A Fractal Simulation Method for Simulating the Resource Abundance of Oil and Gas and Its Application

In this study, a fractal simulation method for simulating resource abundance is proposed based on the evaluation results of the exploration risk and prediction technology for the spatial distribution of oil and gas resources at home and abroad. In addition, a key technical workflow for simulating resource abundance was developed. Furthermore, the model for predicting resource abundance has been modified, and the objective functions for conditional simulation have been improved. A series of prediction technologies for predicting the spatial distribution of oil and gas resources have been developed, and the difficulties in visualizing the exploration risks and predicting the spatial distribution of oil and gas resources have been solved. Prediction technologies have been applied to the Jurassic Sangonghe Formation in the hinterland of the Junggar Basin, and good results have been obtained. The results indicated that within the known area, taking the known abundance as the constraint condition, the coincidence rate of the simulated quantities of the original model and the improved model with the actual reserves reached 99.98% after the conditional simulation, indicating that the conditional simulation was effective. In addition, with the improved model, the predicted remaining resources are 0.7899$$\times 10^{8}$$ × 10 8 t, which is 65% of the discovered reserves, and the original model predicts that the remaining resources are 3.5033$$\,\times \,10^{8}$$ × 10 8 t, which is 2.89 times greater than the discovered reserves. Compared with the area in the middle stage of exploration, the results of the improved model are more consistent, and the results of the original model are obviously larger, indicating that the improved model has a good predictive effect for the unknown area. Finally, according to the risk probability and remaining resource distribution, the favorable areas for exploration were optimized as follows: the neighborhood of the triangular area formed by Well Lunan1, Well Shimo1, and Well Shi008, the area near Well Mo11, the area east of Well Mo5, the area west of Well Pen7, the area southwest of Well Shidong1, and the surroundings, as well as the area north of Well Fang2. The application results show that these prediction technologies are effective and can provide important reference and decision-making for resource evaluation and target optimization.

An Embedded Model Estimator for Non-Stationary Random Functions Using Multiple Secondary Variables

An algorithm for non-stationary spatial modelling using multiple secondary variables is developed herein, which combines geostatistics with quantile random forests to provide a new interpolation and stochastic simulation. This paper introduces the method and shows that its results are consistent and similar in nature to those applying to geostatistical modelling and to quantile random forests. The method allows for embedding of simpler interpolation techniques, such as kriging, to further condition the model. The algorithm works by estimating a conditional distribution for the target variable at each target location. The family of such distributions is called the envelope of the target variable. From this, it is possible to obtain spatial estimates, quantiles and uncertainty. An algorithm is also developed to produce conditional simulations from the envelope. As they sample from the envelope, realizations are therefore locally influenced by relative changes of importance of secondary variables, trends and variability.

Stochastic Modeling of Stratospheric Temperature

This study suggests a stochastic model for time series of daily zonal (circumpolar) mean stratospheric temperature at a given pressure level. It can be seen as an extension of previous studies which have developed stochastic models for surface temperatures. The proposed model is a combination of a deterministic seasonality function and a Lévy-driven multidimensional Ornstein–Uhlenbeck process, which is a mean-reverting stochastic process. More specifically, the deseasonalized temperature model is an order 4 continuous-time autoregressive model, meaning that the stratospheric temperature is modeled to be directly dependent on the temperature over four preceding days, while the model’s longer-range memory stems from its recursive nature. This study is based on temperature data from the European Centre for Medium-Range Weather Forecasts ERA-Interim reanalysis model product. The residuals of the autoregressive model are well represented by normal inverse Gaussian-distributed random variables scaled with a time-dependent volatility function. A monthly variability in speed of mean reversion of stratospheric temperature is found, hence suggesting a generalization of the fourth-order continuous-time autoregressive model. A stochastic stratospheric temperature model, as proposed in this paper, can be used in geophysical analyses to improve the understanding of stratospheric dynamics. In particular, such characterizations of stratospheric temperature may be a step towards greater insight in modeling and prediction of large-scale middle atmospheric events, such as sudden stratospheric warming. Through stratosphere–troposphere coupling, the stratosphere is hence a source of extended tropospheric predictability at weekly to monthly timescales, which is of great importance in several societal and industry sectors.

Quantification of Fracture Roughness by Change Probabilities and Hurst Exponents

The objective of the current study is to utilize an innovative method called “change probabilities” for describing fracture roughness. In order to detect and visualize anisotropy of rock joint surfaces, the roughness of one-dimensional profiles taken in different directions is quantified. The central quantifiers, change probabilities, are based on counting monotonic changes in discretizations of a profile. These probabilities, which usually vary with the scale, can be reinterpreted as scale-dependent Hurst exponents. For a large class of Gaussian stochastic processes, change probabilities are shown to be directly related to the classical Hurst exponent, which generalizes a relationship known for fractional Brownian motion. While related to this classical roughness measure, the proposed method is more generally applicable, therefore increasing the flexibility of modeling and investigating surface profiles. In particular, it allows a quick and efficient visualization and detection of roughness anisotropy and scale dependence of roughness.