We study the applicability of Generative Adversarial Networks (GANs) for generating the synthetic data related to well construction and geological characterisation of the near-wellbore area. We focus on 1D mud logs (time-series) and 2D core images. GANs are known to have difficulties with their quality assessment in general. Moreover, generic GAN's performance assessment methods cannot be suitable for the petroleum domain. A petroleum engineer expects the GANs to generate data with specific physical and geological properties, not just a colourful picture. We have trained over 40 GAN models and generated synthetic data with them. Then, we have involved several experts to analyse the generated data in order to address the question of whether it is possible to substitute human analysis with a mathematical metric. We found that some quantitative mathematical metrics can represent our experts’ perceptions. In particular, we show that for 2D core images, Mode Score metric with standard inception v3 model is the best proxy for all considered qualitative metrics of expert's perception according to the Kendall correlation (for two qualitative metrics the correlation is strong, the absolute value is above 0.7, and for other two it is moderate, the absolute value is between 0.5 and 0.7); for mud logs time-series, Mode Score and Frechet Inception Distance with the InceptionTime model provide the strong (above 0.7) correlation with objects reconstruction quality, whereas Inception Score has almost strong correlation (with Kendalls’-tau coefficient 0.69) with experts’ perception of objects generation quality. With these results, experts manual annotation of generated objects during GAN model selection process can be reduced to calculating the corresponding quantitative metrics.