Combining adaptive dictionary learning with nonlocal similarity for full-waveform inversion

Figures & data

Figure 1. Three classes of training patches and corresponding dictionaries: (a) the true Marmousi model; (b)–(d) 128 patches from three clusters; (e)–(g) dictionaries trained from corresponding patch clusters.

Figure 2. Three classes of training patches and corresponding dictionaries: (a) the inversion result obtained at the end of the first inner loop; (b)–(d) 128 patches from three clusters; (e)–(g) dictionaries trained from corresponding patch clusters.

Figure 3. Flowchart of the ASNS-FWI algorithm.

Table 1. Quantitative results of overthrust model. The brackets represent results without RTV.

		Final results
	Initial	ASNS-FWI	TV-FWI	CS-FWI
SSIM	0.3727	0.7242 (0.6926)	0.5815	0.5641
FSIM	0.8487	0.9817 (0.9811)	0.9549	0.9644
PSNR	9.0064	17.1692 (17.1217)	13.8285	14.5825
RMSE	0.3545	0.1385 (0.1392)	0.2035	0.1865
Running times (s)	–	3092 (3089)	2484	2620

Table 2. Quantitative results of Marmousi model. The brackets represent results without RTV.

		Final results
	Initial	ASNS-FWI	TV-FWI	CS-FWI
SSIM	0.5898	0.7859 (0.7848)	0.7319	0.6320
FSIM	0.8237	0.9729 (0.9724)	0.9416	0.9516
PSNR	17.6142	21.5382 (21.5223)	20.1386	19.3138
RMSE	0.1316	0.0837(0.0839)	0.0986	0.1082
Running times (s)	–	2716 (2712)	2302	2419

Figure 4. Inversion results of the Overthrust model: (a) the true velocity model; (b) the initial velocity model; (c) the ASNS-FWI result; (d) the ASNS-FWI result without RTV; (e) the TV-FWI result; (f) the CS-FWI result.

Figure 5. The vertical velocity profiles extracted from the Overthrust model.

Figure 6. Inversion results of the Marmousi model: (a) the true velocity model; (b) the initial velocity model; (c) the ASNS-FWI result; (d) the ASNS-FWI result without RTV; (e) the TV-FWI result; (f) the CS-FWI result. Note that the total lack of lateral variation in the initial velocity.

Figure 7. The vertical velocity profiles extracted from the Marmousi model.

Figure 8. Inversion results under 5% white noise in seismic data: (a) the ASNS-FWI result (Overthrust model); (b) the ASNS-FWI result (Marmousi model); (c) the TV-FWI result (Overthrust model); (d) the TV-FWI result (Marmousi model).