Curvature Depth Analysis of Gridded Aeromagnetic DataJ. Phillips, R. Saltus, and D. DanielsU.S. Geological Survey

EGS XXVII General Assembly

Nice, April 21-26, 2002U.S. Department of the InteriorU.S. Geological Survey

Objectives

• Establish a relationship between the curvature of special functions and magnetic source depth, and use it to develop a new depth analysis method.

• Correct shallow depth solutions to a known minimum depth surface by increasing their structural index.

• Apply the new method to real data examples.

Special Functions: F(x) and F(x,y)• Horizontal Gradient Magnitude• Local Wavenumber• Squared Analytic Signal Amplitude:

222

),(

z

M

y

M

x

MyxF

Special Functions for Magnetic Profiles

For a source at (x0,z0) , F(x) will peak over the source and have the functional form:

20

20

200

)(

)()(

zxx

zxFxF

Curvature of Special Functions

CurvatureDefinition

20

20

0

00

20

00

2/32

22

/)(

)(2

)(

)(2

)(2)(

))/(1(

/)(

dxxFd

xF

xK

xFz

z

xFxK

dxdF

dxFdxK

At Peak of Special Function

Curvature Depth:

Profile Example

Curvature Depths for Gridded Magnetic Data

Where K(x,y) is the “most negative curvature” (Roberts, 2001):

),(

),(2),(

yxK

yxFyxz

feydxcxybyaxyxFif

cbabayxK

22

22

),(

)()(),(

Structural Index Values

Contact Thick Dike Thin Sheet 0.0 0.5 1.0

Ribbon Pipe Finite Pipe Dipole 1.5 2.0 2.5 3.0

Correcting shallow depths by increasing the structural index

1

1

2

AS

TRUE

ASTRUE

z

zs

szz

zTRUE (SI=s)

zAS (SI=0.0)

Wisconsin Aeromagnetic Data

Aeromagnetic Map Precambrian Surface

Wisconsin Curvature Depth Results

Depth

SI

National Petroleum Reserve Alaska (NPRA) Aeromagnetic Data

Aeromagnetic Map Seismic Basement

NPRA Curvature Depth Results

Curvature Depths Structural Indices

Intra-Sedimentary Magnetic Sources

Located on aeromagnetic map Minimum elevation above seismic basement

Seismic Intrusions

Flow ChartMag.grd PLUGGRID Mag.plg AS4 Mag.a32

ADDGRD (m)

Maga32.msk CURVDEP Maga32.dep CURV Curv.pst

Obsurf.grd

ADDGRD (+)

Maga32d.asl

Basement.grd CURVSI Ascor.out

Assi.out

GRIDSAMP (1)

Samp1.pst

GRIDSAMP (6)

Samp2.pstx y p1 p2 p3 p4 p5 p6

x y z -- str -- -- SI

Conclusions

• Local curvature can be used to transform special functions F(x,y) of magnetic fields into depth functions z(x,y).

• Shallow depth estimates can be corrected to a known minimum depth surface by increasing the structural index.

• Real data examples show the utility of curvature depth estimates.