Seismic velocity estimation from well log data with genetic algorithms in comparison to neural networks and multilinear approaches

• A genetic algorithm approach for predicting the missing parts of velocity logs
• Derive simple equations linking a set of input logs with seismic velocities
• Compare the genetic algorithms, neural networks and multilinear approaches

Predicting missing log data is a useful capability for geophysicists. Geophysical measurements in boreholes are frequently affected by gaps in the recording of one or more logs. In particular, sonic and shear sonic logs are often recorded over limited intervals along the well path, but the information these logs contain is crucial for many geophysical applications. Estimating missing log intervals from a set of recorded logs is therefore of great interest. In this work, I propose to estimate the data in missing parts of velocity logs using a genetic algorithm (GA) optimisation and I demonstrate that this method is capable of extracting linear or exponential relations that link the velocity to other available logs. The technique was tested on different sets of logs (gamma ray, resistivity, density, neutron, sonic and shear sonic) from three wells drilled in different geological settings and through different lithologies (sedimentary and intrusive rocks). The effectiveness of this methodology is demonstrated by a series of blind tests and by evaluating the correlation coefficients between the true versus predicted velocity values. The combination of GA optimisation with a Gibbs sampler (GS) and subsequent Monte Carlo simulations allows the uncertainties in the final predicted velocities to be reliably quantified. The GA method is also compared with the neural networks (NN) approach and classical multilinear regression. The comparisons show that the GA, NN and multilinear methods provide velocity estimates with the same predictive capability when the relation between the input logs and the seismic velocity is approximately linear. The GA and NN approaches are more robust when the relations are non-linear. However, in all cases, the main advantages of the GA optimisation procedure over the NN approach is that it directly provides an interpretable and simple equation that relates the input and predicted logs. Moreover, the GA method is not affected by the disadvantages that characterise gradient descent techniques such as the NN method.