TY - JOUR
T1 - Structurally constrained inversion by means of a Minimum Gradient Support regularizer
T2 - examples of FD-EMI data inversion constrained by GPR reflection data
AU - Klose, Tim
AU - Guillemoteau, Julien
AU - Vignoli, Giulio
AU - Walter, Judith
AU - Herrmann, Andreas
AU - Tronicke, Jens
N1 - Publisher Copyright:
© 2023 The Author(s).
PY - 2023/6/1
Y1 - 2023/6/1
N2 - Many geophysical inverse problems are known to be ill-posed and, thus, requiring some kind of regularization in order to provide a unique and stable solution. A possible approach to overcome the inversion ill-posedness consists in constraining the position of the model interfaces. For a grid-based parameterization, such a structurally constrained inversion can be implemented by adopting the usual smooth regularization scheme in which the local weight of the regularization is reduced where an interface is expected. By doing so, sharp contrasts are promoted at interface locations while standard smoothness constraints keep affecting the other regions of the model. In this work, we present a structurally constrained approach and test it on the inversion of frequency-domain electromagnetic induction (FD-EMI) data using a regularization approach based on the Minimum Gradient Support stabilizer, which is capable to promote sharp transitions everywhere in the model, i.e., also in areas where no structural a prioriinformation is available. Using 1D and 2D synthetic data examples, we compare the proposed approach to a structurally constrained smooth inversion as well as to more standard (i.e., not structurally constrained) smooth and sharp inversions. Our results demonstrate that the proposed approach helps in finding a better and more reliable reconstruction of the subsurface electrical conductivity distribution, including its structural characteristics. Furthermore, we demonstrate that it allows to promote sharp parameter variations in areas where no structural information are available. Lastly, we apply our structurally constrained scheme to FD-EMI field data collected at a field site in Eastern Germany to image the thickness of peat deposits along two selected profiles. In this field example, we use collocated constant offset ground-penetrating radar (GPR) data to derive structural a priori information to constrain the inversion of the FD-EMI data. The results of this case study demonstrate the effectiveness and flexibility of the proposed approach.
AB - Many geophysical inverse problems are known to be ill-posed and, thus, requiring some kind of regularization in order to provide a unique and stable solution. A possible approach to overcome the inversion ill-posedness consists in constraining the position of the model interfaces. For a grid-based parameterization, such a structurally constrained inversion can be implemented by adopting the usual smooth regularization scheme in which the local weight of the regularization is reduced where an interface is expected. By doing so, sharp contrasts are promoted at interface locations while standard smoothness constraints keep affecting the other regions of the model. In this work, we present a structurally constrained approach and test it on the inversion of frequency-domain electromagnetic induction (FD-EMI) data using a regularization approach based on the Minimum Gradient Support stabilizer, which is capable to promote sharp transitions everywhere in the model, i.e., also in areas where no structural a prioriinformation is available. Using 1D and 2D synthetic data examples, we compare the proposed approach to a structurally constrained smooth inversion as well as to more standard (i.e., not structurally constrained) smooth and sharp inversions. Our results demonstrate that the proposed approach helps in finding a better and more reliable reconstruction of the subsurface electrical conductivity distribution, including its structural characteristics. Furthermore, we demonstrate that it allows to promote sharp parameter variations in areas where no structural information are available. Lastly, we apply our structurally constrained scheme to FD-EMI field data collected at a field site in Eastern Germany to image the thickness of peat deposits along two selected profiles. In this field example, we use collocated constant offset ground-penetrating radar (GPR) data to derive structural a priori information to constrain the inversion of the FD-EMI data. The results of this case study demonstrate the effectiveness and flexibility of the proposed approach.
KW - Controlled source electromagnetics (CSEM)
KW - Electrical properties
KW - Frequency Domain Electromagnetics
KW - Ground penetrating radar
KW - Inverse theory
KW - Inversion
UR - http://www.scopus.com/inward/record.url?scp=85156134388&partnerID=8YFLogxK
U2 - 10.1093/gji/ggad041
DO - 10.1093/gji/ggad041
M3 - Article
AN - SCOPUS:85156134388
SN - 0956-540X
VL - 233
SP - 1938
EP - 1949
JO - Geophysical Journal International
JF - Geophysical Journal International
IS - 3
ER -