scholarly journals Generalization of level-set inversion to an arbitrary number of geological units in a regularized least-squares framework

Geophysics ◽  
2021 ◽  
pp. 1-76
Author(s):  
Jérémie Giraud ◽  
Mark Lindsay ◽  
Mark Jessell
Keyword(s):  
Least Squares ◽  
Level Set ◽  
Arbitrary Number ◽  
Tectonic Setting ◽  
Physical Property ◽  
Inversion Method ◽  
Regularized Least Squares ◽  
Signed Distance ◽  
Geological Unit ◽  
Geological Units

We present an inversion method for the recovery of the geometry of an arbitrary number of geological units using a regularized least-squares framework. The method addresses cases where each geological unit can be modeled using a constant physical property. Each geological unit or group assigned with the same physical property value is modeled using the signed-distance to its interface with other units. We invert for this quantity and recover the location of interfaces between units using the level-set method. We formulate and solve the inverse problem in a least-squares sense by inverting for such signed-distances. The sensitivity matrix to perturbations of the interfaces is obtained using the chain rule and model mapping from the signed-distance is used to recover physical properties. Exploiting the flexibility of the framework we develop allows any number of rocks units to be considered. In addition, it allows the design and use of regularization incorporating prior information to encourage specific features in the inverted model. We apply this general inversion approach to gravity data favoring minimum adjustments of the interfaces between rock units to fit the data. The method is first tested using noisy synthetic data generated for a model comprised of six distinct units and several scenarios are investigated. It is then applied to field data from the Yerrida Basin (Australia) where we investigate the geometry of a prospective greenstone belt. The synthetic example demonstrates the proof-of-concept of the proposed methodology, while the field application provides insights into, and potential re-interpretation of, the tectonic setting of the area.

Multiple level-set joint inversion of traveltime and gravity data with application to ore delineation: A synthetic study

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. R13-R30 ◽  
Author(s):  
Polina Zheglova ◽  
Peter G. Lelièvre ◽  
Colin G. Farquharson
Keyword(s):  
Physical Properties ◽  
Level Set Method ◽  
Level Set ◽  
Joint Inversion ◽  
Gravity Data ◽  
Level Set Methods ◽  
Physical Property ◽  
Magnetic Data ◽  
Inversion Method ◽  
Multiple Level

We have developed a multiple level-set method for simultaneous inversion of gravity and seismic traveltime data. The method recovers the boundaries between regions with distinct physical properties assumed constant and known, creating structurally consistent models of two subsurface properties: P-wave velocity and density. In single level-set methods, only two rock units can be considered: background and inclusion. Such methods have been applied to examples representing various geophysical scenarios, including in the context of joint inversion. In multiple level-set methods, several units can be considered, which make them far more applicable to real earth scenarios. Recently, a multiple level-set method has been proposed for inversion of magnetic data. We extend the multiple level-set formulation to joint inversion of gravity and traveltime data, improving upon previous work, and we investigate applicability of such an inversion method in ore delineation. In mineral exploration environments, traditional seismic imaging and inversion methods are challenging because of the small target size and the specific physical property contrasts involved. First-arrival seismic traveltime and gravity data complement each other, and we found that joint multiple level-set inversion is more beneficial than separate inversions, especially with limited data and slow targets. Our method is more robust than the joint inversion method based on clustering of physical properties in recovery of piecewise homogeneous models not well-constrained by the data. To justify the known property assumption, we found the degree of robustness of the multiple level-set joint inversion to uncertainties arising from incomplete knowledge of small-scale subsurface physical property variations and target composition.

Inversion of detrital zircon data to constrain spatially varying erosion rates

2020 ◽  
Author(s):  
Fien De Doncker ◽  
Frédéric Herman ◽  
Matthew Fox
Keyword(s):  
Least Squares ◽  
Detrital Zircon ◽  
Erosion Rate ◽  
Least Squares Method ◽  
A Priori ◽  
Age Distribution ◽  
Inversion Method ◽  
Provenance Analysis ◽  
Erosion Rates ◽  
Geological Unit

<p>Landscapes evolve through surface processes that are often transient in space and time. To understand the underlying geomorphic processes, one must assess how erosion rates vary spatially. This can be done using provenance analysis. Here, we introduce a formal inversion method to derive erosion patterns using detrital zircon age data as fingerprints. Zircons are omnipresent in Earth’s crust and contain information about the time since (re)crystallization in their U/Th-Pb ratio. For each geological unit having undergone a specific tectonic or magmatic history, one can find a unique age-frequency signature. Hence, erosion and sedimentation of grains originating from diverse source areas lead to a mix of the varying age-frequency signatures in sediments found at the outlet of a catchment. Considering that the age signal is not altered during erosion-transportation-deposition events, and given that recent technological advances enable precise dating of large amounts of grains, U/Th-Pb zircon ages provide an appropriate fingerprinting tool. Our inversion approach relies on the least-squares method with a priori information and model covariance to deal with non-uniqueness. We show with synthetic and natural examples that we are able to retrieve erosion rate patterns of a catchment when the age distribution for each geological unit is well known. Furthermore, relying on the nested form of catchments and their subcatchments, we demonstrate that adding samples taken at the outlet of subcatchments improves the estimation of erosion rate patterns. We conclude that the least squares inverse model applied on detrital zircon data has great potential for investigating erosion rates.</p>

RPC Estimation via $\ell_1$-Norm-Regularized Least Squares (L1LS)

2015 ◽  
Vol 53 (8) ◽  
pp. 4554-4567 ◽  
Author(s):  
Tengfei Long ◽  
Weili Jiao ◽  
Guojin He
Keyword(s):  
Least Squares ◽  
Regularized Least Squares
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