3D electrical resistivity inversion using prior spatial shape constraints

To minimize the number of solutions in 3D resistivity inversion, an inherent problem in inversion, the amount of data considered have to be large and prior constraints need to be applied. Geological and geophysical data regarding the extent of a geological anomaly are important prior information. We propose the use of shape constraints in 3D electrical resistivity inversion, Three weighted orthogonal vectors （a normal and two tangent vectors） were used to control the resistivity differences at the boundaries of the anomaly. The spatial shape of the anomaly and the constraints on the boundaries of the anomaly are thus established. We incorporated the spatial shape constraints in the objective function of the 3D resistivity inversion and constructed the 3D resistivity inversion equation with spatial shape constraints. Subsequently, we used numerical modeling based on prior spatial shape data to constrain the direction vectors and weights of the 3D resistivity inversion. We established a reasonable range between the direction vectors and weights, and verified the feasibility and effectiveness of using spatial shape prior constraints in reducing excessive structures and the number of solutions. We applied the prior spatially shape-constrained inversion method to locate the aquifer at the Guangzhou subway. The spatial shape constraints were taken from ground penetrating radar data. The inversion results for the location and shape of the aquifer agree well with drilling data, and the number of inversion solutions is significantly reduced.

力是物质的第五维空间

世界是由多种多样的物质所组成的,物质又是在空间和时间中不断地运动着的,因此,物质具有多维性,运动着的物质所产生的作用力是物质的第五维空间。 什么是物质?革命导师列宁是这样正确地阐明了物质定义:“物质是标志着客观实在的哲学范畴,这种客观实在是通过感觉感知的,它不依赖我们的感觉而存在,为我们的感觉所复写、摄影、反映。物质的客观实在性是物质的根本特性,而运动则是物质存在的形式和根本属性。 物质的客观实在性和运动性。