133 5. Full waveform inversion Note that fmin does not play a role here. For fmax = 100 Hz, the discretization is very fine. Suppose that the image is 1 km deep and 5 km long, with a record up to 1 s. The number of samples can be easily computed. For a simple example, the storage for a single wave field is evaluated in Table 5.1, right column. This is feasible for the 10 Hz case, but not for the 100 Hz. The important aspect is that the storage depends on fmax 3 in 2D and f max 4 in 3D (with the introduction of Δy). In practice, the maximum processed frequency is limited because of limited memory and CPU resources. 5.5 Examples Below we present an example of the capabilities of FWI, as well as its applicability for a 2D synthetic dataset. The choice of synthetic versus real data is driven by the a posteriori control of the results. At the end of the section we discuss the additional difficulties related to real data (Basker et al. 2016). Geophysical context The synthetic data is inspired from a real data acquisition in the geotechnical context (Deidda and Balia, 2001). It consists of three main parts: an unconsolidated sediment layer with silt and clay in the deeper part, a concrete layer at around 4-5 m depth and a compacted back fill material in the shallow part (Figure 5.3). For the analysis, we use the same synthetic model (with P-wave velocity and density) as presented in Pérez Solano et al., 2014. Despite the apparent relatively simple structure, the difficulty in this model comes from its lateral variations. Figure 5.3 Exact vp (top, in m/s) and density (bottom, in kg/m3) models, from (Pérez Solano et al., 2014).
RkJQdWJsaXNoZXIy NjA3NzQ=