Prior Applications of Neural Networks in Geophysics

Abstract

As mentioned previously in the primary sections of chapter one, there are several, and varied applications of neural networks in geophysics; here we give a short list of some of these applications:

• Modeling of crustal velocity using Artificial Neural Networks (case study: Iran Geodynamic GPS Network (Ghaffari and Mohammadzadeh 2015)

• Crustal velocity field modeling with neural network and polynomials, SIDERIS, M.G. (Ed.), Moghtased-Azar and Zaletnyik (2009)

• Artificial neural network pruning approach for modular neural networks (Yilmaz 2013)

• Modular neural networks for seismic tomography (Barráez et al. 2002)

• Estimating one-dimensional models from frequency domain measurements

• Quantifying sand fraction from seismic attributes using modular artificial neural networks

• Borehole electrical resistivity modeling using neural networks

• Determination of facies from well logs using modular neural networks (Bhatt and Helle 2002)

• Inversion of self-potential anomalies caused by 2D-inclined sheets (Hesham 2009).

• 2D inverse modeling of residual gravity anomalies from Simple geometric shapes using Modular Feed-forward Neural Network (Eshaghzadeh and Hajian 2018)

Appendices

Appendix 1 of Chapter Two

The procedure of teaching algorithms for MLP networks consist of 4 steps: defining network architecture, defining parameters related to network and learning algorithm (iterations, maximum epoch number and etc., training the network and finally validating and simulating (generalizing) the trained network. This general process is illustrated in Fig. 2.109.

Fig. 2.109

General flowchart of random noise attenuating by ANN

In the example described here, a synthetic noisy seismic CMP gather is chosen and the ability of ANN in random noise attenuation is shown in a simple manner.

As random noise components are supposed not to be predictable in adjacent traces, the logic used for attenuating random noise is based on attenuating whatever is not confirmed to be coherence data.

By comparing the elements of a 7 by 3 neighborhood data and by user’s decision, the network will be trained with some examples (14 training pairs are used here). In Fig. 2.110 the noisy data and the selected adjacent traces from trace No. 1 to No. 3 is illustrated. These three traces are selected for extracting training pairs. The expert knowledge is required here in order to make the decision for choosing best points for marking noise contaminated data as well as pure coherence data related points. The decision could take place as a number (0 for noisy and 1 for noise free points). It should be mentioned that as an advanced algorithm, partly noise contaminated data also should be present in the trained network but in this appendix, the simplicity of the algorithm was the priority. Selected pairs are chosen from trace No. 2 as the training points are supposed to be check in a 7 by 3 neighborhood.

Fig. 2.110

A synthetic noisy CMP gather and the first 3 traces selected for training ANN

After training the network, simulation process will be held. In doing so, the input will be the 7 by 3 neighborhood amplitude (as training input data) for each sample. Now, the weight for each sample could show whether the sample belongs to noise or coherence data space (as training output data).

The results of the Generalizing trained network will be a matrix that contains weights for all data. Denoised version of input data will be achieved by production of weights into noisy data. The results are shown in Fig. 2.111.

Fig. 2.111

Noisy data (right) and denoised version (left) using feed forward back propagation ANN

Appendix 2 of Chapter Two

Brief list of Training functions in Matlab’s NN Toolbox is presented in Table 2.47.

Table 2.47 List of Training functions in NN toolbox of Matlab