A Determination of an Abrupt Motion of the Sea Bottom by Using Snapshot Data of Water Waves

Figure 9

Comparison of the regularized wave spectrum with the exact wave spectrum for four cases of regularization parameters 𝛼 ((a)–(d): noise level 10⁻⁶). Legend: the dotted and solid lines stand for the exact wave spectrum 𝐹₀(𝑘) in (6.2) and the (Tikhonov) regularized solution 𝑞_𝛼 in (5.3), respectively.

(a) 𝛼=10⁻²

(b) 𝛼=10⁻⁴

(c) 𝛼=10⁻⁹

(d) 𝛼=10⁻¹⁵

(e) Residual (the 𝐿₂ norm of difference between the exact and regularized spectra divided by the 𝐿₂ norm of the exact)