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Geophysics > Geophysics Final Exam > Flashcards

Geophysics Final Exam Flashcards

1
Q

Rock Physics Checklist

A

I V P G I M

Identity
Volume fraction
Physical Properties
Geometry
Interactions
Methods
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2
Q

Combining Rock Physics

A

X^a = sum(f*X^a)

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3
Q

Inverse Problem

A

Use the measured geophysical response, physics, and prior knowledge to interpret what’s going on in the subsurface

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4
Q

Wave-based Imaging Methods

A

GPR (EM) waves

Seismic (mechanical) waves

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5
Q

Forward Problem

A

Know the structure, physics, etc. to predict the geophysical response

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6
Q

Wave

A

V = wavelength * frequency

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7
Q

Amplitude (A)

A

Maximum magnitude of displacement from rest

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8
Q

Wavelength

A

Distance required to complete one cycle of displacement (peak to peak or trough to trough)

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9
Q

Period (T)

A

Time required to complete one cycle of displacement [time]

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10
Q

Frequency (f)

A

The number of cycles completed in a given time period [Hz]

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11
Q

Attenuation

A

The loss of energy as the wave propagates

1) Geometric spreading
2) Intrinsic attenuation (e.g. loss of energy to heat)
3) Scattering

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12
Q

Wavefront

A

A curve (or surface) connecting points of constant phase (i.e. connecting peaks or troughs)

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13
Q

Wavefield

A

The collection of all waves at one point in time (e.g. photo of ripples on a pond)

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14
Q

Ray

A

The path traced out by following a fixed point on a wavefront. Perpendicular to wavefront

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15
Q

Dispersion

A

When the velocity of a wave depends on frequency

most waves are made up of many frequency components

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16
Q

Compression

A

An applied stress causes a change in the volume of the rock

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17
Q

Bulk Modulus

A

K = -dP / dV/V

Inverse of compressability

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18
Q

Compressability

A

B = -dV/dP / V

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19
Q

Poisson’s Ratio

A

u = -e1 / e3

Ratio of perpendicular strain to parallel strain (relative to applied stress)

Related to Bulk: K = E / 3(1-2u)
Related to Shear: G = E / 2(1-u)

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20
Q

Shear

A

Applied stress causes deformation (E) (strain) but no change in volume occurs

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21
Q

Shear Modulus

A

G = shear stress / shear strain

rigidity

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22
Q

Young’s Modulus

A

E = uniaxial applied stress / observed strain

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23
Q

Surface Waves

A

Rayleigh wave – elliptical retro-grade motion with exponentially decaying amplitude with depth

Love wave – shear motion polarized in the plane of the surface (side to side)

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24
Q

Properties that control Radar

A

1) Electrical conductivity, sigma
2) Magnetic permeability, u
* 3) Dielectric Permittivity, e

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25
Q

Dielectric Permittivity (e)

A

Relates charge separation (polarization) to the applied electric field: p = e*E

e = K*e_o

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26
Q

Dielectric Constant (K)

A

Describes the ability of a material to store energy due to charge polarization. Is the relative permittivity of a dielectric material

K = e / e_o

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27
Q

Dielectric Constant (K) vs. Dielectric Permittivity (e)

A

K = e / e_o

e = K*e_o

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28
Q

Dielectric Constant and Velocity

A

V = c / (K^1/2)

c = speed of light = 3E8 m/s

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29
Q

WARR

A

Wide Angle Reflection and Refraction

– move receiver but keep source fixed

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30
Q

CMP

A

Common Midpoint

– keep the center fixed, move source and receiver from center

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31
Q

COP

A

Constant Offset Profile

– move source and receiver together at same interval

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32
Q

P-wave

A

Primary wave

Vp = (K + 4/3G / density)^1/2

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33
Q

S-wave

A

Secondary wave

Vs = (G / density)^1/2

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34
Q

Vp / Vs

A

(K/G + 4/3)^1/2 = (1-u / 1/2-u)^1/2

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35
Q

Slope and Intercept

A

Square the traveltime eq: t^2 = 1/V2 x^2 + 4h^2 / V1^2

Plot x^2 vs t^2 to get a straight line:

slope = 1 / V1^2

intercept = 4h^2 / V1^2

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36
Q

Arrivals

A

Radar: Air first

Seismic: Air last

Both: Direct waves straight, reflection curved to join ground wave, refraction separates from reflection at ground wave

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37
Q

t vs. x:

Radar or Seismic?

A

Radar = no groundroll

Seismic = air last

    • units
    • calc velocities
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38
Q

Frequency vs. Resolution

A

Higher frequencies:

    • better resolution
    • shallower
    • more attenuation

Lower frequencies:

    • poor resolution
    • deeper
    • less attenuation
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39
Q

Absorption

A

Loss of E due to (a) intrinsic attenuation (heat loss) and (b) scattering

Ii=I1e^(-q (ri-r1) )

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40
Q

Reflection Strength

A

Depends mostly on:

1) Reflection coefficient
2) Attenuation

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41
Q

Radar Reflection Coefficient (R) (normal incidence)

A

R = amplitude of reflection / amplitude of incidence

R = V2 - V1 / V2 + V1 = sqrt(K2) - sqrt(K1) / sqrt(K2) + sqrt(K1)

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42
Q

Seismic Reflection Coefficient (R) (normal incidence)

A

R = p2 V2 - p1 V1 / p2 V2 + p1 V1 = z2 - z1 / z2 + z1

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43
Q

Energy Density / Intensity (I)

A

I = E/S = E / 4pi r^2

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44
Q

Direct wave

A

t = x / v

45
Q

Reflection

A

t = 2 / Vrms ( x^2 /4 + h^2)^1/2

x^2 - t^2

46
Q

Refraction

A

t = ( 2 h1 (V2^2 - V1^2)^1/2 ) / (V1V2) ) + x/V2

47
Q

Diffraction

A

t = 2/V ((x - xs)^2 + h^2)^1/2

48
Q

Traveltime (t)

A

t = 2a/V1 = 2(x^2 / 4 + h^2)^1/2 / V1

49
Q

Dix Equation

A

Vn^2 = ([Vrms^2]n tn - [Vrms^2]n-1 tn-1) / (tn - tn-1)

50
Q

Resistivity of Rocks

A

Surface charge:
– clays = conductive

Porosity:
– high = LOW resistivity, HIGH conductivity

51
Q

2nd Layer Velocity

A

V2 = sqrt( (Vrms(dt1 + dt2) - V1^2 dt1) / dt2)

52
Q

2nd Layer Thickness

A

h2 = dt2 V2

53
Q

Thickness (h) vs. Wavelength (w)

A

h&raquo_space; w:
distinct reflections apparent

h = w:
bottom layer is mirrored

h = w/2:
not as clear

h = w/4:
looks like 1 reflection overall

54
Q

Reflection Coefficient (R)

A

Quantifies the fraction of energy returned to the surface by a contrast in properties

55
Q

Mulitples

A

Primary reflection: tn = 2h/V1

1st multiple: tm1 = 2t_p = 4h/V1

2nd multiple: tm2 = 3t_p = 2h/V1

56
Q

Snell’s Law

A

Sin O2 = V2/V1 sin O1

O1 = angle of incidence
O2 = angle of transmission
57
Q

Critical Angle (Oc)

A

Oc = sin^-1 (V1/V2)

58
Q

Critical Distance (Xc)

A

Distance at which a refracted wave is generated

Xc = 2h / [(V2/V1)^2 - 1]^1/2

59
Q

N Layer Refraction Traveltime

A

tn = X/Vn + 2/Vn sum( (hi (Vn^2 - Vi^2)^(1/2)) / Vi )

60
Q

Ohm’s Law

A

V = I*R

V = voltage
I = current
R = resistance
61
Q

Resistivity vs. Conductivity

A

resistivity = 1 / conductivity

conductivity = 1 / resistivity

62
Q

Resistance (R)

A

R = L / A * p

p = resistivity
A = cross sectional area
L = length

p = A/L V/I = K V/I

63
Q

Archie’s Law

A

nonclays:
Peff = a * O^-m * Sw^-n * Pw

clays:
Peff = [(a * O^-m * Sw^-n * Pw)^-1 + o_surface]^-1

O = porosity
Sw = saturation
Pw = fluid resistivity
a = 0.41 - 2.13
m = 1.64 - 2.23
n = 1.1 - 2.6
64
Q

Fluid Conductivity

A

Ow = 10^3 * F * sum( abs(Zi) * Ci * ui

F = 9.648E4 C/mol
Zi = valence of ion
Ci = concentration (mol/L)
ui = ionic mobility ((m/s)/N)
65
Q

Voltage

A

at point p:

Vp = pI/2pi *( 1/r1 - 1/r2)

p = dVmeas/I * 2pi[1/r1 - 1/r2 - 1/r3 + 1/r4]^-1

66
Q

Depth of Resistivity Arrays

A

Wenner: h = a/2

Schlumberger: h = L/3

Dipole-Dipole: h = na

67
Q

Electrode Array Geometric Factors (K)

A

Wenner: K = 2pi*a

Schlumberger: K = pi/a^2 [1 - b^2/4a^2]

Dipole-Dipole: K = pi * n * (n + t) * (n + 2) * a

Square: K = pi*a *(2 + sqrt(2))

68
Q

Direct Current (DC)

A

Current flows continuously in direction of applied voltage

69
Q

Applied Current (AC)

A

Current switches direction with applied voltage

70
Q

Pure Capacitor (C)

A

Ability to hold a charge
C = Q / V

C = capacitance
Q = charge
V = applied voltage
71
Q

Chargeability

A

= Vp / Vo –> difficult to get Vp accurately

Apparent = A / Vo

A = integral (area) of Vp over a specified time window

72
Q

Spectral (Frequency-Domain) Induced Polarization (SIP)

A

Apply a sine wave of a particular frequency. Compare the amplitude and phase (i.e. time shift) of the observed voltage relative to the applied current

73
Q

Complex Conductivity (sigma = o)

A

o(f) = o’(f) + io’‘(f)

o' = real conductivity --> energy loss (conduction)
i = sqrt(-1)
o'' = imaginary conductivity --> energy storage (polarization)
74
Q

Electrical Double Layer

A

Mineral surfaces are usually charged.

Causes an imbalance of charge near the pore walls

75
Q

Membrane / Electrolytic Polarization

A

Pore throat constriction - charge on mineral surface leads to a build-up at pore throats

Constriction by clay particles - ions accumulate on either side of a charged particle in the pore space

76
Q

Self Potential (SP)

A

Redox reactions = electrochemical

Groundwater flow = electrokinetics

77
Q

Tomography Traveltime (t)

A

through each cell (tj):

tj = sum( Lj / Vj ) = sum( Lj sj )

sj = 1 / Vj = slowness of cell j
Lj = length of ray in cell j
78
Q

Least-Squares Data Fitting

A

Steps:

1) Collect data –> (x,y)
2) Define a model –> y=mx+b
3) Define a measure of error –> “least squares”
4) Find parameters of the model that minimize error

79
Q

Tomography Forward Problem

A

t = L s

d = G m

d=data
G=design matrix
m=vector with all model parameters

80
Q

Tomography Inverse Model

A

m = ( G^T G + a I )^-1 ( G^T y - a mo )

a = trade-off/regularization parameter
I = MxM identity matrix
mo = best guess of m

Not as good (will blow up):
m = ( G^T G )^-1 G^T y

81
Q

Newton’s Law

A

Fg = G m1 m2 / r^2

G = 6.672E-11 m^3/kgs^2
Fg = gravitational force = 9.8 m/s^2
m1, m2 = masses of objects
r = distance between the centers of the objects

82
Q

Units of Gravity

A

1 Gal = 0.01 m/s^2

g = 981 Gal

83
Q

Absolute Gravity (g)

A

The actual value of acceleration due to gravity measured at a point in space

84
Q

Relative Gravity (dg)

A

CHANGE in gravity from a background value

=> useful for measuring variations in density

85
Q

Spherical Earth vs. Non-spherical Earth

A

Spherical: r1=r2, g1=g2

Non-spherical: r1 x=x r2, g1 x=x g2
Polar radius is ~21km shorter than the equatorial radius

86
Q

Forward Model for Gravity Anomaly

A

dg = G (4/3 pi a^3) (dp) z / ((x-xs)^2 + (z-zs)^2)^3/2

G = 6.672E-11 m^3/kgs^2
xs, zs = position and depth of “sphere” center
a = radius of sphere
dp = p2 - p1 = density difference between inclusion & background

87
Q

Inverse Problem

A
    • Fit data using prior knowledge
    • Collect additional data
    • Reduce the problem to remove non-uniqueness
88
Q

Half Max Gravity Anomaly (dg_1/2max)

A

dg_1/2max = G (4/3 pi a^3) dp z / ( X_1/2max^2 + z^2)^3/2

89
Q

Corrections to Gravity Observations

A

B I L T F I T

1) Bouger correction
2) Instrument drift
3) Latitude
4) Terrain correction
5) Free-air correction
6) Isostatic correction
7) Tides

90
Q

Bouger Anomaly

A

Reported gravity anomaly
> signal actually related to ground inclusion

dg = g_obs - sum( corrections - g_base )

91
Q

Gravity Anomaly (dgz)

A

dgz = G SSS dp(x,y,z) z/r^3 dxdydz

92
Q

dgi

1 block

A

dgi = A/r^3 + B/2r^5 ( (5z (3z^2 - r^2)/r^2) - 4z ) + 3C(x^2 - y^2) / r^5

r^2 = x^2 + y^2 + z^2
x, y, z = distances between measurement point and block i
A = 8G dp_i abc
B = A (2c^2 - a^2 - b^2) / 6
C = A (a^2 - b^2) / 24
2a, 2b, 2c = lengths of block i in x, y, z direction

93
Q

Resistivity Array Choice

A

Depends on:

1) Type of structure to be mapped
2) Sensitivity of the resistivity meter
3) Background noise level

 Things to consider:

1) Depth of investigation
2) Sensitivity of the array to vertical & horizontal structures
3) Data coverage
4) Signal strength

94
Q

Chargeability

A

= Vp / Vo > difficult to get Vp accurately

Apparent = A / Vo

A = integral (area) of Vp over a specified time window

95
Q

Spectral (Frequency-Domain) Induced Polarization (SIP)

A

Apply a sine wave of a particular frequency.

Compare the amplitude and phase (i.e. time shift) of the observed voltage relative to the applied current

96
Q

Complex Conductivity (sigma = o)

A

o(f) = o’(f) + io’‘(f)

o’ = real conductivity > energy loss (conduction)

i = sqrt(-1)

o’’ = imaginary conductivity > energy storage (polarization)

97
Q

Self Potential (SP)

A

Redox reactions = electrochemical

Groundwater flow = electrokinetics

98
Q

Least-Squares Data Fitting

A

Steps:

1) Collect data > (x,y)
2) Define a model > y=mx+b
3) Define a measure of error > “least squares”
4) Find parameters of the model that minimize error

99
Q

Relative Gravity (dg)

A

CHANGE in gravity from a background value

> useful for measuring variations in density

100
Q

Spherical Earth vs. Non-spherical Earth

A

Spherical: r1=r2, g1=g2

Non-spherical: r1 x=x r2, g1 x=x g2

Polar radius is ~21km shorter than the equatorial radius

101
Q

Inverse Problem

A

– Fit data using prior knowledge

– Collect additional data

– Reduce the problem to remove non-uniqueness

102
Q

Center of Mass (xs, zs) and Mass of Inclusion (m)

A

xs = get from peak of dg curve

zs = 1.305X_1/2

? m = 255dgmax(X_1/2)^2 ?

103
Q

Gravimeter

A

– Sensitive - can detect change of 0.01 mGal

– Rely on a mass pivoted on a beam attached to a spring

– Buildings/mtns/etc. influence gravity, measurements

104
Q

Gravitational Potential (u)

A

Represents the WORK ( / energy ) required to bring a unit mass from infinity to a position, r, away from the Earth

105
Q

Gravity Forward Model

A

dg = M dp
[dg1; dg2;…dgN] = [K11, K12,…K1M; K21, K22,…K2M…] * [dp1; dp2; dpN]

dp = (M^T M + I a) M^T dg

K = constant that depends on model properties (grid size) and measurement location

106
Q

Spectral (Frequency-Domain) Induced Polarization (SIP)

A

Apply a sine wave of a particular frequency.

Compare the amplitude and phase (i.e. time shift) of the observed voltage relative to the applied current

107
Q

Tomography Forward Problem

A

t = L s

d = G m

d=data
G=design matrix
m=vector with all model parameters

108
Q

Tomography Inverse Model

A

m = ( G^T G + a I )^-1 ( G^T y - a mo )

a = regularization parameter
I = MxM identity matrix
mo = best guess of m

Not as good (will blow up):
m = ( G^T G )^-1 G^T y

109
Q

Forward Model for Gravity Anomaly

A

dg = G (4/3 pi a^3) (dp) z / ((x-xs)^2 + (z-zs)^2)^3/2

G = 6.672E-11 m^3/kgs^2
xs, zs = position and depth of “sphere” center
a = radius of sphere
dp = p2 - p1 = density difference between inclusion and background

Geophysics (1 decks)

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