# Potential of Phase-Amplitude-Based Multi-Scale Full Waveform Inversion with Total-Variation Regularization for Seismic Imaging of Deep-Seated Ores

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## Abstract

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## 1. Introduction

## 2. Review of Full Waveform Inversion

## 3. PAFWI with Total-Variation Regularization

## 4. Numerical Test

#### 4.1. The PAFWI Adjoint Sources

#### 4.2. Ore-Hosting Model Test

#### 4.3. TV Parameter Test

#### 4.4. Noise Testing

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

## Appendix B

## Appendix C

## References

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**Figure 1.**A complex ore-hosting velocity model which is modified from a geological model in the Luzong Basin, China (Sun et al., 2015 [14]).

**Figure 2.**Velocity model consists of multiple ore bodies; (

**a**) Ore-hosting velocity model; (

**b**) Initial velocity model.

**Figure 3.**Seismic source function; (

**a**) A low-cut 6 Hz Ricker wavelet; (

**b**) The spectrum of the low-cut Ricker wavelet.

**Figure 4.**Adjoint sources with different amplitude factors; (

**a**) p = 1, which is the traditional FWI method; (

**b**) p = 0.6; (

**c**) p = 0.3; (

**d**) p = 0.

**Figure 5.**The TV-PAFWI results with different amplitude factors of (

**a**) p = 1 which is the TV-FWI method; (

**b**) p = 0.6; (

**c**) p = 0.3; (

**d**) p = 0, for the low frequency data and ${\lambda}_{TV}=0.3$.

**Figure 6.**TV-PAFWI + FWI with high frequency data (6–20 Hz), using the models shown in Figure 5a–d as the initial models with amplitude factors are (

**a**) p = 1, which is the TV-FWI method; (

**b**) p = 0.6; (

**c**) p = 0.3; (

**d**) p = 0.

**Figure 7.**The TV-PAFWI velocity profiles (at 3.5 km in the ore-hosting velocity model in Figure 6a–d, respectively), with different amplitude factors are (

**a**) p = 1, which is the TV-FWI method; (

**b**) p = 0.6; (

**c**) p = 0.3; (

**d**) p = 0.

**Figure 8.**TV-PAFWI with low frequency data (6–12 Hz) and amplitude factor (p = 0) also with different TV parameters (

**a**) ${\lambda}_{TV}=0$; (

**b**) ${\lambda}_{TV}=1$.

**Figure 10.**TV-PAFWI with amplitude factor (p = 0), also with different TV parameters (

**a**) ${\lambda}_{TV}=0$; (

**b**) ${\lambda}_{TV}=0.6$.

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**MDPI and ACS Style**

Xu, Y.; Hu, Y.; Xie, Z.; Han, L.; Zhang, Y.; Yuan, J.; Wan, X.; Deng, X.
Potential of Phase-Amplitude-Based Multi-Scale Full Waveform Inversion with Total-Variation Regularization for Seismic Imaging of Deep-Seated Ores. *Minerals* **2022**, *12*, 877.
https://doi.org/10.3390/min12070877

**AMA Style**

Xu Y, Hu Y, Xie Z, Han L, Zhang Y, Yuan J, Wan X, Deng X.
Potential of Phase-Amplitude-Based Multi-Scale Full Waveform Inversion with Total-Variation Regularization for Seismic Imaging of Deep-Seated Ores. *Minerals*. 2022; 12(7):877.
https://doi.org/10.3390/min12070877

**Chicago/Turabian Style**

Xu, Yongzhong, Yong Hu, Zhou Xie, Liguo Han, Yintao Zhang, Jingyi Yuan, Xiaoguo Wan, and Xingliang Deng.
2022. "Potential of Phase-Amplitude-Based Multi-Scale Full Waveform Inversion with Total-Variation Regularization for Seismic Imaging of Deep-Seated Ores" *Minerals* 12, no. 7: 877.
https://doi.org/10.3390/min12070877