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1. Joint inversion for 1-D crustal seismic S - and P -wave velocity structures with interfaces and its application to the Wabash Valley Seismic Zone

   https://doi.org/10.1093/gji/ggab092  

   Liu, Yuchen; Zhu, Lupei (March 2021, Geophysical Journal International)

   null (Ed.)

   SUMMARY Interfaces are important part of Earth’s layering structure. Here, we developed a new model parametrization and iterative linearized inversion method that determines 1-D crustal velocity structure using surface wave dispersion, teleseismic P-wave receiver functions and Ps and PmP traveltimes. Unlike previous joint inversion methods, the new model parametrization includes interface depths and layer Vp/Vs ratios so that smoothness constraint can be conveniently applied to velocities of individual layers without affecting the velocity discontinuity across the interfaces. It also allows adding interface-related observation such as traveltimes of Ps and PmP in the joint inversion to eliminate the trade-off between interface depth and Vp/Vs ratio and therefore to reduce the uncertainties of results. Numerical tests show that the method is computationally efficient and the inversion results are robust and independent of the initial model. Application of the method to a dense linear array across the Wabash Valley Seismic Zone (WVSZ) produced a high-resolution crustal image in this seismically active region. The results show a 51–55-km-thick crust with a mid-crustal interface at 14–17 km. The crustal Vp/Vs ratio varies from 1.69 to 1.90. There are three pillow-like, ∼100 km apart high-velocity bodies sitting at the base of the crust and directly above each of them are a low-velocity anomaly in the middle crust and a high-velocity anomaly in the upper crust. They are interpreted to be produced by mantle magmatic intrusions and remelting during rifting events in the end of the Precambrian. The current diffuse seismicity in the WVSZ might be rooted in this ancient distributed rifting structure. 

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2. Bispectrum Inversion With Application to Multireference Alignment

   https://doi.org/10.1109/TSP.2017.2775591  

   Bendory, Tamir; Boumal, Nicolas; Ma, Chao; Zhao, Zhizhen; Singer, Amit (February 2018, IEEE Transactions on Signal Processing)
3. Joint inversion of compact operators

   https://doi.org/10.1515/jiip-2019-0068  

   Mead, Jodi L.; Ford, James F. (February 2020, Journal of Inverse and Ill-posed Problems)

   Abstract Joint inversion of multiple data types was studied as early as 1975 in [K. Vozoff and D. L. Jupp,Joint inversion of geophysical data,Geophys. J. Internat. 42 1975, 3, 977–991],where the authors used the singular value decomposition to determine the degree of ill-conditioning of joint inverse problems. The authors demonstrated in several examples that combining two physical models in a joint inversion, and by effectively stacking discrete linear models, improved the conditioning as compared to individual inversions. This work extends the notion of using the singular value decomposition to determine the conditioning of discrete joint inversion to using the singular value expansion to determine the well-posedness of joint operators. We provide a convergent technique for approximating the singular values of continuous joint operators. In the case of self-adjoint operators, we give an algebraic expression for the joint singular values in terms of the singular values of the individual operators. This expression allows us to show that while rare, there are situations where ill-posedness may be not improved through joint inversion and in fact can degrade the conditioning of an individual inversion. The expression also quantifies the benefits of including repeated measurements in an inversion. We give an example of joint inversion with two moderately ill-posed Green’s function solutions, and quantify the improvement over individual inversions. This work provides a framework in which to identify data types that are advantageous to combine in a joint inversion. 

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4. Joint inversion of GPR and ER data

   https://doi.org/10.1190/segam2018-2997794.1  

   Domenzain, Diego; Bradford, John; Mead, Jodi (August 2018, SEG Technical Program Expanded Abstracts 2018)
5. Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion

   https://doi.org/10.1190/geo2016-0663.1  

   Yang, Yunan; Engquist, Björn; Sun, Junzhe; Hamfeldt, Brittany F. (January 2018, GEOPHYSICS)