A multiple level-set method for 3D inversion of magnetic data

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. J61-J81 ◽  
Author(s):  
Wenbin Li ◽  
Wangtao Lu ◽  
Jianliang Qian ◽  
Yaoguo Li
Keyword(s):  
Inverse Problem ◽  
Magnetic Susceptibility ◽  
Level Set Method ◽  
Level Set ◽  
A Priori ◽  
Magnetic Data ◽  
Specific Class ◽  
Multiple Level ◽  
Set Functions ◽  
Level Set Functions

We have developed a multiple level-set method for inverting magnetic data produced by weak induced magnetization only. The method is designed to deal with a specific class of 3D magnetic inverse problems in which the magnetic susceptibility is known and the objective of the inversion is to find the boundary or geometric shape of the causative bodies. We adopt the conceptual representation of the subsurface geologic structure by a set of magnetic bodies, each having a uniform magnetic susceptibility embedded in a nonmagnetic background. This representation enables us to reformulate the magnetic inverse problem into a domain inverse problem for those unknown domains defining the supports of the magnetic causative bodies. Because each body may take on a variety of shapes, and we may not know the number of bodies a priori either, we use multiple level-set functions to parameterize these domains so that the domain inverse problem can be further reduced to an optimization problem of multiple level-set functions. To efficiently compute gradients of the nonlinear functional arising from the multiple level-set formulation, we take advantage of the rapid decay of the magnetic kernels with distance to significantly speed up the matrix-vector multiplications in the minimization process. We apply the new method to the synthetic and field data sets and determine its effectiveness.

scholarly journals Identifying arbitrary parameter zonation using multiple level set functions

2018 ◽  
Vol 364 ◽  
pp. 257-273
Author(s):  
Zhiming Lu ◽  
Velimir V. Vesselinov ◽  
Hongzhuan Lei
Keyword(s):  
Level Set ◽  
Arbitrary Parameter ◽  
Multiple Level ◽  
Set Functions ◽  
Level Set Functions

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.

Kantorovich-Rubinstein misfit for inverting gravity-gradient data by the level-set method

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. G55-G73
Author(s):  
Guanghui Huang ◽  
Xinming Zhang ◽  
Jianliang Qian
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Random Noise ◽  
Magnetic Data ◽  
Gravity Gradient ◽  
Local Minima ◽  
Target Model ◽  
Level Set Function ◽  
Level Set Evolution ◽  
Set Function

We have developed a novel Kantorovich-Rubinstein (KR) norm-based misfit function to measure the mismatch between gravity-gradient data for the inverse gradiometry problem. Under the assumption that an anomalous mass body has an unknown compact support with a prescribed constant value of density contrast, we implicitly parameterize the unknown mass body by a level-set function. Because the geometry of an underlying anomalous mass body may experience various changes during inversion in terms of level-set evolution, the classic least-squares ([Formula: see text]-norm-based) and the [Formula: see text]-norm-based misfit functions for governing the level-set evolution may potentially induce local minima if an initial guess of the level-set function is far from that of the target model. The KR norm from the optimal transport theory computes the data misfit by comparing the modeled data and the measured data in a global manner, leading to better resolution of the differences between the inverted model and the target model. Combining the KR norm with the level-set method yields a new effective methodology that is not only able to mitigate local minima but is also robust against random noise for the inverse gradiometry problem. Numerical experiments further demonstrate that the new KR norm-based misfit function is able to recover deep dipping flanks of SEG/EAGE salt models even at extremely low signal-to-noise ratios. The new methodology can be readily applied to gravity and magnetic data as well.

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