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Inversion of Residual Gravity

Anomalies Using Neural Network

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Introduction

Gravity data interpretation aims to estimate

depth and location of causative target

Gravity data interpretation non-unique

Modular neural network (MNN) inversion is

used to compute depth and shape factor of

causative

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Why Neural Networks?

Provides unique solution for noisy data

Can model linear and highly non-linear

input/output mapping

Less time complexity

Wide range of input starting models

NNs-global search algorithm

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Neural Networks

Can be considered as universal approximation

f sigmoid transfer function

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Neural Networks(continued)

Training Neural NetworksNN is taught with simulated /measured samples from atraining set of models

The process of the training mainly adjusts the weight parameters (w) in the network

in which the error between the NN model predictions and the desired output [E(w)]

is minimized, where E(w) is a nonlinear function of w.

Iterations are used to explore the weight space where an initial guess would be

implemented first and then iteratively update w as followwnew =wold + dn

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Modular Neural Network

Network is decomposed to several modules Outputs of modules are mediated by an

integrated unit called gating network

The gating network decides which moduleproduced the most accurate response to the

training

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Formulation of Problem The gravity effect at any point P (x, y) on the surface

caused by simple geometric-shaped bodies such as aninfinite horizontal cylinder, a semifinite vertical cylinder,and sphere is given by

where, A is an amplitude coefficient related to the radius

and density contrast of the buried causative target, z is the

depth, x is the position coordinate, and q is the shapefactor which describes the source geometry and has thevalue of 0.5, 1.0, and 1.5 for an infinite horizontal cylinder,a semifinite vertical cylinder and sphere, respectively.

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Formulation (continued)

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Application

Chromite deposit in Camaguey province, Cuba

101 points for the input layer; 50 nodes wereused in the hidden layer, sigmoid transfer

function, 3 local experts

This anomaly was sampled at 73 points ofinput data over 73 m distance with 1-m

interval

The parameter ranges that have been used fortraining the network are

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The depth, z, ranges from 10 to 30 m, with 20

points in this range, The shape factor, q, ranges

from 0.3 to 2, with 5 points in this range, Theamplitude coefficient, A, ranges from 5,000 to

10,500, with 10 points in this range.

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Questions

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Thank You!!