دانلود رایگان ترجمه مقاله محاسبه تغییرات در مولفه های گرادیان گرانشی (نشریه اسپرینگر ۲۰۱۶)

محاسبه میزان تغییرات مولفه های گرادیان ثقل از روی مشاهدات GRACE و مدل تحلیلی

Computation of the changes in gravitational gradient components from GRACE observations and analytical model

Abstract

In this study the gravitational gradient changes caused by faulting on a finite rectangular plane buried in a homogenous half-space are computed using an analytical model which is a function of fault parameters. The sensitivity analysis of the analytical model with optional parameters revealed that the model is sensitive to the most of the fault parameters such as slip, depth, dip and is not sensitive to the strike. Also the results show that the model is sensitive to the length and the width of the fault. Moreover, the gravitation and gravitational gradient changes for the case of the Maule earthquake on 27 February 2010 are directly computed by GRACE observations without need to fault parameters information. Since the high-frequency contents in gravitational field variation can be amplified by deriving the gravitational gradients, the GRACE-derived coseismic gravitational gradient changes clearly delineate the fault lines and better define the extent of the coseismic deformation.

۱ Introduction

Modeling of crustal deformation and exploring the physical impact of this phenomenon is one of the most popular subjects in a ground science particularly in geodesy and geophysics. Numerous studies have been undertaken by many scientists to study co-seismic deformation in a half-space Earth model, a spherical earth model, and even a 3D earth model. For a half-space earth model, Steketee (1958), Maruyama (1964) and Okada (1985), etc. presented analytical expressions for calculating the surface displacement, tilt, and strain resulting from various dislocations. Especially, Okada (1985) summarized previous studies and presented a complete set of analytical formulae for calculating these geodetic deformations. One of the analytical models of computing the gravitational changes due to deformation was presented by Okubo model (Okubo 1991). Okubo (1991) computed gravitational potential changes in a homogenous elastic half space for a point dislocation. He developed his theory to rectangular fault in a half space and computed gravitational potential and gravity changes in the form of fault parameters. Okubo (1992) proposed closed-form expressions to describe potential and gravity changes resulting from dislocations. Because of their mathematical simplicity, these formulations (e.g., Okada 1985; Okubo 1992) have been widely applied to study seismic faults. All of the mathematical models explained above were developed for a deformed earth surface because most traditional gravity measurements are performed on the earth surface. However, advances in modern geodetic techniques, such as GPS, InSAR, altimetry, and GRACE enable better detection of co-seismic deformations such as displacement, gravity change, and strain.

One of the observations resources for comparison to geodynamic models are gravity observations. Earthquake causes redistribution of mass and gravity changes. Some part of this change is due to hydrology and the main part is due to tectonic motion. Changes of gravity field can be detected by observation of the gravity field at different times. Coseismic deformations observed on the Earth surface or modeled by conventional dislocation theory can be compared directly with those observed by gravity satellite missions. Satellite measurements of time-variable gravity field are new data type, capable to modeling and detecting global mass transfers within the Earth. Such a global mass redistribution may lead to significant changes in the Earth’s gravity field that is detectable by gravimetric satellites. However, the regional mass transfer such as localized tectonic processes due to earthquake and volcano, can have an indicative influence on gravity fields that may be sensed by GRACE (Ogawa and Heki 2007; Han et al. 2010, 2013; Heki and Matsuo 2010; Linage et al. 2009).

In this study the analytical model of Okubo (1992) is used which computes the gravity changes due to a dislocation on a rectangular fault plane within an elastic, isotropic and homogenous half-space. The formulation of that model is expanded to compute the gravitational gradient changes due to a fault in an elastic and homogenous half space. Also a sensitivity analysis is applied to analytical model to show that the model is sensitive to the fault parameters and is comparable with observations. Moreover, we infer the full gravitational gradient tensor from the GRACE Stokes coefficients by taking the second derivatives of the gravitational potential in a given orthogonal coordinate system without any required information about fault parameters, and apply these quantities to compare with analytical model and discuss the coseismic deformation resulting from the Maule Chilean undersea earthquakes. With the emphasis on the high-frequency components resulting from the second derivatives of the potential, the coseismic gravitational gradient changes delineate more clearly the rupture line, and reveal refined mass redistribution features caused by the earthquakes. In addition, some of the gradient components, which are inherently less vulnerable to GRACE stripe errors, help to refine the edges of the mass anomaly.