Next: Numerical Examples Up: Optimization of Non-Linear Gravity Previous: Generalized Simulated Annealing
Next: Numerical
Examples Up: Optimization
of Non-Linear Gravity Previous: Generalized
Simulated Annealing
A gravity survey provides the distribution of the gravity field on a reference surface. The gravity curve, presents the regional, as well as the residual anomalies which are the base for the interpretation of buried bodies. After all the usual corrections, we have the Bouguer anomaly which represents the attraction due to density differences within the Earth. In terms of the signal analysis, as quoted by Oldenburg [21], we can state that a gravity profile is frequently characterized by a smooth regional trend, overlapped by an information with usually greater frequency. The interpretation of gravity anomalies has application in both exploration and solid earth geophysics. Oldenburg [21], for instance, used a gravity survey perpendicular to continental margin for data inversion, and established the position of the Mohorovicic discontinuity. The geological interpretation of gravity anomalies consists basically of the determination of the magnitude and position of the masses. Up to 1948, little attention has been given to the direct calculation of masses from the anomaly values.
The usual procedure, as explained by Bullard and Cooper [22], was to use master set tables and diagrams of forward modeling of different mass distributions. These gravity fields were compared with a given observed field anomaly, in order to estimate the best solution from such an ``atlas''. In contrast to this process called forward modeling, the inverse problem in gravity prospection is the determination of the anomaly density, given by the values of the gravity field. In general, the geometry of the anomalous body is considered to be known for both forward and inverse modeling. As an inverse problem, gravity inversion is also connected to the question of non-uniqueness. According to Al-Chalabi [23] the ambiguity has several causes: incomplete knowledge of the anomaly length, the fact that the anomaly is represented by models which are simpler than the true model, and, of course, observational errors are always present in the gravity field data. Since ambiguity is always present, many different models will satisfy the input data.
In the 2-D case, the assumption is made that the structure has an infinite
extension in the an y horizontal direction, so that the density
will be a function of z (vertical coordinate) and x (horizontal
coordinate), i.e. 
. Obviously in nature there are no 2-D geological structures. The 2-D figure
is as Talwani [24] stated, a simplication
for modeling calculations. But the question arises in the validity of 2-D
modeling, i.e., how far the prism should extend in the y direction
in order to neglect the error in the 2-D modeling. We can calculate the
difference between the gravity field generated by the limited prism in
the y direction and the body with infinite extension. Telford et
al. [20], state that in general a body
can be considered 2-D when its strike length is about 20 times all the
other dimensions, including the depth below the surface, and when the cross-section
is the same at all points along the strike.
In terms of linearity, the inverse problem can be linear or not as prevoiusly explained. In the next section we present 3 synthetic examples in order to study the feasibility of applying the GSA in inverse gravity problems.
