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

Figure 7

Comparison of the recovered sudden displacement of the sea bottom with the exact displacement for four cases of regularization parameters 𝛼 ((a)–(d): noise level 10⁻⁴). Legend: the dotted and solid lines stand for the exact 𝐹₀(𝑥) in (6.1) and the recovered sudden displacement of the sea bottom, respectively. The lines show good agreement with each other when the regularization parameter 𝛼=10⁻⁸.

(a) 𝛼=10⁻²

(b) 𝛼=10⁻⁴

(c) 𝛼=10⁻⁸

(d) 𝛼=10⁻¹¹

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