Sparse inversions have proven to be useful for interpreting potential‐field data because the recovered models are characterized by sharp boundaries, compact features and elevated values, compared with conventional smoothness‐based inversion results. However, several open problems remain to be addressed, including the bound dependence and staircasing problems. The former results in recovered anomalous values being close to the upper bound, while the latter leads to recovered anomalous bodies with either horizontal or vertical boundaries. We have developed a mixed Lp norm regularization strategy to address these two problems. Inversion results based on two synthetic examples confirm the validity of our approach.
Mineral exploration under a thick sedimentary cover naturally relies on geophysical methods. High-resolution airborne magnetic and gravity gradient data were acquired over Northeast Iowa to characterize the geology of the concealed Precambrian rocks and to evaluate the prospectivity of mineral deposits. Previous researchers interpret the magnetic and gravity gradient data in the form of a 2D geological map of the Precambrian basement rocks, which provides important geophysical constraints on the geological history and mineral potentials over the Decorah area located in the northeast of Iowa. However, their interpretations are based on 2D data maps and limited to the two horizontal dimensions. To fully tap into the rich information contained in the high-resolution airborne geophysical data, and to further our understanding of the undercover geology, we have performed both separate and joint inversions of magnetic and gravity gradient data to obtain 3D density contrast models and 3D susceptibility models, based on which we carried out geology differentiation. Based on separately inverted physical property values, we identified 10 geological units and their spatial distributions in 3D which are all summarized in a 3D quasi-geology model. The extension of 2D geological interpretation to 3D allows for the discovery of four previously unidentified geological units, a more detailed classification of the Yavapai country rock, and and the identification of the highly anomalous core of the mafic intrusions. Joint inversion allows for classification of a few geological units further into several sub-classes. Our work demonstrates the added value of the construction of a 3D quasi-geology model based on 3D separate and joint inversions.
The gas content in shale reservoir is of great importance in reservoir evaluation. Shale reservoir has various gas including free gas, adsorpted gas and soluted gas. Free gas take an important part for the total gas content. Hence, we investigated three equations for water saturation calculating and compared and improved them based on theoretical analysis in order to find a siutable one for the shale reservoir characterization. The results indicate that the Archie formula has several limitations applied to complex pore structure, which leads to high water saturation. Since the Archie formula was proposed by experimental data in pure sandstone without enough consideration about the clay of shale reservoir. The Waxman-Smits is suitable to shale gas reservoirs through theoretical analysis, but there are several uncertain parameters. The conductivity of formation water is necessary parameter in calculation of formation water saturation, but calculating the conductivity of formation water is difficult in shale gas reservoir because of its intricate characterization of pore structure and conductivity. Waxman-Smits model take account for the clay conductivity, but there are several uncertain parameters which are hard to obtained, resuting high error. For instance, the equivalent conductivity of exchange cations (B) and the capacitance of exchange anions (Qv) can not be defined accurately relied on experimental calculation, which causes indefinite influence on results. Thus, we concluded that selecting the improved Indonesia equation is a better method to calculate water saturation. This study provided a comprehensive analysis and an accurate way for water satruartion evaluation in shale reservoir.
Summary Accurate delineation of salt body shapes is critical for hydrocarbon exploration. Various imaging methods based on seismic data have been developed. Due to the density contrast between salt and sedimentary rocks, gravity data have also been used as a de-risking tool to constrain the salt body shapes. However, quantifying uncertainties of the salt body shapes recovered from gravity data remains under-explored. Our goal is to understand and quantify how different constraints affect uncertainties of the salt body shapes reconstructed from gravity data. We adopt a trans-dimensional Markov chain Monte Carlo (MCMC) approach to explore the uncertainties. To address the computational challenges with MCMC sampling, we resort to two methods: sparse geometry parameterization and randomized parallel tempering. The first employs a set of simple geometries (e.g., ellipses) to approximate the complex shapes of salt bodies, greatly reducing the number of parameters to be sampled and making the MCMC approach computationally feasible. The second serves to further improve the acceptance ratio and computational efficiency. To quantify the uncertainties of the recovered salt body shapes, we design several scenarios to simulate different constraints on the top boundary of salt bodies from seismic imaging. We develop a new method to impose structural constraints on the top boundaries of salt bodies. This new method combines a set of fixed ellipses with randomly sampled ellipses through a concave hull. The results from different scenarios are compared to understand how uncertainties are reduced when stronger constraints are imposed. In addition, to make our uncertainty quantification results more relevant for practitioners, we propose to compute the salt probability models which show the spatial distribution of probabilities of salt materials at each cell. Lastly, we investigate the effect of an uncertain salt density on the salt body reconstruction and the case of depth-varying densities in the sedimentary background. We apply our methods to the modified 2D SEG-EAGE and Sigsbee salt models and quantify the uncertainties of the recovered salt body shapes in different scenarios. Our results highlight the importance of properly interpreting the uncertainty estimates in light of prior information and information content in the data.
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