A Probabilistic Unified Depth Velocity Model and Associated Uncertainties Estimation Based on Bayesian Approach

Abstract

Abstract There are high emphasis and expectations placed on obtaining the most accurate depth structure map from seismic data. These maps set the expectations, for drilling depth prognosis and hydrocarbon volumetric estimation of reservoirs. The viability of a hydrocarbon prospect and the success of drilling to tap the resources heavily relies on depth map accuracies. However, achieving precisions have been challenging due to the limitations of the seismic data. This paper describes a novel integrated depth modeling workflow that successfully quantifies the depth uncertainties through a geostatistical simulation-based approach of integrating seismic interpretation inputs, well tops, and seismic velocity together with their associated uncertainties. The method proposed to conciliate seismic uncertainties and to address structural depth uncertainty is called stochastic time to depth conversion. It is a geostatistical driven approach that uses Bayesian Co-Kriging and relies on well depth markers using appropriate time-derived external drifts. The method accounts for uncertainties attached to the seismic time of events picked and velocity uncertainty integrated into a single stochastic workflow. Time Uncertainty is related to the seismic data quality aspects such as resolution limit and tunning thickness and velocity uncertainty is due to imperfectness of the velocity model due to anisotropy or inaccuracies in velocity picking. Both uncertainties can be defined by a 1st standard deviation sigma value or defined by a lateral varying sigma map. Realizations of depth maps are simulated, and the best-estimated depth map is produced. A confidence interval that envelopes the multiple realized horizons can provide meaningful measures of depth uncertainty for drilling depth prognosis giving a window of anticipation of where the top of the reservoir may be encountered. The stochastic approach allows for proper quantification of gross rock volume (GRV) uncertainty which impacts hydrocarbon in-place estimations. Ranking of all GRV outcomes is now possible using the expectation curve where the P10, P50, and the P90 volumes and associated maps can be identified. These maps could then contribute to structural modeling of the low, base, and high case scenarios allowing for hydrocarbon in-place sensitivity analysis. The geostatistics-based time-to-depth method offers a consistent framework to address the bias at the core of the upstream Front-End Loading (FEL) process which ultimately maximizes the accuracy of depth models and improved E&P decision-making. The method is based on Bayesian Co-Kriging and offers the consistent integration of all sources of uncertainty throughout all layers within a unique probability model. Field data applications show that the stochastic depth modeling method is reliable due to its strong dependence on mathematically sound geostatistical principles, scalable that integrates the sequential processes.