# Practical Tips for 3D Regional Gravity Inversion

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## Abstract

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## 1. Introduction

## 2. Inversion Parameters Setting

#### 2.1. Model Volume V

#### 2.2. Border Size $\Delta b$

#### 2.3. Model Resolution $\Delta x$, $\Delta y$, $\Delta z$

- the volume of each prism should be small enough to consider constant the mass density within the prism itself;
- $\Delta x$, $\Delta y$ and $\Delta z$ should be chosen in such a way to have a discretization error smaller than the observation error;
- $\Delta x$, $\Delta y$ and $\Delta z$ should be chosen in such a way to reduce as much as possible the computational burden;

#### 2.4. Data Reduction

## 3. Conclusions

- we can invert for density anomalies up to a depth of 25 km if we remove from the observations the effect of the density anomalies below 25 km from an a-priori mantle density model (this will entail an error of about $1.5$ mGal);
- we consider borders, in the data reduction, of 165 km around the volume V (this will entail an error of about 3 mGal). The density anomalies in the border can be taken from global models (e.g., CRUST1.0) or even by extrapolating in a constant way the a-priori information available on the density in the volume V;
- V can be discretized on a set of prisms with side 2500 m and a thickness variable between 100 m at the top and 150 m at a depth of 20 km. The discretization in the x and y directions is dictated, in the studied scenario, by the available computational power\time;
- to compute the Bouguer anomaly, we can use the etopo1 model, smoothed with a moving average of size 5 km.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Schematic representation of the parameters defining the 3D model for the gravity inversion discussed in this paper.

**Figure 2.**Average density of the considered models (black solid line) and its 1$\sigma $ accuracy (red solid lines); mean density in the lithospheric upper mantle and in the asthenosphere from the LithoRef18 model [28] (blue dotted line); Moho and lithospheric asthenosphere boundary (LAB) from LithoRef18 (black dashed lines).

**Figure 3.**Omission error STD (black solid line) as a function of the maximum depth of the model and $1\sigma $ accuracy of the mantle gravitational effect (red solid line) from ${\widehat{\overline{z}}}_{V}^{-}$ to a constant ${z}_{Max}$ as a function of ${\widehat{\overline{z}}}_{V}^{-}$.

**Figure 4.**Gravitational effect generated by a volume V, with size 100 km in the x and y directions and ${\overline{z}}_{V}^{-}=-25$ km with a constant density equal to 2670 kg m${}^{-3}$ on a profile in the x direction at the center of V (

**a**); STD of the effect of the borders for the volume V as a function of the border size (

**b**); border size $\Delta b$ as a function of the maximum depth of V given different observation error STD (

**c**).

**Figure 5.**Density model at a depth of 22 km from the CRUST1.0 model (

**a**), and density model extrapolated by the nearest neighbor algorithm (

**b**). The black rectangles at the center of each map represent the study area.

**Figure 6.**Signal due to the a-priori model with 500 m resolution (

**a**); its differences with respect to the signal generated from the 1000 m resolution (

**b**), 1500 m resolution (

**c**) and 2500 resolution (

**d**) models.

**Figure 8.**Covariance of $\Delta g$ (blue line) of the gravitational effect of the etopo1 model (red line) and of the gravitational effect of the etopo1 model smoothed by means of a moving average with size 5 km (black line).

Model | Year | Reference |
---|---|---|

S20RTS | 2004 | Ritsema et al. [17] |

S363ANI | 2008 | Kustowsi et al. [18] |

LRSP30 | 2009 | Boschi et al. [19] |

SAW642ANB | 2010 | Panning et al. [20] |

TX2011 | 2002 | Grand [21] |

S40RTS | 2011 | Ritsema et al. [22] |

SEMUM | 2011 | Lekić et al. [23] |

DR2012 | 2012 | Debayle et al. [24] |

SEMUM2 | 2013 | French et al. [25] |

SAVANI | 2014 | Auer et al. [26] |

CAM2016 | 2016 | Ho et al. [27] |

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**MDPI and ACS Style**

Sampietro, D.; Capponi, M.
Practical Tips for 3D Regional Gravity Inversion. *Geosciences* **2019**, *9*, 351.
https://doi.org/10.3390/geosciences9080351

**AMA Style**

Sampietro D, Capponi M.
Practical Tips for 3D Regional Gravity Inversion. *Geosciences*. 2019; 9(8):351.
https://doi.org/10.3390/geosciences9080351

**Chicago/Turabian Style**

Sampietro, Daniele, and Martina Capponi.
2019. "Practical Tips for 3D Regional Gravity Inversion" *Geosciences* 9, no. 8: 351.
https://doi.org/10.3390/geosciences9080351