Application of horizontal gravity-gradient stack for estimation of surface layer density in mountainous areas

Abstract

The author proposes a new approach for analysing datasets of the differential curvature of a gravity-gradient tensor for density evaluation of the surface layer without a prior density assumption. The method, called the horizontal gravity-gradient stack–moving window correlation (HGGS-MWC) method, is based on a successive MWCs between the acquired data and the data of differential curvature responses of the surface layer calculated based on a digital elevation model. For improving the correlation, a HGGS processing method was devised and patented. It is applied to both datasets before the MWC processing. A point-source differential curvature response has the characteristic of forming a peculiar and symmetrical shape of a quadrant and distributing peaks and troughs over an underlying anomalous mass. These peaks and troughs are near or far away from their centre depending on the depth of the anomalous mass. This enables one to design a filter to enhance the responses of the surface layer. In addition, the HGGS processing affects both the contraction of the gravitational response and the attenuation of responses from deeper subsurface layers. The HGGS-MWC method leads to the production of values of the mass surface roughness ratio (MSR) in the wavenumber domain that are inherent to the measuring plane of surveys and determines the phase relation between the mass of the surface layer and the surface roughness. The MSR is a good indicator of whether a mass surplus or deficit relative to the regional average mass exists under a convex surface layer. Application to the observed datasets was performed in the area where serious landslides were triggered by the 2008 Iwate-Miyagi inland earthquake. Based on a flight height of 150 m, the mass variations of the surface layer, which is down to 300 m below the surface, are properly evaluated by analysing the wavelengths in the data mainly within the range of 270–650 m and perceivably up to 1,650 m. The specific areas can be delineated where low-density deposits, such as possible volcanic ashes and pumices associated with high water content, sit on high mountains with steep slopes. The information is useful for disaster prevention by playing a role in selecting potential areas for conducting further precise surveys. Regional density variations whose wavelengths are longer than 1,650 m remain unsolved and are an issue for future studies. With the issue solved, the results for the density distribution of the surface layer obtained by the HGGS-MWC method will serve for terrain corrections of the vertical gravity-gradient data and gravity data as well.

KEYWORDS:

• Differential curvature of gravity-gradient tensor
• horizontal gravity-gradient stack
• surface layer density
• moving window correlation
• disaster prevention

Acknowledgments

Special thanks are given to JOGMEC and GSI. The author used the publicly available JOGMEC gravity-gradient database compiled in the report HeliFALCON^TM Airborne Gravity Gradiometer Survey, and GSI’s publicly open download services for DEM data. The author acknowledges valuable discussions with Drs. Ryuji Kubota, Atsushi Oshida and Yasuo Tamura, former adviser, of Kawasaki Geological Engineering Co. Ltd. and manuscript review by several reviewers that has led to improvement of this paper.

Disclosure statement

No potential conflict of interest was reported by the author.