Lecture: Gravity Anomalies

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Gravity Anomalies

• Relative contrasts in density are the main cause of gravity anomalies

• The shape of the anomalies (2D profiles, or 3D maps) is characteristic for certain

geometries in the subsurface, e.g.:

– Geometric bodies

– Planes of contrast (vertical, dipping, horizontal)

• For more complex real-world structures,

forward modeling approach using many small

bodies or regular polygons is typical

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Sophisticated geological modeling, using all available information from outcrop geology,

geophysical methods

QuickTime™ and a

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Indirect Interpretation

Forward modeling

1. A model that is thought to represent the likely geology is constructed.

2. The predicted anomaly due to this model is calculated.

3. The computed and observed anomaly are compared.

4. The model is adjusted, minimizing the difference between the observed and computed anomalies.

5. The solution is non-unique!

Fig. 6.20

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Applied Geophysics – Corrections and analysis

Spreadsheet: Grav2Dcolumn

Gravity Anomalies: 2D forward calculation

for rectangular parallelepipeds with greater vertical extent than horizontal see Dobrin and Savit eq 12-34

Define density structure

Profile 1 Profile2

Adjust 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 OK

1 0.3 4 4.4 OK 0.9 0 0 OK

2 0.3 4 4.4 OK 0.9 0 0 OK

3 0.3 4 4.3 OK 0.9 0 0 OK

4 0.3 4 4.3 OK 0.9 0 0 OK

5 0.3 4 4.4 OK 0.9 0 0 OK

6 0.3 4 4.4 OK 0.9 0 0 OK

7 0.3 4 4.5 OK 0.9 0 0 OK

8 0.3 4 4.6 OK 0.9 0 0 OK

9 0.3 4 4.7 OK 0.9 0 0 OK

10 0.3 4 4.8 OK 0.9 8 12 OK

11 0.3 4 4.7 OK 0.9 0 0 OK

12 0.3 4 4.6 OK 0.9 0 0 OK

13 0.3 4 4.5 OK 0.9 0 0 OK

14 0.3 4 4.4 OK 0.9 0 0 OK

15 0.3 4 4.4 OK 0.9 0 0 OK

16 0.3 4 4.3 OK 0.9 0 0 OK

17 0.3 4 4.3 OK 0.9 0 0 OK

18 0.3 4 4.4 OK 0.9 0 0 OK

19 0.3 4 4.4 OK 0.9 0 0 OK

20 0.3 0 0 OK 0.9 0 0 OK

Gravity anom aly

0.00 0.50 1.00 1.50 2.00 2.50

0 2 4 6 8 10 12 14 16 18 20

distance (km )

dgz (mGal)

Profile 1 Profile 2

Profile 1 0

2 4 6 8 10 12 14

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

depth (km)

Profile 2

0 2 4 6 8 10 12 14

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

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Estimating density as model input

• A priori information about rock types in region:

– Maps, cross sections, and samples – Boreholes

– Seismic velocity

– Nettleton’s method

• Guess!

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Density Determination

Nettleton’s Method

•Gravity data over an isolated prominence (e.g., a hill) are reduced using a series of different trial densities for the Bouguer and terrain corrections.

•The density that yields a Bouguer anomaly with the least correlation with topography is taken to represent the average density of the

prominence.

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Indirect Density Determination

P-Wave Velocities

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Gravity Anomalies

r2

g_r = Gm

The gravitational attraction in the direction of the mass is given by:Δ

Since a gravity meter only measures the vertical component of the attraction Δg_z, the gravity anomaly Δg caused by the mass is:

3 2 cos or

r g Gmz r

g = Gm Δ =

Δ θ

From Kearey et al., 2002

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Simple shape anomalies

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Example: Depth to bedrock from precise gravity anomaly in Reading Massachusetts

(After Kick, 1985) Stations 40 ft apart

Elevations surveyed to ± 0.03 meter

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Mapping basin depth

Examples

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Mapping basin depth

Thicker sediments:

More susceptible to subsidence with the removal of water Examples

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Bouguer Gravity Anomaly Map of New Mexico

Generated from 42,786 gravity measurements on the ground Bouguer

reduction density of 2.67 g/cc

Courtesy Chuck Heywood, USGS

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QuickTime™ and a TIFF (Uncompressed) decompressor

are needed to see this picture.

Using gravity data to define

groundwater aquifer depth, extent

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Salt dome

Anomaly:

• Near circular

• Δg_max ~ 16 mGal

• x_1/2 ~ 3700 m Examples

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Buried sphere

( )

[

² ²

]

³ ²

2 3

1 1 3

4 z z x

g

_z

GR

+

= Δ

Δ π ρ

Analytic expressions for simple geometric shapes

e.g. a buried sphere

2

302

1

.

1 x

z =

Depth rule

Note: it is only the density contrast that is important

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Salt dome

Anomaly:

• Near circular

• Δg_max ~ 16 mGal

• x_1/2 ~ 3700 m

Assume spherical salt body:

• Depth to center ~ 4800 m Assume Δρ -250 kg/m³:

• Radius ~ 3800 m Depth to top of salt:

• 4800-3800 = 1000 m Examples

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Salt dome – seismic line

From gravity, assuming spherical salt body:

• Depth to center ~ 4800 m

• Radius ~ 3800 m

• Top of salt at ~ 1000 m Examples

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Salt dome – density contrasts

Given the geometry, can estimate density

contrasts Examples

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Direct Interpretation

Inflection Point

•The location of an inflection point on gravity anomaly, i.e. the position where the horizontal gravity gradient changes most rapidly, can provide information on the nature of the edge of an anomalous body.

•Over structures with outward dipping

contacts the inflection points lie near the base of the anomaly

•Over structures with inward dipping contacts (sedimentary basins) the inflection points lie near the uppermost edge of a body.

•Over a tabular body, the inflection points delineate the edges of the body.

From Kearey et al., 2002

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Fault location

Gravity is very sensitive to vertical geologic contacts

The vertical gradient is particularly sensitive to

“edges”

Examples: Gravity gradient-based methods

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Fault location

Identifying fault locations is the first step in hazard mitigation.

Faults generate strong gradients.

Examples