TY - JOUR
ID - 35981
TI - Gravity data interpretation using the algorithm fourth horizontal derivatives and s- curves method
JO - Journal of the Earth and Space Physics
JA - JESPHYS
LA - en
SN - 2538-371X
AU - Bahrami, Faezeh
AU - Ardestani, Vahid
AD - M. Sc. Student of Geophysics, Islamic Azad University, Hamadan, Iran
AD - Professor, Earth Physics Department, Institute of Geophysics, University of Tehran, Iran
Y1 - 2013
PY - 2013
VL - 39
IS - 4
SP - 73
EP - 82
KW - gravity anomalies
KW - Depth and shape estimation
KW - Numerical fourth horizontal derivative
KW - The s- curves method
DO - 10.22059/jesphys.2013.35981
N2 - The gravity method is one of the first geophysical techniques used in oil and gas exploration. An algorithm is developed for a fast quantitative interpretation of gravity data generated by geometrically simple but also the estimated depths and other model parameters of a buried structure.
Following Abdelrahman et al (1989). The general gravity anomaly expression produced by a sphere, an infinite long horizontal cylinder and a semi- infinite vertical cylinder can be represented by the following equation
(1)
where
and z is the depth of the body, xi is the horizontal position coordinate, σ is the density contrast, G is the universal gravitational constant and R is the radius and q is factor related to the shape of the buried structure and is equal to 0.5,1.0,and 1.5 for the semi- infinite vertical cylinder, horizontal cylinder and the sphere respectively.
Consider nine observation point (xi -4s), (xi -3s), (xi -2s), (xi -s), (xi ), (xi +s), (xi +2s), (xi +3s), (xi + 4s), along the anomaly profile where s=1,2,3,M spacing units and is called the window length.
Using equation (1) the simplest first numerical horizontal gravity gradient (dg/dx)
(2)
the second horizontal derivative gravity anomaly is obtainedfrom equation (2) as
(3)
the third horizontal gradient is(3)
(4)
Similarly, the fourth horizontal gradient is (4)
5)
Which yields;
Where
(7)
Equation (5) can also be solved using a simple iteration method.
Equations (5) can be used to determine the depth and the shape of a buried structure using the window curves method. The validity of the method is tested on synthetic data white and without random errors.
The method was applied to a gravity anomaly from the Abade of Iran .The results shows that the s-curves intersect each other in a narrow region where 7.220