Potential-field sharp-boundary inversion will allow us to identify the sharp petrophysical deposit boundaries inside the host rocks. With the purpose to find a more simple and convenient way to achieve a sharp-boundary and well-focused image for 3D focusing inversion, we analyze and discuss the influence of the focusing parameter in several commonly used stabilizing functionals, such as minimum support (MS), minimum gradient support (MGS), modified total variation ([Formula: see text]TV) stabilizing functional, etc. Then, we evaluate an adjustable exponential stabilizing (AES) functional, the focus of which is adjustable by the base and the exponent of the exponential functional, and we apply it to 3D density and magnetic susceptibility inversion for synthetic and field data. Compared with MS, MGS, [Formula: see text]TV, and other stabilizers, the proposed stabilizer can generate well-focused images and provide sharp boundaries. We also determine that sharp-boundary images produced by the proposed AES stabilizer have a weak dependence on the focusing parameter. Furthermore, we can obtain a stable and focused result by controlling the focusing parameter in the exponent of AES adaptively increasing with the iterations. The model tests and inversion of field data verify the flexibility and stability of this adjustable stabilizer.
During the numerical calculation by FE (Finite Element) method, N-R (Newton-Raphson) iterative method will be used to solve the problem such that material performing with elasto-plastic character and geometric non-linearity. However, if the problem has macro scale DOFs (degree of freedom), the classical N-R method is shown to make a low efficiency on the whole process. For this reason, in this paper, an improved N-R iterative method is proposed by creating proper mandatory limiters to change the step size of displacement field increment. In this way, the size of single iterative step is enlarged in the new method with tangent stiffness matrix used as classical N-R iterative theory as well. Furthermore, to test stability of the new method, two models of structure are chosen to be calculated with this method. In the conclusion, the improved N-R iterative method is indicated to be an efficient and stable numerical method which could solve nonlinear problems, especially with macro scale DOFs.
Carbonate reef reservoir buried deeply, show great heterogeneity, Therefore, effective reservoir prediction is the key to the biohermal reservoir. In practical research, based on of the single well sequence stratigraphic framework, combined with these sequence stratigraphic framework and seismic section, found the reservoir development area in the longitudinal, which sq1-HST and sq3-HST is the main period of reservoir development, and then through the seismic Seismic multiple-attribute inversion, predicted porosity of system tracts of reservoir development in the sequence stratigraphic framework. Porosity inversion results shown, Changxing formation reservoir is mainly distributed in the central and north-central of Jiannan area.
Except for producing smoothing models, magnetotelluric inversion also requires focused inversion, which can image sharp boundaries and clear interfaces of electrical structures. The proposed minimum support (MS) and minimum gradient support (MGS) have good focusing ability; however, their focusing effect is highly dependent on the selection of the focusing parameter. In this study, for finding a more stable way to achieve a well-focused image, we propose an exponential minimum support (EMS) stabilizing functional, which combines the properties of the exponential stabilizer and MS, and demonstrate the enhanced focusing ability and smaller dependence on the magnitude of the focusing parameter. Moreover, we construct a model constraint with the hybrid stabilizing functionals EMS and the smoothest (SM) and fulfill the optimization based on Occams inversion scheme. Through theoretical analysis and model tests, we determine the selection schemes of regularization parameter, weighting parameter between EMS and SM, and focusing coefficient in EMS to ensure the stability and reliability of this method. Afterward, we perform the inversions of the synthetic and field data. By comparing the inversion results of the two synthetic wedge models using hybrid EMS and SM and those obtained using other stabilizers, we demonstrate that the hybrid method is capable of imaging sharp boundaries and is stable for a wide range of the focusing parameter values. The inversion result of the COPROD2 field dataset clearly images the high-conductivity anomalies at depths of 1060 km and also depicts the highly conductive features within the upper mantle at depths greater than 100 km. The model tests and field data application verify the stability and capability of this method. Thus, this novel regularization approach provides a tool for sharp boundary inversion and a new reference model for deep structural interpretation.
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