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Applied Geophysics – Analysis and examples
Analysis and examples
Reading: Today: p39-64Next Lecture: p65-75
Gravity:
Applied Geophysics – Analysis and examples
Spreadsheet: Grav2Dcolumn
Gravity Anomalies: 2D forward calculation for rectangular parallelepipeds with greater vertical extent than horizontalsee Dobrin and Savit eq 12-34
Define density structure
Adjust bold numbers…coulum center (km)
density contrast (g/cm3)
top (km)
bottom (km)
error check
0 0.5 0 0 OK1 0.5 0 0 OK2 0.5 7 9 OK3 0.5 6 10 OK4 0.5 5.5 9.5 OK5 0.5 5 9 OK6 0.5 4.7 8 OK7 0.5 4.5 7 OK8 0.5 4.4 6 OK9 0.5 4.3 5.5 OK10 0.5 0 0 OK11 0.5 0 0 OK12 0.5 0 0 OK13 0.5 0 0 OK14 0.5 0 0 OK15 0.5 0 0 OK16 0.5 0 0 OK17 1 1 2 OK18 0.5 0 0 OK19 0.5 0 0 OK20 0.5 0 0 OK
Calculated gravity anomaly
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
0 2 4 6 8 10 12 14 16 18 20distance (km)
dgz
(mG
al)
0
2
4
6
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10
12
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
dept
h (k
m)
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Applied Geophysics – Analysis and examples
Ambiguity - I
Applied Geophysics – Analysis and examples
Ambiguity - II
( )[ ] 23222
3
11
34
zxzGRgz
+
∆=∆ ρπ
3
Applied Geophysics – Analysis and examples
Spreadsheet: Grav2Dcolumn
Gravity Anomalies: 2D forward calculation for rectangular parallelepipeds with greater vertical extent than horizontalsee Dobrin and Savit eq 12-34
Define density structure
Profile 1 Profile2Adjust bold numbers… Adjust bold numbers…
coulum center (km)
density contrast (g/cm3)
top (km)
bottom (km)
error check
density contrast (g/cm3) top (km)
bottom (km)
error check
0 0.3 0 0 OK 0.9 0 0 OK1 0.3 4 4.4 OK 0.9 0 0 OK2 0.3 4 4.4 OK 0.9 0 0 OK3 0.3 4 4.3 OK 0.9 0 0 OK4 0.3 4 4.3 OK 0.9 0 0 OK5 0.3 4 4.4 OK 0.9 0 0 OK6 0.3 4 4.4 OK 0.9 0 0 OK7 0.3 4 4.5 OK 0.9 0 0 OK8 0.3 4 4.6 OK 0.9 0 0 OK9 0.3 4 4.7 OK 0.9 0 0 OK10 0.3 4 4.8 OK 0.9 8 12 OK11 0.3 4 4.7 OK 0.9 0 0 OK12 0.3 4 4.6 OK 0.9 0 0 OK13 0.3 4 4.5 OK 0.9 0 0 OK14 0.3 4 4.4 OK 0.9 0 0 OK15 0.3 4 4.4 OK 0.9 0 0 OK16 0.3 4 4.3 OK 0.9 0 0 OK17 0.3 4 4.3 OK 0.9 0 0 OK18 0.3 4 4.4 OK 0.9 0 0 OK19 0.3 4 4.4 OK 0.9 0 0 OK20 0.3 0 0 OK 0.9 0 0 OK
Gravity anomaly
0.00
0.50
1.00
1.50
2.00
2.50
0 2 4 6 8 10 12 14 16 18 20distance (km)
dgz
(mG
al)
Pro file 1Pro file 2
Profile 1
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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
dept
h (k
m)
Profile 2
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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Applied Geophysics – Analysis and examples
Isolating gravity anomalies
Enhance the anomalies of interest
Gravity anomaly map.Already applied
corrections: Latitude, Free-air, Bouguer,
Terrain
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Applied Geophysics – Analysis and examples
Regional trend removal
Small geological features near the surface cause small wavelength anomalies.
Large scale structures at greater depth cause longer wavelength anomalies.
Remove regional trends:• graphical approach• computer approach
High-pass filter
Regional trends appears as a uniform variation of equally spaced contours.
Applied Geophysics – Analysis and examples
Regional trend removal
survey ∆g minus regional trend
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Applied Geophysics – Analysis and examples
Regional trend removed
Applied Geophysics – Analysis and examples
Removing noiseNoise sources• instrument inaccuracies• drift corrections• site surveying
(correction errors)
Low-pass filter
These random errors in ∆g result in high frequency scatter in the data
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Applied Geophysics – Analysis and examples
Removing noise
survey ∆g- regional trend
minus high frequency noise
Applied Geophysics – Analysis and examples
Noise removed
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Applied Geophysics – Analysis and examples
Wavelength filteringWe have just applied two filters to our data:
1. Regional trend removal: high-pass filter2. Noise filter: low-pass filter
i.e. we have band-passed our data to isolate/enhance gravity anomalies with the wavelength of interest
Band-pass filter
Applied Geophysics – Analysis and examples
Spatial domain
Subtracting averages1. at each data point draw a circle2. average the gravity observations
around circumference3. subtract mean from value at center
pointRecovers anomalies with a wavelength close to the diameter of the circle
Wavelength filtering
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Applied Geophysics – Analysis and examples
Wave number domainWavelength filtering
1. Fourier transform the data: f(x,y) F(kx,ky)2. set high and low wavelengths to zero: F’(kx,ky)3. Fourier transform back: F’(kx,ky) f’(x,y)
F’
F
k
k
Applied Geophysics – Analysis and examples
Continuation filters
This project the potential field to either higher or lower elevations
• Upward continuation – enhances deeper sources• Downward continuation – enhances shallow sources
Derivative filters
• Enhance shallow anomalies• Used to find edges of anomalies
For shallow bodies with vertical edges the max horizontal gradient will occur over the edge
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Applied Geophysics – Analysis and examples
General approachMethodology of interpretation
1. Compile data along profiles or as a map
This includes applying all corrections for surface variations
2. Apply isolation and enhancement techniques i.e. filters
Identify residuals of interest, source shape outlines
3. Apply approximate interpretation techniques
Use simple shape formula to estimate size and depth of sources
4. Use forward techniques to determine source parameters
Application of forward approaches ensures the postulated structure makes geological sense
5. Apply inverse techniques to determine source parameters
Translate results into meaningful geologic model
…don’t fall into the blind inversion trap
Applied Geophysics – Analysis and examples
Forward modelingMethodology of interpretation
1. Make a skilled guess of the structure (the model)2. Calculate the anomaly this would produce3. Compare to the observations (the data)4. Adjust the model and recalculate etc…
Each iteration could be done by hand, automated, or a combination (best)
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Applied Geophysics – Analysis and examples
Spreadsheet: Grav2DcolumnSpreadsheet: Grav2Dcolumn
Gravity Anomalies: 2D forward calculation for rectangular parallelepipeds with greater vertical extent than horizontalsee Dobrin and Savit eq 12-34
Define density structure
Profile 1 Profile2Adjust bold numbers… Adjust bold numbers…
coulum center (km)
density contrast (g/cm3)
top (km)
bottom (km)
error check
density contrast (g/cm3) top (km)
bottom (km)
error check
0 -0.3 0 0 OK 0 0 0 OK1 -0.3 4 4.4 OK 0 0 0 OK2 -0.3 4 4.4 OK 0 0 0 OK3 -0.3 4 4.3 OK 0 0 0 OK4 -0.3 4 4.3 OK 0 0 0 OK5 -0.3 4 4.4 OK 0 0 0 OK6 -0.3 4 4.4 OK 0 0 0 OK7 -0.3 4 4.5 OK 0 0 0 OK8 -0.3 4 4.6 OK 0 0 0 OK9 -0.3 4 4.7 OK 0 0 0 OK10 -0.3 4 4.8 OK -0.9 8 12 OK11 -0.3 4 4.7 OK 0 0 0 OK12 -0.3 4 4.6 OK 0 0 0 OK13 -0.3 4 4.5 OK 0 0 0 OK14 -0.3 4 4.4 OK 0 0 0 OK15 -0.3 4 4.4 OK 0 0 0 OK16 -0.3 4 4.3 OK 0 0 0 OK17 -0.3 4 4.3 OK 0 0 0 OK18 -0.3 4 4.4 OK 0 0 0 OK19 -0.3 4 4.4 OK 0 0 0 OK20 -0.3 0 0 OK 0 0 0 OK
Gravity anomaly
-2.50
-2.00
-1.50
-1.00
-0.50
0.000 2 4 6 8 10 12 14 16 18 20
distance (km)
dgz
(mG
al)
Profile 1Profile 2
Profile 1
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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
dept
h (k
m)
Applied Geophysics – Analysis and examples
Spreadsheet: Grav2DcolumnSpreadsheet: Grav2Dcolumn
Gravity Anomalies: 2D forward calculation for rectangular parallelepipeds with greater vertical extent than horizontalsee Dobrin and Savit eq 12-34
Define density structure
Profile 1 Profile2Adjust bold numbers… Adjust bold numbers…
coulum center (km)
density contrast (g/cm3)
top (km)
bottom (km)
error check
density contrast (g/cm3) top (km)
bottom (km)
error check
0 -0.3 0 0 OK 0 0 0 OK1 -0.3 4 4.4 OK 0 0 0 OK2 -0.3 4 4.4 OK 0 0 0 OK3 -0.3 4 4.3 OK 0 0 0 OK4 -0.3 4 4.3 OK 0 0 0 OK5 -0.3 4 4.4 OK 0 0 0 OK6 -0.3 4 4.4 OK 0 0 0 OK7 -0.3 4 4.5 OK 0 0 0 OK8 -0.3 4 4.6 OK 0 0 0 OK9 -0.3 4 4.7 OK 0 0 0 OK10 -0.3 4 4.8 OK -0.9 8 12 OK11 -0.3 4 4.7 OK 0 0 0 OK12 -0.3 4 4.6 OK 0 0 0 OK13 -0.3 4 4.5 OK 0 0 0 OK14 -0.3 4 4.4 OK 0 0 0 OK15 -0.3 4 4.4 OK 0 0 0 OK16 -0.3 4 4.3 OK 0 0 0 OK17 -0.3 4 4.3 OK 0 0 0 OK18 -0.3 4 4.4 OK 0 0 0 OK19 -0.3 4 4.4 OK 0 0 0 OK20 -0.3 0 0 OK 0 0 0 OK
Gravity anomaly
-2.50
-2.00
-1.50
-1.00
-0.50
0.000 2 4 6 8 10 12 14 16 18 20
distance (km)
dgz
(mG
al)
Profile 1Profile 2
Profile 1
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dept
h (k
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Profile 2
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h (k
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…remember the ambiguity
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Applied Geophysics – Analysis and examples
Inverse modelingMethodology of interpretation
Forward modeling:• Make a skilled guess of the structure (the model)• Calculate the anomaly this would produce• Compare to the observations (the data)• Adjust the model and recalculate etc…
Inverse modeling essentially replaces step 4 with a mathematically determined model adjustment γ
γ∆
∂∂=∆ gg
Usually we fix certain parameters such as source geometry or depth, and invert for remaining parameters e.g. density contrast
Applied Geophysics – Analysis and examples
Salt dome
Anomaly:• Near circular• ∆gmax ~ 16 mGal• x1/2 ~ 3700 m
Assume spherical salt body:• Depth to center ~ 4800 m
Assume ∆ρ -250 kg/m3:• Radius ~ 3800 m
Depth to top of salt:• 4800-3800 = 1000 m
Examples
12
Applied Geophysics – Analysis and examples
Salt dome – seismic lineFrom gravity, assuming spherical salt body:
• Depth to center ~ 4800 m• Radius ~ 3800 m• Top of salt at ~ 1000 m
Examples
Applied Geophysics – Analysis and examples
Salt dome – density contrasts
Given the geometry, can estimate density
contrasts
Examples
13
Applied Geophysics – Analysis and examples
Fault locationGravity is very sensitive to vertical geologic contacts
The vertical gradient is particularly sensitive to “edges”
Examples
Applied Geophysics – Analysis and examples
Fault location
Identifying fault locations is the first step in hazard mitigation.
Faults generate strong gradients.
Examples
14
Applied Geophysics – Analysis and examples
Mapping basin depthExamples
Applied Geophysics – Analysis and examples
Mapping basin depth
Thicker sediments:
More susceptible to subsidence with the removal of water
Examples
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