on other planetsdifferent on other planets works only at earth’s surfaceworks only at earth’s surface

GravityGravity

The magnitude of measured gravity depends The magnitude of measured gravity depends on 5 factors:on 5 factors:

1) latitude:1) latitude: shape of the earthshape of the earth rotation (centripidal force)rotation (centripidal force)

2. elevation (r)2. elevation (r) 3. topography3. topography 4. Tides (solar and lunar positions)4. Tides (solar and lunar positions) 5. Presence and density of sub-surface mass5. Presence and density of sub-surface mass Because we’re interested in #5, we need to know and Because we’re interested in #5, we need to know and

allow for all the other factorsallow for all the other factors

Gravity: some notesGravity: some notes

satellites fly along surfaces of equal gravitational satellites fly along surfaces of equal gravitational potentialpotential

The geoid is a surface of equal potential which is The geoid is a surface of equal potential which is approximated by mean sea level.approximated by mean sea level.

the geoid would be a sphere except that:the geoid would be a sphere except that: a. the earth is not a perfect sphere; equator is 43km larger a. the earth is not a perfect sphere; equator is 43km larger

diameterdiameter b. anomalous deep-seated mass distributions within the earth,the b. anomalous deep-seated mass distributions within the earth,the

geoid departs from the ideal by +70 to -100m geoid departs from the ideal by +70 to -100m

Our GEOID models correct for “all” of these effectsOur GEOID models correct for “all” of these effects we use this reference to correct our we use this reference to correct our

measurementsmeasurements

GEOID ModelGEOID Model

These heights are relative to a “suitable elipsoid”These heights are relative to a “suitable elipsoid”

Gravity: more notesGravity: more notes

What happens to the GEOID if there is a buried mass?What happens to the GEOID if there is a buried mass?

the Geoid rises over massesthe Geoid rises over masses local gravity is greater, solocal gravity is greater, so

you have to go higher to achieveyou have to go higher to achieve as constant valueas constant value

Gravity notesGravity notes

survey with instruments eg bubble level: survey with instruments eg bubble level: would actually tell you you're level relative to would actually tell you you're level relative to

GEOID when it is NOT perpendicular to the GEOID when it is NOT perpendicular to the earth's surfaceearth's surface

"a ball would not roll on the geoid""a ball would not roll on the geoid" water surfaces define the geoid (almost)water surfaces define the geoid (almost)

Local mass variations Local mass variations affect measurementsaffect measurements

true whether mass true whether mass variation is “positive” variation is “positive” or “negative”or “negative”

here a buried mass here a buried mass affects the readingaffects the reading

Here a nearby mass affects the readingHere a nearby mass affects the reading ask your geodesy prof about how this correction is ask your geodesy prof about how this correction is

appliedapplied

GravityGravity

Corrections: as in much of science, you look for Corrections: as in much of science, you look for anomalies: anomalies:

so you make all the corrections and then the so you make all the corrections and then the difference between what you expect it to look like difference between what you expect it to look like and what it actually looks like is called an and what it actually looks like is called an anomalyanomaly..

1. latitude correction: brings us to a known location 1. latitude correction: brings us to a known location on the reference spheroid.on the reference spheroid. This is a given; we also correct for tides, instrument calibration This is a given; we also correct for tides, instrument calibration

etc. at this stepetc. at this step the rest may or may not be done, depending on the goal of the the rest may or may not be done, depending on the goal of the

project.project.

GravityGravity

2. Elevation correction:2. Elevation correction: reduce to the elevation of the reference spheroid; reduce to the elevation of the reference spheroid; this accounts for the variations with rthis accounts for the variations with r22 of gravitational attraction. of gravitational attraction. correct for the gradient of g in Aircorrect for the gradient of g in Air

ggfreefree airair = 0.3086*h where h is the elevation (in = 0.3086*h where h is the elevation (in meters)meters) This is called the This is called the Free AirFree Air correction correction it’s subtracted from the measurementit’s subtracted from the measurement what's left is called the "free-air anomaly"what's left is called the "free-air anomaly"

Free air anomalies indicate:Free air anomalies indicate: a. buried massesa. buried masses b. isostatic disequilibriumb. isostatic disequilibrium

GravityGravity 3. Bouger correction: corrects for the density of material between 3. Bouger correction: corrects for the density of material between

the gravity station and the reference surface. the gravity station and the reference surface. at sea reference is the sea floorat sea reference is the sea floor on land reference is sea levelon land reference is sea level these two meet at coastthese two meet at coast

ggBougerBouger = 0.04185 = 0.04185h h h is the thickness of the layer you ah is the thickness of the layer you are trying to compensate for (water or rock)re trying to compensate for (water or rock) is the density of that layer;is the density of that layer; need to know what kind of rock is thereneed to know what kind of rock is there

Flat, elevated areas above sea level characteristically have large Flat, elevated areas above sea level characteristically have large negative Bouger anomalies,negative Bouger anomalies,

Ocean basins have large positive Bouger anomaliesOcean basins have large positive Bouger anomalies ggfreefree airair - g - gBougerBouger = Bouger anomaly = Bouger anomaly may also apply a “terrain correction”may also apply a “terrain correction”

GravityGravity Isostasy: Bouger anomalies compensate for Isostasy: Bouger anomalies compensate for

the density of rocks between the station and the density of rocks between the station and the reference surface only.the reference surface only. You find negative anomalies over the continents and You find negative anomalies over the continents and

positive anomalies over the oceans. positive anomalies over the oceans. But, crustal masses are like icebergs floating on the mantle, But, crustal masses are like icebergs floating on the mantle,

they have deep roots. they have deep roots. If you look at the depth to the mantle and apply this "isostatic If you look at the depth to the mantle and apply this "isostatic

correction", you get the isostatic anomaly.correction", you get the isostatic anomaly.

The pressure is the same at all places because The pressure is the same at all places because the wood weighs the same as the water it displacesthe wood weighs the same as the water it displaces

The extra mass (the mountain) forces a depresession The extra mass (the mountain) forces a depresession in the Mohoin the Moho

GravityGravity

• In the geological application, elevated areas have deep expressionIn the geological application, elevated areas have deep expression• the crust is thicker in these placesthe crust is thicker in these places• if you compare the gravity there, you get if you compare the gravity there, you get lower than expectedlower than expected values because the integrated mass is lessvalues because the integrated mass is less

Crustal ThicknessesCrustal Thicknesses

P wave velocitiesP wave velocities Layer 1 = Layer 1 =

sedimentssediments 1.6-2.5km/sec1.6-2.5km/sec

Layer 2 = BasaltLayer 2 = Basalt 5-6km/sec 5-6km/sec

(pillows)(pillows) 6-7km/sec 6-7km/sec

(dikes)(dikes) Layer 3= GabbroLayer 3= Gabbro

7km/sec7km/sec Continental crust is Continental crust is

thicker than oceanic thicker than oceanic crust.crust.

Note:Note: SeychellesSeychelles Ontong JavaOntong Java IcelandIceland

GravityGravity

To compensate for “mountain roots”, we need to know To compensate for “mountain roots”, we need to know how deep they extend and what their mass ishow deep they extend and what their mass is The depth is = depth to the Moho (crustal thickness)The depth is = depth to the Moho (crustal thickness) Crustal density is pretty uniform, so we use a generic Crustal density is pretty uniform, so we use a generic

numbernumber Note that you need geophysical data (depth to the Note that you need geophysical data (depth to the

Moho) in order to make this correction!!Moho) in order to make this correction!! What's left is the What's left is the Isostatic AnomalyIsostatic Anomaly and it indicates and it indicates

places which are out of isostatic equilibrium.places which are out of isostatic equilibrium. clearly the most interesting of anomaliesclearly the most interesting of anomalies but most difficult to producebut most difficult to produce

Where Isostatic Anomaly is zero, no activity is presentWhere Isostatic Anomaly is zero, no activity is present Where it’s positive or negative, plates are on the move!Where it’s positive or negative, plates are on the move!

GravityGravity

Isostatic anomaly = Observed + latitude correction + altitude Isostatic anomaly = Observed + latitude correction + altitude correction (Free air correction) + Bouger correction + terrain correction (Free air correction) + Bouger correction + terrain correction + tide correction + Isostatic correctioncorrection + tide correction + Isostatic correction

Most of the earth is in reasonable isostatic equilibrium,Most of the earth is in reasonable isostatic equilibrium, ie the masses of the mountains are compensated for by low density roots, ie the masses of the mountains are compensated for by low density roots, the basins are low due to the the basins are low due to the

high density and small thicknesshigh density and small thickness

of oceanic crust.of oceanic crust.

However anomalies do exist.However anomalies do exist.

Land surface

Free air

Bouger

Isostatic

GravityGravity

Places to Places to find isostatic find isostatic anomaliesanomalies

1. places 1. places where ice where ice sheets have sheets have recently recently receded are receded are reboundingrebounding 300m in 300m in

last 10,000 last 10,000 years!!!years!!!

Remember, Remember, this was a this was a LOT of ice!LOT of ice!

2. active tectonism 2. active tectonism trenchestrenches mid ocean ridgesmid ocean ridges other faulting areasother faulting areas

3. active volcanism like in Hawaii or Puerto 3. active volcanism like in Hawaii or Puerto Rico.Rico.

Even the continental US still has some surprising Even the continental US still has some surprising gravity anomalies!gravity anomalies!