Essay On Static Function

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For the application of cross-gradient function, the coupled parameter models are assumed to have similar structures. Therefore, the structures of true models are designed in the similar way in the following examples, and the physicochemical relationship between the medium elastic and electromagnetic properties are not strictly defined. In this situation, the elastic and electromagnetic properties are negatively associated in example 1 and positively associated in examples 2 and 3. The initial models are critical for the solution of FWI problem. In practice, the initial P-wave velocity and permittivity model could be recovered by velocity analysis, and the initial conductivity model could be provided by electrical resistivity tomography. In…show more content…
Synthetic recorded data for GPR and seismic FWI are generated with the true models. The values of the three initial models constantly increase with depth. In this example, 12 sources and 130 receivers are located on the surface with a spacing of 2.0 and 0.2 m, respectively. The positions of the sources and receivers are shown in Fig. 2. The source type is a Ricker wavelet with a center frequency of 200 Hz in the seismic FWI and 20 MHz in GPR FWI. Seven frequencies are inverted in both the seismic FWI (100, 130, 160, 190, 220, 250, and 280 Hz) and GPR FWI (4, 6, 8, 10, 13, 16, and 19 MHz). Fig. 3 shows the individual and joint inversion results. In the individual inversion, there is a significant structural difference between the three inverted parameter models. The general shapes of the two anomalies only can be observed in the P-wave velocity model (Fig. 3a). In contrast, the features of the two cross-shaped anomalies are faintly constructed in the permittivity model (Fig. 3c) and are absent in the conductivity model (Fig. 3e). The sedimentary layers are not clearly recovered in all the models, especially in the conductivity model (Fig. 3e). These parameter models were integrated using the joint FWI approach. The structural similarities between these parameter models are significantly enhanced in the joint inversion. The P-wave
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