We introduce a depth scaling strategy to improve the accuracy of frequency-domain elastic full waveform inversion (FWI) using the new pseudo-Hessian matrix for seismic data without low-frequency components. The depth scaling strategy is based on the fact that the damping factor in the Levenberg-Marquardt method controls the energy concentration in the gradient. In other words, a large damping factor makes the Levenberg-Marquardt method similar to the steepest-descent method, by which shallow structures are mainly recovered. With a small damping factor, the Levenberg-Marquardt method becomes similar to the Gauss-Newton methods by which we can resolve deep structures as well as shallow structures. In our depth scaling strategy, a large damping factor is used in the early stage and then decreases automatically with the trend of error as the iteration goes on. With the depth scaling strategy, we can gradually move the parameter-searching region from shallow to deep parts. This flexible damping factor plays a role in retarding the model parameter update for shallow parts and mainly inverting deeper parts in the later stage of inversion. By doing so, we can improve deep parts in inversion results. The depth scaling strategy is applied to synthetic data without lowfrequency components for a modified version of the SEG/EAGE overthrust model. Numerical examples show that the flexible damping factor yields better results than the constant damping factor when reliable low-frequency components are missing.

Introduction
 Inverse Problem
 Depth Scaling Strategy
 Numerical Examples
 Conclusions
 References

• Ju-Won Oh(Physical Science and Engineering Division, 4700, King Abdullah University of Science and Technology, Thuwal 23955-6900, Kingdom of Saudi Arabia)
• Shin-Woong Kim(Department of Energy Systems Engineering, Seoul National University, Seoul 08826, South Korea)
• Dong-Joo Min(Department of Energy Systems Engineering, Seoul National University, Seoul 08826, South Korea) Corresponding author
• Seok-Joon Moon(Department of Energy Systems Engineering, Seoul National University, Seoul 08826, South Korea)
• Jong-Ha Hwang(Department of Energy Systems Engineering, Seoul National University, Seoul 08826, South Korea)