Modeling 3‐D density distribution in the mantle from inversion of geoid anomalies: Application to the Yellowstone Province

Abstract

[1] We developed a three-dimensional scheme to invert geoid anomalies aiming to map density variations in the mantle. Using an ellipsoidal-Earth approximation, the model space is represented by tesseroids. To assess the quality of the density models, the resolution and covariance matrices were computed. From a synthetic geoid anomaly caused by a plume tail with Gaussian noise added, the inversion code was able to recover a plausible solution about the density contrast and geometry when it is compared to the synthetic model. To test the inversion algorithm in a natural case study, geoid anomalies from the Yellowstone Province (YP) were inverted. From the Earth Gravitational Model 2008 expanded up to degree 2160, lower crust-and mantle-related negative geoid anomalies with amplitude of approximately 70 m were obtained after removing long-wavelength components (>5400 km) and crustal effects. We estimated three density models for the YP. The first model, the EDM-1 (estimated density model), uses a starting model with density contrast equal to 0. The other two models, the EDM-2 and EDM-3, use an initial density derived from two S-velocity models for the western United States, the Dynamic North America Models of S Waves by Obrebsky et al. (2011) and the Northwestern United States Teleseismic Tomography of S Waves (NWUS11-S) by James et al. (2011). In these three models, a lower and an upper bound for the density solution was also imposed as a priori information. Regardless of the initial constraints, the inversion of the residual geoid indicates that the lower crust and the upper mantle of the YP have a predominantly negative density contrast (~À50 kg/m 3 ) relative to the surrounding mantle. This solution reveals that the density contrast extends at least to 660 km depth. Regional correlation analysis between the EDM-1 and NWUS11-S indicates an anticorrelation (coefficient of~À0.7) at 400 km depth. Our study suggests that the mantle density derived from the inversion of geoid could be integrated with seismic velocity models to image mantle anomalous features beyond the depth limit of investigation achieved combining gravity and seismic tomography.

3‐D inversion of gravity data in spherical coordinates with application to the GRAIL data

“…They are not directly applicable to the inversion of global gravity data, which are inherently in the spherical coordinates. For large‐scale geometry of mass concentration in planetary interior, the use of Cartesian coordinates approximation cannot be justified either, and the use of a global spherical mesh and spherical coordinates needs to be considered for accurate modeling [e.g., Liang et al , ; Chaves and Ussami , ; Uieda and Barbosa , ]. Similar to the inversion in the Cartesian coordinates, the inverse problems in spherical coordinates must address the same set of issues: How do we carry out the forward modeling and what are the kernel functions?…”

Evaluation of the fourth-order tesseroid formula and new combination approach to precisely determine gravitational potential

“…i j k . Fortunately, various international authors (e.g., Wild-Pfeiffer, 2008;Tsoulis et al, 2009;Chaves and Ussami, 2013;Shen and Han, 2013;Du et al, 2015) quoted only the second-order expression given by Heck and Seitz (2007), which is correct because of (Deng et al, 2016).…”

“…Many researchers (Forsberg, 1984;Kiamehr and Sjöberg, 2005;Kiamehr, 2006;Hirt et al, 2010;Sjöberg and Bagherbandi, 2011;Jena et al, 2012;Tenzer et al, 2012;Chaves and Ussami, 2013;Claessens and Hirt, 2013;Majumdar and Bhattacharyya, 2014;Rexer and Hirt, 2014) discussed the problems of precisely calculating the gravity effect (gravity anomaly, gravitational potential, gravity vector, gravity gradient, and so on) caused by terrain effects in recent decades. In these studies, various topography models are used, such as Earth2014 global topography model (Hirt and Rexer, 2015), SRTM digital elevation data (Jarvis et al, 2008), based on constant (e.g., 2.67 g cm 3 ), CRUST2.0 (Bassin et al, 2000), CRUST1.0 (Laske et al, 2013), or GEMMA (Reguzzoni and Sampietro, 2015) density distributions.…”

“…Scholars still use the second-order tesseroid formula based on the Taylor series expansion, which was proposed by Heck and Seitz (2007), and then used by vaious iii authors (Tsoulis et al, 2009;Chaves and Ussami, 2013;Claessens and Hirt, 2013;Grombein et al, 2013;Han, 2013, 2016;Hirt and Kuhn, 2014) However, compared with the ultra-high resolution of the topography model (Earth2014, SRTM, GTOPO30, and others) and successive higher accuracy requirement, the second-order tesseroid formula (based on the Taylor series expansion) is insufficient at the very vicinity of the computation point. Thus, formulating a fourth-order or even higher-order tesseroid formula for high-accuracy calculation especially for the mass-elements in the very vicinity of the computation point is necessary.…”

Crustal and Upper Mantle Density Structure Beneath the Qinghai-Tibet Plateau and Surrounding Areas Derived from EGM2008 Geoid Anomalies

“…To derive the density contrast from gravitational observations, we established the objective function in Equation (4) based on the theory of Lagrange multipliers, the method which has been used to invert the geoid anomalies in Yellowstone Province [16]. This theory considers both the error in the observations and the error in the ridge regression of the parameter.…”