Waveform inversion is a kind of method to reveal the underground structure and lithology through minimizing the residual error between predicted wavefield and true seismic record using full‐wavefield information. In this paper, we briefly present the principle of the conventional Quasi‐Newton algorithm, and then exploit a new modified Quasi‐Newton equation to modify the conventional Davidon‐Fletcher‐Powell (DFP) and Broyden‐Fletcher‐Goldfarb‐Shanno (BFGS) algorithms. Different from past Quasi‐Newton methods, this modified BFGS considers gradient values, model information and objective function values to approximate the inverse matrix of Hessian matrix. Moreover, it almost does not increase the calculation amount for each iteration. The numerical experiment shows that compared with the conventional Quasi‐Newton method, the modified BFGS algorithm can not only preserve the inverse accuracy, but also significantly improve calculation efficiency.
Lithium vanadium oxide (Li3VO4, LVO) is a promising anode material for lithium-ion batteries (LIBs) due to its high theoretical capacity (394 mAh g−1) and safe working potential (0.5–1.0 V vs. Li+/Li). However, its electrical conductivity is low which leads to poor electrochemical performance. Graphene (GN) shows excellent electrical conductivity and high specific surface area, holding great promise in improving the electrochemical performance of electrode materials for LIBs. In this paper, LVO was prepared by different methods. SEM results showed the obtained LVO by sol-gel method possesses uniform nanoparticle morphology. Next, LVO/GN composite was synthesized by sol-gel method. The flexible GN could improve the distribution of LVO, forming a high conductive network. Thus, the LVO/GN composite showed outstanding cycling performance and rate performance. The LVO/GN composite can provide a high initial capacity of 350.2 mAh g−1 at 0.5 C. After 200 cycles, the capacity of LVO/GN composite remains 86.8%. When the current density increased from 0.2 C to 2 C, the capacity of LVO/GN composite only reduced from 360.4 mAh g−1 to 250.4 mAh g−1, demonstrating an excellent performance rate.
A workflow for inverting high-velocity conglomerates by simultaneous joint inversion (SJI) of seismic and nonseismic data was developed during a depth-migration project using land 3D data sets from western China. Large localized velocity variations caused by conglomerates severely limited the effectiveness of ray-based seismic tomography in generating an accurate velocity field. Single-domain inversion indicated different responses of particular lithologies for various nonseismic methods, and well-log crossplots enabled estimation of the relationships between models generated from different geophysical measurements. Using the high-resistivity property of the conglomerates, SJI of seismic first-break and magnetotelluric (MT) data was conducted to estimate spatial thickness and velocity. Combining the relatively low-resolution information derived from the MT data with the higher-resolution seismic image, the distribution of conglomerates could be interpreted with the help of well markers and well-logging horizons. The velocity model then was adjusted iteratively. The model that was updated by using the SJI workflow showed better consistency with borehole data compared with the initial tomographic model. The depth-migrated image created by using the updated model showed more geologically plausible structures both at target level and in the overburden.
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