Acoustic Impedance Inversion Using Gaussian Metropolis–Hastings Sampling with Data Driving
Abstract
:1. Introduction
2. Methodology
2.1. Forward Model
2.2. Metropolis–Hastings Sampling
Algorithm 1 The process of Metropolis–Hastings (MH) sampling about vector |
Input: initial parameter , length of Markov Chain N, length of part of Markov Chain Output: inversion result 1: The initial value 2: Compute 3: For t = 1,…..N do 4: Compute the sample from the sampling function 5: Compute the PDF 6: Compute discriminant function 7: Compute the value 8: Compute 9: End for 10: |
2.3. Bayesian AI Inversion Based on GMHDD
Algorithm 2 The inversion based on Gaussian MH sampling with data driving (GMHDD) |
Input: Output: Inversion result 1: While 2: Choose the single trace of seismic data and impedance 3: While 4: Compute likelihood function 5: Renew the impedance 6: Compute likelihood function 7: Solve the discriminant function 8: Obtain 9: Get 10: 11: End 12: Compute the inversion result 13: Compute 14: End |
3. Experiments
3.1. Marmousi2 Model
3.2. Field Data
4. Conclusions and Discussion
Author Contributions
Funding
Conflicts of Interest
References
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Methods | RMSE (m/s*g/cm3) | SNR (dB) |
---|---|---|
Initial Model | 782.27 | 6.97 |
UMH | 314.78 | 15.66 |
GMH | 314.27 | 15.69 |
GMHDD | 130.26 | 16.29 |
Methods | Initial Model | UMH | GMH | GMHDD |
---|---|---|---|---|
RMSE (m/s*g/cm3) | 819.95 | 199.16 | 277.36 | 158.52 |
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Wu, H.; Chen, Y.; Li, S.; Peng, Z. Acoustic Impedance Inversion Using Gaussian Metropolis–Hastings Sampling with Data Driving. Energies 2019, 12, 2744. https://doi.org/10.3390/en12142744
Wu H, Chen Y, Li S, Peng Z. Acoustic Impedance Inversion Using Gaussian Metropolis–Hastings Sampling with Data Driving. Energies. 2019; 12(14):2744. https://doi.org/10.3390/en12142744
Chicago/Turabian StyleWu, Hao, Yingpin Chen, Shu Li, and Zhenming Peng. 2019. "Acoustic Impedance Inversion Using Gaussian Metropolis–Hastings Sampling with Data Driving" Energies 12, no. 14: 2744. https://doi.org/10.3390/en12142744