Gravity inversion and uncertainty assessment of basement relief via Particle Swarm Optimization

Pallero, J. L. G.; Martínez, Jorge Coque; Bonvalot, Sylvain; Fudym, Olivier

doi:10.1016/j.jappgeo.2015.03.008

Cited by 93 publications

(80 citation statements)

References 43 publications

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“…The initial model was estimated using a formulation based on the Bouguer's plate correction formula (see Pallero et al . ):

z_{j}^{b} = \frac{Δ g_{j}^{o b s}}{2 π G Δ ρ}

where

z_{j}^{b}

is the initial depth for the j th prism,

Δ g_{j}^{o b s}

is the observed gravity anomaly at the centre of the prism (if there is not an observation point at this location, its value can be interpolated), G is the universal gravitational constant, and

Δ ρ

is the density contrast,

- 800 kg / {normalm}^{3}

in our case. The initial model has been finally computed as follows:

z^{0} = 0.5 z^{b}

.…”

Section: Numerical Experimentsmentioning

confidence: 88%

“…The value used for the regional trend parameters were

a = 2.358

mGal and

b = - 3.228 mGal / km

, which is the same that has been estimated in Pallero et al . (). We take these values in order to use the same residual Bouguer anomaly and compare the final results of the basement relief estimated by the presented DCT method and the PSO estimation from Pallero et al .…”

Section: Numerical Experimentsmentioning

confidence: 97%

“…The density contrast used in the inversion between these sedimentary fluvial formations and the andesitic basement is

Δ ρ = ρ_{s} - ρ_{b} = - 800 kg / {normalm}^{3}

(Gabalda, Nalpas and Bonvalot ), which was also the value used in Pallero et al . () for the same inversion using particle swarm optimisation (PSO) for the inversion using the DCT pseudo‐inverse, in order to compare the results with the ones obtained with PSO.…”

Section: Numerical Experimentsmentioning

confidence: 99%

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Linear geophysical inversion via the discrete cosine pseudo‐inverse: application to potential fields

Fernández-Martínez

Fernández-Muñiz

Pallero

et al. 2017

Geophysical Prospecting

Self Cite

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In this paper, we present a methodology to perform geophysical inversion of large‐scale linear systems via a covariance‐free orthogonal transformation: the discrete cosine transform. The methodology consists of compressing the matrix of the linear system as a digital image and using the interesting properties of orthogonal transformations to define an approximation of the Moore–Penrose pseudo‐inverse. This methodology is also highly scalable since the model reduction achieved by these techniques increases with the number of parameters of the linear system involved due to the high correlation needed for these parameters to accomplish very detailed forward predictions and allows for a very fast computation of the inverse problem solution. We show the application of this methodology to a simple synthetic two‐dimensional gravimetric problem for different dimensionalities and different levels of white Gaussian noise and to a synthetic linear system whose system matrix has been generated via geostatistical simulation to produce a random field with a given spatial correlation. The numerical results show that the discrete cosine transform pseudo‐inverse outperforms the classical least‐squares techniques, mainly in the presence of noise, since the solutions that are obtained are more stable and fit the observed data with the lowest root‐mean‐square error. Besides, we show that model reduction is a very effective way of parameter regularisation when the conditioning of the reduced discrete cosine transform matrix is taken into account. We finally show its application to the inversion of a real gravity profile in the Atacama Desert (north Chile) obtaining very successful results in this non‐linear inverse problem. The methodology presented here has a general character and can be applied to solve any linear and non‐linear inverse problems (through linearisation) arising in technology and, particularly, in geophysics, independently of the geophysical model discretisation and dimensionality. Nevertheless, the results shown in this paper are better in the case of ill‐conditioned inverse problems for which the matrix compression is more efficient. In that sense, a natural extension of this methodology would be its application to the set of normal equations.

show abstract

“…The initial model was estimated using a formulation based on the Bouguer's plate correction formula (see Pallero et al . ):

z_{j}^{b} = \frac{Δ g_{j}^{o b s}}{2 π G Δ ρ}

where

z_{j}^{b}

is the initial depth for the j th prism,

Δ g_{j}^{o b s}

is the observed gravity anomaly at the centre of the prism (if there is not an observation point at this location, its value can be interpolated), G is the universal gravitational constant, and

Δ ρ

is the density contrast,

- 800 kg / {normalm}^{3}

in our case. The initial model has been finally computed as follows:

z^{0} = 0.5 z^{b}

.…”

Section: Numerical Experimentsmentioning

confidence: 88%

“…The value used for the regional trend parameters were

a = 2.358

mGal and

b = - 3.228 mGal / km

Section: Numerical Experimentsmentioning

confidence: 97%

“…The density contrast used in the inversion between these sedimentary fluvial formations and the andesitic basement is

Δ ρ = ρ_{s} - ρ_{b} = - 800 kg / {normalm}^{3}

Section: Numerical Experimentsmentioning

confidence: 99%

See 1 more Smart Citation

Linear geophysical inversion via the discrete cosine pseudo‐inverse: application to potential fields

Fernández-Martínez

Fernández-Muñiz

Pallero

et al. 2017

Geophysical Prospecting

Self Cite

View full text Add to dashboard Cite

show abstract

“…), gravity (Pallero et al . , ) and self‐potential (SP; Santos ; Peksen et al . ; Gokturkler and Balkaya ).…”

Section: Hybrid Optimizationmentioning

confidence: 99%

A hybrid optimization scheme for self‐potential measurements due to multiple sheet‐like bodies in arbitrary 2D resistivity distributions

Giannakis

Tsourlos

Papazachos

et al. 2019

Geophysical Prospecting

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Self‐potential is a passive geophysical method that can be applied in a straightforward manner with minimum requirements in the field. Nonetheless, interpretation of self‐potential data is particularly challenging due to the inherited non‐uniqueness present in all potential methods. Incorporating information regarding the target of interest can facilitate interpretation and increase the reliability of the final output. In the current paper, a novel method for detecting multiple sheet‐like targets is presented. A numerical framework is initially described that simulates sheet‐like bodies in an arbitrary 2D resistivity distribution. A scattered field formulation based on finite differences is employed that allows the edges of the sheet to be independent of the grid geometry. A novel analytical solution for two‐layered models is derived and subsequently used to validate the accuracy of the proposed numerical scheme. Lastly, a hybrid optimization is proposed that couples linear least‐squares with particle‐swarm optimization in order to effectively locate the edges of multiple sheet‐like bodies. Through numerical and real data, it is proven that the hybrid optimization overcomes local minimal that occurs in complex resistivity distributions and converges substantially faster compared to traditional particle‐swarm optimization.

show abstract

“…Moreover, it has been widely used in different branches of earth science studies such as mineral exploration, hydrogeological, environmental studies, geodesic, seismological studies, isostatic compensation, subsurface cavity detection, archaeo-geophysics, glacier thicknesses, subsurface modelling and engineering applications as well [Telford et al 1990, Reynolds 1997, Kearey et al 2002, Jacoby and Smilde 2009, Hinze et al 2013]. The idea is based on measuring the variations in the Earth's gravitational as well as magnetic field due to the effects of anomalous density and magnetic susceptibility differences between the subsurface rocks [Al-Garni 2013, Ekinci et al 2013, Pallero et al 2015, Ekinci and Yiğitbaş 2015. Within those investigations cited above, mineral or ore explorations take a significant place because of the economic reasons.…”

Section: Introductionmentioning

confidence: 99%

Global nonlinear optimization for the interpretation of source parameters from total gradient of gravity and magnetic anomalies caused by thin dyke

Biswas

Parija²,

Kumar³

2017

Annals of Geophysics

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Gravity inversion and uncertainty assessment of basement relief via Particle Swarm Optimization

Cited by 93 publications

References 43 publications

Linear geophysical inversion via the discrete cosine pseudo‐inverse: application to potential fields

Linear geophysical inversion via the discrete cosine pseudo‐inverse: application to potential fields

A hybrid optimization scheme for self‐potential measurements due to multiple sheet‐like bodies in arbitrary 2D resistivity distributions

Global nonlinear optimization for the interpretation of source parameters from total gradient of gravity and magnetic anomalies caused by thin dyke

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