DC resistivity element-free forward modelling method based on partition of unity quadrature (PUQ)

Abstract

The invention provides a DC resistivity element-free forward modelling method based on partition of unity quadrature (PUQ); the method comprises the following steps: building a computational domain according to the medium resistivity distribution in a 2D earth electricity model, and geometrical morphology and hypsography form of a resistivity anomalous body, and using irregularly distributed nodesto disperse the earth electricity model; using the partition of unity quadrature (PUQ) convert a global computational domain integral equation of the DC resistivity method into a node local domain integral equation; building node local integral domains, and employing a Gauss integral to compute an integral formula in each node local integral domain, thus obtaining a computational domain disperseequation; solving the disperse equation to as to obtain a node electric field value, and calculating to obtain an apparent resistivity parameter of an observation point. Based on the random node distribution disperse model, the method uses the partition of unity quadrature (PUQ) to convert the global domain integral into the node local domain integral without needing inter-node connection information and unit, and removing grid constraints; the method has a strong adaptation and flexibility on a random complex earth electricity model.

Description

technical field [0001] The invention relates to a DC resistivity forward modeling method in the field of exploration geophysics, in particular to a DC resistivity unit-free forward modeling method based on unit decomposition and integration with high precision, high flexibility and high adaptability of complex geoelectric models. Background technique [0002] The DC resistivity method is an important method in geophysical prospecting, which is widely used in solid mineral resource exploration, hydrogeological prospecting, environmental governance and monitoring, engineering geophysical prospecting and other fields. The measured apparent resistivity has a direct relationship with the resistivity of the underground medium. The distribution of underground resistivity anomalies can be judged by observing the apparent resistivity on the surface or in the well by artificially supplying electricity to the underground. With the development of DC resistivity method exploration techno...

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Problems solved by technology

With the development of DC resistivity method exploration technology, there is an increasing demand for high-precision, high-adaptability and flexible forward modeling methods for complex geoelectric models. The element-free method is an emerging numerical simulation method (Belytschko, et al., 1994; Hadinia and Jafari, 2015), which only needs node information in the local support domain, does not rely on grid link information, and has the characteristics of high flexibility and adaptability due to the use of The high-precision interpolation method has the characteristics of high precision and has been widely studied. At present, the element-free method has been applied in the forward simulation of DC resistivity. For example, Ma Changying and Liu Jianxin published in the Journal of Geophysics in 2017 "DC Resistivity Forward Modeling Simulation Based on Global Weak Form Element-Free Method", but in the process of DC resistivity forward simulation based on local weak form element-free method, it is necessary to divide the background unit in the calculation domain, which still requires Units are dependent, which to a certain extent loses the nature of no units. At the same time, the distribution of background units directly affects the simulation accuracy. It is difficult to use a unified standard background unit division method to obtain the optimal background unit distribution for different models and node distributions. Dense background unit subdivision is often used to adapt to different models and node distributions to ensure simulation accuracy

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