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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

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Applied Geophysics – Analysis and examples

Ambiguity - I

Applied Geophysics – Analysis and examples

Ambiguity - II

( )[ ] 23222

3

11

34

zxzGRgz

+

∆=∆ ρπ

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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

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Pro file 1Pro file 2

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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

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Profile 1Profile 2

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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

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-2.00

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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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…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

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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

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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

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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