Some class of nonlinear inequalities with gradient constraints in Orlicz spaces

In the present paper, we show the existence of solutions of some nonlinear inequalities of the form 〈Au + g(x, u,∇ u), v −u〉 ≥〈 f, v −u〉 with gradient constraint that depend on the solution itself, where A is a Leray-Lions operator defined on Orlicz spaces, g is a nonlinearity and f ∈ L1.

Joint inversion of two-dimensional magnetotelluric and surface wave dispersion data with cross-gradient constraints

SUMMARY Multiphysics imaging for data inversion is of growing importance in many branches of science and engineering. Cross-gradient constraint has been considered as a feasible way to reduce the non-uniqueness problem inherent in inversion process by finding geometrically consistent images from multigeophysical data. Based on OCCAM inversion algorithm, a direct inversion method of 2-D profile velocity structure with surface wave dispersion data is proposed. Then we jointly invert the profiles of magnetotelluric and surface wave dispersion data with cross-gradient constraints. Three synthetic models, including block homogeneous or heterogeneous models with consistent or inconsistent discontinuities in velocity and resistivity, are presented to gauge the performance of the joint inversion scheme. We find that owning to the complementary advantages of the two geophysical data sets, the models recovered with structure coupling constraints exhibit higher resolution in the classification of complex geologic units and settle some imaging problems caused by the separate inversion methods. Finally, a realistic velocity model from the NE Tibetan Plateau and its corresponding resistivity model calculated by empirical law are used to test the effectiveness of the joint inversion scheme in the real geological environment.

Joint MT and Gravity Inversion Using Structural Constraints: A Case Study from the Linjiang Copper Mining Area, Jilin, China

We present a joint 2D inversion approach for magnetotelluric (MT) and gravity data with elastic-net regularization and cross-gradient constraints. We describe the main features of the approach and verify the inversion results against a synthetic model. The results indicate that the best fit solution using the L2 is overly smooth, while the best fit solution for the L1 norm is too sparse. However, the elastic-net regularization method, a convex combination term of L2 norm and L1 norm, can not only enforce the stability to preserve local smoothness, but can also enforce the sparsity to preserve sharp boundaries. Cross-gradient constraints lead to models with close structural resemblance and improve the estimates of the resistivity and density of the synthetic dataset. We apply the novel approach to field datasets from a copper mining area in the northeast of China. Our results show that the method can generate much more detail and a sharper boundary as well as better depth resolution. Relative to the existing solution, the large area divergence phenomenon under the anomalous bodies is eliminated, and the fine anomalous bodies boundary appeared in the smooth region. This method can provide important technical support for detecting deep concealed deposits.