## 3 Experiments
### Experiment on the Overthrust Model  
The impedance of the Overthrust model and its corresponding synthetic data are also that same as in [23] and are shown in Figure 7. For this model, five traces were selected as the training set from the synthetic seismic data and impedance data by isometric sampling, 39 traces were randomly selected from the remaining 392 traces as the validation set, and the whole 401 traces were the test set. Due to the small amount of sample data, there may be overfitting. Data enhancement methods are usually used to avoid overfitting. In contrast to the Marmousi2 model test, we used cubic spline interpolation to generate 20 new impedance and seismic data traces between every two selected traces in this model. Ultimately, we used 85 traces to train the network. The interpolation data are shown in Figure 8. The frequency-wavenumber spectra of the original and interpolated seismic data are shown in Figure 9 for comparison. The number of epochs was set to 1000 and the other hyperparameters and network structure were same as those of the Marmousi2 model. The validation MSEs of the two tasks with different weights are shown in Table 4. The performance of the model for a single task is shown in the first and the last rows. When the validation loss is minimal during the 1000 epochs, the corresponding \(\sigma_{pre}\) = 0.192 and \(\sigma_{rec}\) = 0.120, then we can calculate that the optimal weight is 0.28: 0.72, and the MSE of the two tasks under this weight is 0.0079 and 0.00001. Figure 10 shows the variation with epochs of \(\sigma_{pre}\), \(\sigma_{rec}\) and the corresponding \(w_{pre}\), \(w_{rec}\). It can be seen that the MSEs obtained by the multi-task network under different weights for both tasks are all smaller than that obtained by the single-task network, and the optimal weight minimizes the MSEs. The training and validation loss curves of different tasks under the optimal weight are shown in Figure 11. Figure 12 illustrates the profiles predicted by the single-task network (Figure 12a) and the hard parameter sharing multi-task network (Figure 12b) with the optimal weight. The MSEs of the predicted profiles are 0.0119 and 0.0063, respectively, which also shows that the hard parameter sharing multi-task network outperforms the single-task network. Similarly, we chose two traces to further demonstrate the performance of the proposed method. Figure 13 shows the predicted results of impedance prediction for the 99 th (Figure 13a) and 316 th (Figure 13b) traces, and their corresponding PCC between the predicted value and the ground truth are shown in Table 5. It is clear that the impedance predicted by the hard parameter sharing multi-task network (green) matches the true impedance (red) better than that by the single-task network (blue). The blue and green dotted lines in Figure 13 represent residuals between the true impedance and the impedance predicted by the two networks. In addition, the MSEs between the prediction of different SNR data and the true impedance are presented in Table 6. It shows that, with the exception of 0 dB noise, the accuracy of the multi-task network is higher than that of the single-task network under the other five testing data with different SNRs, which further proves the advantage of the proposed method. Figure 7: Overthrust model dataset: (**a**) impedance; (**b**) synthetic seismic data generated with 30 Hz \(0^{\circ}\) phase Ricker wavelet. Figure 8: Interpolated data of the Overthrust model. (**a**) impedance; (**b**) synthetic seismic data. Figure 9: The frequency-wavenumber spectra of the original (**a**) and interpolated seismic data (**b**).