Multiridge Method for Studying Ground-Deformation Sources: Application to Volcanic Environments

R Castaldo,M Fedi,P Tizzani,A Barone

doi:10.1038/s41598-018-31841-4

Abstract

Volcanic phenomena are currently monitored by the detection of physical and chemical observations. Generally, the ground deformation field is the most relevant shallow expression of the geometric and physical parameters variations in the magmatic reservoir. In this study, we propose a novel method for the direct estimation of the geometric parameters of sources responsible for volcanic ground deformation detected via the DInSAR technique. Starting with the biharmonic properties of the deformation field, we define an approach based on the Multiridge and ScalFun methods to achieve relevant information about both the positions and shapes of active sources, such as the Mogi source. Our methodology is definitely different from the methods currently used for modeling ground-deformation sources, mainly based on forward or inverse techniques. In fact, (i) it does not require any assumptions about the source type, and (ii) it is not influenced by the distribution of medium elastic parameters or (iii) the presence of high-frequency noise in the dataset. For synthetic cases, we accurately estimate the depth to the source within a 3% error. Finally, we study the real case of the Okmok volcano ground-deformation field and achieve results compatible with those in previous works.

Highlights

In recent decades, the development of remote sensing technologies has provided relevant efforts in the context of earth science
The interpretation of the ground deformation field via the PFT-based methods derives from Love’s work on the elasticity theory[19]. According to his arguments, when the modeled deformation field is not caused by a source shape-change, the deformation field u can be represented by the coefficients of the partial differential equation (PDE), with respect to the coordinates of a single scalar function (φ)[19]: u(x, y, z)
We have proposed and validated a novel method based on the PFT to study the volcanic environment and estimate the geometric parameters of the source model responsible for the ground deformation field

Summary

Methods

The method is applied to interpret the large number of deformation points achieved by the SBAS-DInSAR technique[29]. The interpretation of the ground deformation field via the PFT-based methods derives from Love’s work on the elasticity theory[19] According to his arguments, when the modeled deformation field is not caused by a source shape-change, the deformation field u can be represented by the coefficients of the partial differential equation (PDE), with respect to the coordinates of a single scalar function (φ)[19]: u(x, y, z). The Multiridge[23] method is a multiscale method based on the analysis of so-called ridges, which are defined as lines passing through the maxima of a field and its derivatives at different scales We emphasize that this method can only be applied in cases when the field can be expressed by harmonic functions. Starting from the z0 source depth retrieved by using the Multiridge method, we can use equation (15) to estimate n, ns and N; these values give us information about the geometry of the source

I: Application of the Potential Theory to the Synthetic Deformation Field

Result

Discussion and Conclusion