National Geoscience Conference 2011 - Department Of Geology ...

NATIONAL GEOSCIENCE CONFERENCE 2011
11 – 12 June 2011 • The Puteri Pacific Johor Bahru, Johor, Malaysia
Paper P1-3
Numerical computation of depth of buried geologic structure from the gravity
anomaly data
Syed Mustafizur Rahman 1* , Noushin Naraghi Araghi 1 , Rosli Saad 1 , M. N. Mohd Nawabi 1 &
Khairul Arifin Bin Mohd Noh 2
1
School of Physics, Universiti Sains Malaysia, 11800 USM, Pulau Pinang, Malaysia
*Email Address: smrahman@usm.my
2
Geoscience and Petroleum Engineering Department, Universiti Teknologi PETRONAS,
Bandar Seri Iskandar, 31750 Tronoh, Perak, Malaysia.
Keywords: geology, structure, gravity, depth, computation
Introduction
The gravity anomaly interpretation is mostly done by iterative methods. Iterations start to compute gravity
anomaly for a model with few known geologic parameters. Computed gravity anomaly is compared with the
observed values and sometimes the model needs to be modified in order to obtain reasonable agreement. Several
methods have been developed to identify the shape (Sharma & Geldart, 1968; Abdelrahman & El-Araby, 1993;
Salem et al., 2003) and depth (Abdelrahman, 1990; Elawadi et al., 2001) of geological structure assuming simple
source geometry from gravity data, though the simple geometries are not geologically realistic in most of the cases.
In many contributions, numerical methods have been presented the estimation of depths of the geological structures
of the gravity anomalies. This research is also introduced a numerical approach to estimate depths of simple models
from residual gravity anomaly.
Methodology
The gravity effect of simple gravity models such as a sphere, an infinite horizontal cylinder, and a semi-finite
vertical cylinder at an observation point (x,z = 0) centered at x = 0 and buried at a depth z can be generalized as:
b m
DCz R
g(
x)
=
(1)
2 2
( x + z ) a
where, D = πGρ and G is the universal gravitational constant, ρ is the density and R is the radius of the shapes. The
values of other variables are expressed below as shown in Table 1.
Using the gravity value g 0
at x = 0, Eq. (1) can be normalized and written as:
2
g(
x)
⎛ z ⎞
g
n
( x)
= = ⎜ ⎟
g
2 2
x z
0 ⎝ + ⎠
where, g 0
= DCz b-2a R m . Eq. (2) can be further written as:
a
(2)
1
1
n n
=
2
2 2
( g ( x)
) a x + ( g ( x)
) a z z
(3)
Eq. (3) has solved for z in this work as:
z
N
N
2
4 ⎛ 2 ⎞
∑ xi
− ⎜∑
xi
⎟
i= 1 ⎝ = 1
=
⎠
N
N N
2
1/ a 2
∑ xi
(1/ g
n
( xi
)} − ∑ xi
∑
i=
1
= 1 i=
1
(1/ g ( x )}
where, N is a number of observations and using Eq. (4), z can be obtained numerically.
n
i
1/ a
Depth computation
Synthetic data
The proposed method has been investigated using synthetic gravity data. The cylinder and sphere models of
having a density contrast of 2.5 x 10 3 kg/m 3 , radius of 5 m and buried at different depths. Though not shown here,
the gravity anomalies were computed along a 100 m profile at an interval of 1 m. A different degree of noises have
also been added over the synthetic gravity data, however the computed depths were also found less erroneous.
Field data
Figure 1 shows the residual gravity anomaly profile of the gravity map of the Humbolt salt dome, TX, USA. This
data has been interpolated with an interval of 0.15 m using splines method. Applying spherical model (C=4/3, b=1,
a=3/2 and t=3) the estimated depths are shown in Table 2.
(4)
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