# Dispersion Curve Interpolation Based on Kriging Method
## 1 Introduction
In this study, a dispersion curve interpolation method in space is proposed, which can complement the noise source imaging data and can be a foreshadowing for subsequent temporal interpolation. Traditional interpolation methods mostly focus on the prediction of nearest neighbor data and, so, may not perform well when considering geological data. In contrast, kriging has been put forward based on geological data, which may make it more suitable in this context. Kriging is a method proposed by the South African geologist [PERSON] to calculate the reserves of minerals [23]. Based on kriging, [PERSON] proposed the concept of geostatistics, an academic subject included in spatial statistics, and elucidated the theories of regionalized variables [24]. Geostatistics aims to solve problems with spatial and temporal dependence through the estimation of statistical parameters. Many geostatistical methods have been proposed through the combination of geostatistics and traditional geoscience. Undeniably, kriging is the primary method among all geostatistical techniques. In dealing with different scientific problems, kriging has developed into ordinary kriging (OK), universal kriging (UK), co-kriging (CK), disjunctive kriging (DK), regression-kriging, neural kriging, and Bayesian kriging. At present, it is widely used by many scientists in the fields of geological modeling [25], reservoir characterization [26], hydrogeology [27; 28], environmental science [29] and remote sensing [30]. The advantage of kriging, compared with traditional interpolation, is that kriging is a local estimation technique of the best linear unbiased estimator for the unknown values of spatial and temporal variables. Therefore, compared with other interpolation methods, kriging has a higher accuracy for geological models and kriging is determined for the dispersion curve interpolation. The aim of this study is to verify the feasibility of dispersion curve interpolation using kriging in space, apply the interpolation method to the real data of the Changbai volcano and analyze whether the interpolation method can complement areas with low ray density. The dispersion curve interpolation method is proposed to complement the data and expand the imaging area in a noise source method in seismology, which can be a foreshadowing for subsequent temporal interpolation. This method introduces the application of geostatistics in seismology from the spatial domain to the temporal domain. Moreover, data expansion can reduce the cost of field work. The outline of this paper is as follows:  
First, we tested whether universal kriging and ordinary kriging can be applied to the interpolation of dispersion curves. The data used in this study and data pre-processing are described in Section 2. The principle of kriging and its application process to the dispersion curves are described in Section 3. Secondly, we interpolated the dispersion curves from a model of the Changbai volcano, and compared it with the original result from ambient noise tomography. The results of the tests and application regarding the Changbai volcano are described in Section 4. Section 5 details the analysis of the results. Finally, in Section 6, we draw our conclusions.