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# A new inversion method of estimation of simultaneous near surface bulk density variations and terrain correction across the Bandar Charak (Hormozgan-Iran)

- Reza Toushmalani
^{1}Email author and - Azizalah Rahmati
^{1}

**3**:135

https://doi.org/10.1186/2193-1801-3-135

© Toushmalani and Rahmati; licensee Springer. 2014

**Received:**16 January 2014**Accepted:**27 February 2014**Published:**10 March 2014

## Abstract

A gravity inversion method based on the Nettleton-Parasnis technique is used to estimate near surface density in an area without exposed outcrop or where outcrop occurrences do not adequately represent the subsurface rock densities. Its accuracy, however, strongly depends on how efficiently the regional trends and very local (terrain) effects are removed from the gravity anomalies processed. Nettleton’s method implemented in a usual inversion scheme and combined with the simultaneous determination of terrain corrections. This method may lead to realistic density estimations of the topographical masses. The author applied this technique in the Bandar Charak (Hormozgan-Iran) with various geological/geophysical properties. These inversion results are comparable to both values obtained from density logs in the mentioned area and other methods like Fractal methods. The calculated densities are 2.4005 gr/cm3. The slightly higher differences between calculated densities and densities of the hand rock samples may be caused by the effect of sediment-filled valleys.

## Keywords

- Inversion method
- Estimation near surface bulk density variations
- Terrain correction

## Introduction

Bulk density serves as an important parameter and it is needed to interpret gravity data and determine subsurface structures. Density can be estimated from hand samples when outcrop rocks are exposed. Samples collected in the field tend to have a bias toward lower values of density because they are more weathered, less fluid-saturated, or otherwise unrepresentative of the overall density. In regions that have no exposed outcrop borehole density, logs are useful for determining subsurface densities.

The researcher determined the estimate of subsurface densities by using an inversion technique based on Nettleton (1939), and Parasnis’s (1952) which has been described in Niti (Mankhemthong et al. 2012). The author applied these techniques to analyze the gravity data. The data has been collected in the Bandar Charak area in Hormozgan- Iran. In this case, Free Air anomaly data corrected from raw observed gravity and station coordinates were considered as observed data. The obtained density estimates from the inversion method were compared to existing density data from well logs’ density and rock outcrop sample measurements. Algorithms of the proposed method were implemented via using MATLAB from Math Works, Inc.

### Geology of Bandar Charak area

**Density determination by sampling and system measurement in Charak region (Source: national oil company of Iran, Farmani (**
2003
**))**

Profiling no. | Coordinate (deg) | Stratum | Lithology | Density (g/cm3) | |
---|---|---|---|---|---|

Long. | Lat. | ||||

L18 | 54°36’48.2” | 26°31’48.6” | Bakhtiari Fm. | Conglomerates & Sandstone | 1.87 |

L18 | 1.90 | ||||

L18 | 1.90 | ||||

L19 | 1.89 | ||||

L19 | 1.86 | ||||

L20 | 54°17’13.1” | 26°47’46.0” | Mishan Fm. | Green Marl | 2.14 |

L20 | 2.12 | ||||

L21 | 2.13 | ||||

L22 | 2.07 | ||||

L22 | 2.14 | ||||

L23 | 54°16’57.4” | 26°48’05.9” | Aghajari Fm. | Sandstone & Marl | 2.03 |

L24 | 2.02 | ||||

L25 | 2.04 | ||||

L26 | 53°38’17.8” | 27°05’17.8” | Bangestan Grp. | Limestones | 2.45 |

L26 | 2.39 | ||||

L27 | 2.41 | ||||

L28 | 2.45 | ||||

L29 | 2.39 | ||||

L30 | 53°38’18.6” | 27°04’57.3” | 2.44 | ||

L31 | 2.43 | ||||

L32 | 2.43 | ||||

L33 | 2.45 | ||||

L34 | 2.44 | ||||

L35 | 53°38’18.6” | 27°04’18.3” | Asmari - Gurpi Fm. | Limestone - Gray Marl | 2.36 |

L36 | 2.32 | ||||

L37 | 2.32 |

### Formulations of Nettleton and parasnis density determination methods

Nettleton’s method is based on the observation that over an area of constant density no gravity anomalies should remain after applying the Bouguer correction (Papp, 2009), and that any residual Bouguer anomaly should represent the gravitational attraction of the body of interest. In the Bouguer correction formula, density value that provide the best fit of the Bouguer gravity represents the best estimate of the near surface density. Nettleton developed these methods as follow:

Where,

BA = Gravity Bouguer anomaly

G_{ob} = Absolute gravity

G_{l} = latitude correction

G_{fc} = Free air correction (0.3086 m Gal/m)

G_{bc} = Bouguer slab correction (0.418ρ m Gal/m) where ρ is a rock density in g/cm^{3}

_{bc}) is ignored, Equation (1) is equivalent to the Free Air anomaly formula.

Where,

Where,

∆h = relative elevation change with respect to the reference station (R).

Parasnis’s method is based on the fact that the Bouguer anomaly can be expressed as an equation of the form of “y = mx + b” (Mankhemthong et al. 2012). If the region between the two stations is assumed to be homogeneous in topographic relief and density (ρ), equation (2) represents a straight line with classic form of y = mx, where the ∆FA are the y-values and 0.418∆h are the x-values. The calculated slope (m) corresponds to the average density (ρ) of the surface density rocks or sediments. The Nettleton and Parasnis methods can be used to determine near surface density if a small enough distance between gravity stations is considered. Therefore, deeper regional gravity effects do not dominate.

∆x, ∆y, ∆h, and ∆FA are known parameters and a, b, and ρ are unknown parameters, while ρ representing the density of the subsurface. Note that Equation (5) is still a linear function of the form of “*d* = *a*_{1}*x*_{1} + *a*_{2}*x*_{2} + *a*_{3}*x*_{3}” Thus, a least squares inversion technique can be used to determine the unknown quantities.

### Development of inversion scheme

Where Y is the vector of reduced ∆FA, A is a matrix of perfectly known parameters containing ∆x, ∆y, and ∆h, and x represents a vector of the unknowns (α, β, and ρ).

_{a}

^{-1}) of given free air anomalies, which are approximately 0.1-0.5 mGal.

^{T}to begin to formulate the least squares solution.

Following the method of Tarantola and Valette (1982), let C_{p}^{-1} be the expected covariance of the unknowns. It is assumed the covariance of the near surface density equal to the covariance of given densities from rock sample and density log measurements (~0.05 g/cm^{3}). <x > is an expected unknown vector of a priori information. In an ideal situation, <x> should be equal to x.

### Inversion results

^{3}, while the lab measurements resulted in an average value of 2.3 g/cm3. Because of Application of Fractal methods to determine the Bouguer density in Charak region, an averaged density value equal to 2.4 g/cm3 was calculated Mehrnia et al. (2013). The result is in a good agreement with lab measurement and Fractal estimations. Moreover, from the obtained data, it is possible to mention these values:

## Conclusions

Near surface density determinations based on the Nettleton-Parasnis inversion method can be utilized for estimating representative surface densities where no outcrop or log data may exist. Densities were determined by using two methods with consistent results: (1) Nettleton’s inversion, (2) rock sampling. Based on the results, the calculated densities are around 2.4005 g/cm^{3}. The greater densities from the inversion method (compared to hand samples) over the mountain loops are probably caused by the effects of un modeled topographic relief or valley fill. The calculated density uncertainties reflected the complexities of near surface lithology and structural geology beneath selected gravity stations and provided valuable information on the range of acceptable densities that can be used in further 2.5-D and 3-D forward or inverse modeling in a region.

## Declarations

## Authors’ Affiliations

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## Copyright

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.