# Strong-Scattering Multiparameter Reconstruction Based on Elastic Direct Envelope Inversion and Full-Waveform Inversion with Anisotropic Total Variation Constraint

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## Abstract

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## 1. Introduction

## 2. Review of Elastic Full-Waveform Inversion and Direct Envelope Inversion

#### 2.1. Elastic Full-Waveform Inversion (EFWI)

#### 2.2. Elastic Direct Envelope Inversion (EDEI)

## 3. EDEI with Anisotropic Total Variation Constraint (EDEI-ATV)

#### 3.1. Anisotropic Total Variation (ATV) Constraint

#### 3.2. EDEI with ATV Constraint (EDEI-ATV)

## 4. Numerical Examples

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**ATV constraint denoising test. (

**a**) Salt velocity model with random noise; (

**b**) ATV constraint denoising result.

**Figure 2.**The modified SEG/EAGE salt dome model for elastic media. (

**a**) True Vp model; (

**b**) True Vs model.

**Figure 3.**Source wavelet and its spectrum. (

**a**) Waveform of source wavelet; (

**b**) Spectrum of source wavelet.

**Figure 6.**Inversion results with and without ATV constraint. (

**a**) Inverted Vp by EDEI; (

**b**) Inverted Vs by EDEI; (

**c**) Inverted Vp by EDEI + EFWI; (

**d**) Inverted Vs by EDEI + EFWI; (

**e**) Inverted Vp by EDEI-ATV; (

**f**) Inverted Vs by EDEI-ATV; (

**g**) Inverted Vp by EDEI-ATV + EFWI-ATV; (

**h**) Inverted Vs by EDEI-ATV + EFWI-ATV.

**Figure 7.**Extracted traces comparison of inversion results. (

**a**) Extracted traces comparison of inverted Vp by EDEI and EDEI-ATV; (

**b**) Extracted traces comparison of inverted Vs by EDEI and EDEI-ATV; (

**c**) Extracted traces comparison of inverted Vp by EDEI+EFWI and EDEI-ATV + EFWI-ATV; (

**d**) Extracted traces comparison of inverted Vs by EDEI + EFWI and EDEI-ATV + EFWI-ATV.

**Figure 8.**Adjoint sources comparison. (

**a**) Z-component of the adjoint source of EFWI; (

**b**) X-component of the adjoint source of EFWI; (

**c**) Z-component of the adjoint source of EDEI; (

**d**) X-component of the adjoint source of EDEI.

**Figure 9.**Data fitting results. (

**a**) Z-component observed data; (

**b**) Z-component synthetic data on Figure 6c,d; (

**c**) Difference profile of Figure 9a,b; (

**d**) Z-component synthetic data on Figure 6g,h; (

**e**) Difference profile of Figure 9a,d; (

**f**) X-component observed data; (

**g**) X-component synthetic data on Figure 6c,d; (

**h**) Difference profile of Figure 9f,g; (

**i**) X-component synthetic data on Figure 6g,h; (

**j**) Difference profile of Figure 9f,i.

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**MDPI and ACS Style**

Zhang, P.; Wu, R.-S.; Han, L.; Zhou, Y. Strong-Scattering Multiparameter Reconstruction Based on Elastic Direct Envelope Inversion and Full-Waveform Inversion with Anisotropic Total Variation Constraint. *Remote Sens.* **2023**, *15*, 746.
https://doi.org/10.3390/rs15030746

**AMA Style**

Zhang P, Wu R-S, Han L, Zhou Y. Strong-Scattering Multiparameter Reconstruction Based on Elastic Direct Envelope Inversion and Full-Waveform Inversion with Anisotropic Total Variation Constraint. *Remote Sensing*. 2023; 15(3):746.
https://doi.org/10.3390/rs15030746

**Chicago/Turabian Style**

Zhang, Pan, Ru-Shan Wu, Liguo Han, and Yixiu Zhou. 2023. "Strong-Scattering Multiparameter Reconstruction Based on Elastic Direct Envelope Inversion and Full-Waveform Inversion with Anisotropic Total Variation Constraint" *Remote Sensing* 15, no. 3: 746.
https://doi.org/10.3390/rs15030746