geop4210_lab1_gravityinterpretation

GEOP 4210 Geophysics Field Camp Instructor: Prof. Xiaobing Zhou 2010

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GEOP 4210 Lab # 1: Gravity Interpretation Using GRAVMAG

1. Introduction GRAVMAG is a 2D computer program that calculates gravity and magnetic field due to solids

(or voids of negative contrast density) of infinite strike length and polygon cross-section. In this

experiment, we focus on the calculation and interpretation of gravity anomaly.

The gravity routine in GRAVMAG calculates the gravity due to a solid (or voids of negative

contrast density) of infinite length and a cross section of polygon that can have up to n = 20

vertices. Such a model can be building blocks of a more complicated model that can be

comprised of several polygons. In reality, any geologic forms that have roughly constant cross-

sectional shape along their length and have lengths several times their cross-sectional width are

simulated as infinite polygons. Gravity routine is used to 1) investigate gravity anomaly

produced by buried mass bodies of various geometries and physical density but the length must

be several times the width of their cross-sections; 2) explore the possible subsurface

configurations responsible for observed gravity anomalies.

Thus, gravity routine can do two tasks: 1) forward modeling: given the coordinates (x, z) of each

vertex and density contrast, the gravity routine calculates the gravity due to a solid of infinite

length and a cross section of polygon that can have up to 20 vertices; 2) gravity interpretation:

GRAVMAG imports field data and derive a subsurface model that fits the field data (however,

you have to always try to predict the rough form of the anomaly curve before computation

begins).

2. Theory The following figure shows the geometry of a solid of infinite length in the y-direction with cross

section of polygon of n vertices.

Figure L1.1

If the coordinates of each vertex (xi, zi) are known, the vertical component of the gravity due to

that n-vertexed polygon is given by

( )∑

−−

+×= +

+n

i

iii

i

i

i

i

czr

rg θθα

α

βργ 1

1

2

5 ln1

102

where

ii

ii

izz

xx

−

−=

+

+

1

1α


2

=

=

+=

+=

−

−=−=

+

++

+++

+

++

1

11

2

1

2

11

22

1

11

arctan

arctan

i

i

i

i

i

i

iii

iii

ii

iiii

iiii

x

z

x

z

zxr

zxr

zz

zxzxzx

θ

θ

αβ

and γ = 6.67 x 10-8

dyne cm2/g

2, distances (r, x, z) are in m, density in g/cm

3 so that the

calculated gravity is in mGal.

From the above formula we can see that if the density contrast and the coordinates of each

vertex are known, the gravity is uniquely determined.

To interpret a gravity survey results (gravity anomaly) use GRAVMAG, 1) always try to predict

the rough form of the anomaly curve before computation begins; 2) attempt a number of

polygons in various configurations.

3. Objectives After this lab, you need to be able to simulate gravity anomaly (mGal) for a predefined model

and interpret field gravity data.

4. Demonstrations 4.1 Forward Modeling: Generating gravity anomaly data for a subsurface model. A subsurface model is shown below. The length is much longer than the width of the cross-

section. The density contrast (= mass density of anomalous body – mean mass density of

surrounding materials) is assumed to be 1.3 g/cm3. A geophysical survey using gravity method is

planned. 30 measurements are to be used at a fixed interval in 100 m (the default traverse length).

Our task is to simulate the gravity anomaly value for each measurement. A table of gravity

anomaly and distance and a plot of gravity anomaly against horizontal position should be

generated.

Figure L1.2


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Step 1 – Launch GRAVMAG.

Download GravMag.exe from

http://www.mtech.edu/mines/geophysical/xzhou/GEOP4210_FieldGeology&Geophysics.html to

the desktop of your computer. Double-click it to launch the computer program GRAVMAG. The

“Model Table” window appears.

Click “Add Body”, the “Model Table” window will become

Figure L1.3

What is shown in the “Model Table” window above is the default 4-verticex polygon of density

contrast of 0.100 g/cm3.


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Since our model has five vertices, we need to add one vertex to the default model that is a four-

vertex polygon before we change the defaulted model to the given model. Click in the lower half

of the “Model Table” window and then click “Add Point” button (you can use “Delete Point”

button to delete a vertex). A point is added. (Added point is placed halfway between the selected

point and the following point).

Step 2 – Model Setup.

From the given model, we list the coordinates of the five vertices in a table for convenience. The

table is shown below.

x Depth (z)

10 10

20 10

40 15

45 25

25 30

10 10

Input the above coordinates and density contrast (1.3g/cm3) into the “Model Table” as shown

below. Use the mouse and/or “Tab” key to change the coordinates of the default model to the

given model. (Note you only need to input the coordinates, the “Segment dip (°) which is the

defined θ in Figure L1.3” is automatically calculated.

Now to view the section plot and the calculated gravity data, click “Window” and select

“Section” from “Model Table” window.


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Click “Window” and select “Gravity Data” from “Model Table” window. The “Gravity Data”

window shows up. The default number of measurement is 11. The range is 100m.

The number of measurements is controlled at upper right. If you change 11 to 30 and then press

“Enter” key, 19 new measurement positions will be added to the end of the list but overall the 30

measurements are not evenly spaced. The get all the 30 measurements evenly spaced, change

“11” to 1, press the “Enter” key or click in the data entry area. Then change the “1” to “31” and press the Enter key or click in the data entry area again. Now the calculated

gravity is evenly spaced and the “Section” window is automatically updated.


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Step 3. Display and save gravity - spacing plot results The gravity versus horizontal position is shown in “Section” plot. You can see the gravity

anomaly profile generated by the polygon mass body.

Step 4. Copy modeled gravity data to Excel Open Excel. From “Gravity Data” window, click “Edit” and then “Copy Data”, then go to Excel

and paste the data into Excel. Now you can make plot and manipulate the calculated data in

Excel.

Step 5. Save Model and Exit GRAVMAG

In “Model Table” window, Click “File” and select “Save Model…”, navigate to your directory

and save the model as “GRAVMAG_forward”. Next time you can open the model file and revise

it without start everything from scratch. Notice that the title for the “Model Table” window has

changed to “GRAVMAG_forward.txt”. You can also copy the model to a Word file or Excel file.

Now open a Word file, in “GRAVMAG_forward.txt” window, click “Edit” and select “Copy

Model”, and paste the model into the open word file. You will see clearly the model. Now click

“File” and select “Exit” from “Model Table” window to exit the GRAVMAG program.

5.2 Gravity Interpretation: determining subsurface structure from gravity

anomaly field data Gravity interpretation in the gravity survey context is to get subsurface structure and density

contrast of a mass body buried in Earth. This is a time-consuming process. What is shown below

is a table of gravity anomaly from a gravity survey after a series of correction (free-air correction,

Bouguer correction, topographic correction, etc.). Assume the density contrast is 1.5g/cm3. The

interval between two gravity measurements is 100m. Interpret these survey data.


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Station ID X (km) Observed gravity anomaly (mGal)

S1 0.0 26.7

S2 0.1 29.2

S3 0.2 31.9

S4 0.3 34.3

S5 0.4 36.6

S6 0.5 38.6

S7 0.6 40.3

S8 0.7 41.6

S9 0.8 42.7

S10 0.9 43.6

S11 1.0 44.2

S12 1.1 44.5

S13 1.2 44.7

S14 1.3 44.9

S15 1.4 45.0

S16 1.5 45.4

S17 1.6 45.8

S18 1.7 46.3

S19 1.8 46.7

S20 1.9 47.0

S21 2.0 47.0

S22 2.1 46.7

S23 2.2 46.2

S24 2.3 45.3

S25 2.4 44.1

S26 2.5 42.6

S27 2.6 40.7

S28 2.7 38.5

S29 2.8 36.0

S30 2.9 33.4

S31 3.0 30.8

Step 6. Preparation Before launching GRAVMAG, we need to get some preliminary model parameters, such as how

many bodies to simulate the observed gravity. From the above table, we know that there are 31

data points and the density contrast is 1.5g/cm3. Use Excel to plot the anomalous gravity –

traverse distance xg −∆ first.

0.0

10.0

20.0

30.0

40.0

50.0

60.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

x (km)

Gra

vity

an

om

aly (

mG

al)

.


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From the xg −∆ curve, we can estimate that there might be two bodies associated with the

anomalous gravity. We use a four-vertex body to approach each body. We adjust the position

and the size of these two bodies to fit the observed data. But before we do that we need to make a

very rough estimate of the model parameters such as how much is the cross-section and depth.

To accomplish this, we assume the two bodies are infinite long cylinders. The vertical gravity

due to a long cylinder that is buried at a depth of h (m) is given by

22

22

hx

hag z

+=

γρπ

where x = 0 is the point just above the center of the cylinder, 213111067.6 −−−×= skgmγ is the

gravitational constant in SI unit, a is the radius in m, ρ is the density contras in kg/m3 (1g/cm

3 =

1000kg/m3). The measured gravity usually is in mGal, 1 mGal = 10

-5m/s

2. Based on the gravity

curve, we choose the center of mass of the two bodies as x1c = 700 m, x2c = 2200 m. We choose

the leftist two points to estimate a1 and h1, and the rightist two points to estimate a2 and h2.

For cylinder one: the two points chosen correspond to (x1 = 0 - x1c = -700m, gz1 = 26.7mGal), (x1

= 100 m – x1c = -600m, gz1 = 29.2mGal), that is

( ) ( )

( ) 2

1

2

1

32131122

125

700

/15001067.62/107.26

h

mhmkgskgmmasm

+−

××××=×

−−−

−π

(1)

( ) ( )

( ) 2

1

2

1

32131122

125

600

/15001067.62/102.29

h

mhmkgskgmmasm

+−

××××=×

−−−

−π

(2)

Taking the ratio of (1) and (2), we find

2

1

2

2

1

2

700

60091438.0

2.29

7.26

h

h

+

+== , mh 1.10141 =

Insert h1 = 1014.1m into (1) and solve for a1, we have

( )mma 79710797.0

1.101415001067.62

1.1014700107.26 3

11

225

1 =×=××××

+××=

−

−

π

For cylinder two: the two points chosen correspond to (x2 = 2900m – x2c = 700m, gz1 =

33.4mGal), (x2 = 3000m – x2c = 800m, gz1 = 30.8mGal), that is

( ) ( )

( ) 2

2

2

2

32131122

225

700

/15001067.62/104.33

h

mhmkgskgmmasm

+

××××=×

−−−

−π

(3)

( ) ( )

( ) 2

2

2

2

32131122

225

800

/15001067.62/108.30

h

mhmkgskgmmasm

+

××××=×

−−−

−π

(4)

Taking the ratio of (3) and (4), we find

2

2

2

2

2

2

700

80008442.1

8.30

4.33

h

h

+

+== , mh 4.11342 =

Insert h2 = 1134.4m into (3) and solve for a2, we have

( )mma 91210912.0

4.113415001067.62

4.1134700104.33 3

11

225

2 =×=××××

+××=

−

−

π


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Thus, the estimated body parameters are:

The coordinates of the corners of body one: ( )mahzmaxxc

217,97 111111 =−=−=−= ,

( )mahzmaxxc

217,1497 111111 =−==+= , ( )mahzmaxxc

1811,1497 111111 =+==+= , and

( )mahzmaxxc

1811,97 111111 =+=−=−= . Similarly, the coordinates of the corners of body

two are: ( )mahzmaxxc

222,1288 222222 =−==−= ,

( )mahzmaxxc

222,3112 222222 =−==+= , ( )mahzmaxxc

2046,3112 222222 =+==+= ,

and ( )mahzmaxxc

2046,1288 222222 =+==−= . These initial estimates are very useful for the

model initialization. Therefore, the initial model is summarized as follows:

Body Density (g/cm3) vertex X (m) Z (m)

1 1.5 1 -97 217

2 1497 217

3 1497 1811

4 -97 1811

2 1.5 1 1288 222

2 3112 222

3 3112 2046

4 1288 2046

Step 7. Launch GRAVMAG

This is a repeat of Step 1 in case you already exited the GRAVMAG program. If GRAVMAG is

still on, omit this step.

Step 8. Enter Data into GRAVMAG

From “Model Table” window, enter two bodies using the estimated parameters in Step 6. The

“Model Table” window looks like below:


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From the “Model Table” window, click “Window” and select “Section” to bring out the “Cross

section” window. Change the default 100m for Bottom (m) and Right to 3000 m and then click

in the plotting area, the “Cross section” window will look like below.

Click “Window” and select “Gravity Data”

from “Cross section” window to bring the

“Gravity Data” window out. Change the

default 11 for “Number of measurements” to

1 and click somewhere in the data entry area.

Type in 31 for “Number of measurements”

and click again in the data entry area. This

results in the desired 31 data points for the

entry of the observed gravity data. Now use

the “Tab” key or arrow key to move from row

to row and enter the observed gravity data.

After your entry, the model table looks like

below. Also, you can see that the RMS Misfit

= 26.11987 mGal which is pretty high. This

means that the observed and calculated does

not yet match well.


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Step 9. Determining Subsurface Model Parameters Click on the “Cross section” window, you can see both the observed and simulated data from the

initial estimated model. Calculated gravity is higher than the observed data. Besides, the two

bodies overlapped, making the resulted gravity curve look like from one body. The observed

curve seems to be a result from two separate bodies. Now, we adjust the two bodies’ positions

and shape to fit the observed data. This takes some time. Finally we come up to a good fitting

which can be seen in both “Cross section” window and “Gravity Data” window. The RMS Misfit

has been reduced to 0.2673098 mGal. (You may get a different fitting, RMS Misfit is an

indicator how well the fitting is.)

From the “Model Table” window, we can see the model parameters. Click “Edit” and select

“Copy Model” and paste to a word file. Here are the model parameters:

Body Density (g/cm3) vertex X (m) Z (m)

1 1.5 1 257.9186 407.6087

2 1255.656 521.7391

3 1309.955 2086.957

4 352.9412 1940.217

2 1.5 1 1520.362 619.5652

2 2701.357 277.1739

3 2769.231 2494.565

4 1547.511 2315.217

5. Assignments 1. Use GRAVMAG to simulate the gravity at a fault. A slab of 1.1km thick is faulted at x

between 3km and 3.5km as shown below.


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The density contrast is 1670kg/m3. The model parameters are shown in the following table.

Slab Vertex X (m) Z (m)

left 1 110 1780

2 3250 1780

3 3050 2880

4 110 2880

right 1 3630 300

2 6830 300

3 6830 1400

4 3430 1400

A gravity survey is to be carried out from 2000m inclusive to 4000m inclusive at an internal of

100 m. Calculate the gravity anomaly due to the faulted slab.

2. What is shown below is a table of gravity anomaly from a gravity survey after a series of

correction (free-air correction, Bouguer correction, terrain correction, etc.). Assume the density

contrast is 1.67g/cm3. The interval between two gravity measurements is 200m. Interpret these

survey data (the model parameters, cross-section, a plot of observed and calculated gravity

versus traverse distance showing how well the fitting is). ID X (m) Observed

S1 0 11.7

S2 200 13.2

S3 400 15.0

S4 600 17.2

S5 800 20.0

S6 1000 23.4

S7 1200 27.6

S8 1400 33.1

S9 1600 39.9

S10 1800 47.6

S11 2000 54.7

S12 2200 60.2

S13 2400 64.5

S14 2600 67.8


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S15 2800 70.2

S16 3000 72.0

S17 3200 73.3

S18 3400 74.2

S19 3600 74.6

S20 3800 74.6

S21 4000 74.3

Hint: For an semi-infinite horizontal slab,

+= −

h

xtg z

1tan

22

πγρ , where t is the thickness of

the slab in m, x = 0m is the point just above the end tip of the slab. This formula might be useful

for model initialization. For infinite or semi-infinite problems, you should assign a long enough

length for the model, you can not input infinite in GRAVMAG.

geop4210_lab1_gravityinterpretation

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