Влияние нелинейности морских волн на результаты

ɋɨɜɪɟɦɟɧɧɵɟ ɩɪɨɛɥɟɦɵ ɞɢɫɬɚɧɰɢɨɧɧɨɝɨ ɡɨɧɞɢɪɨɜɚɧɢɹ Ɂɟɦɥɢ ɢɡ ɤɨɫɦɨɫɚ. 2013. Ɍ. 10. ʋ 1. ɋ. 34–48
ȼɥɢɹɧɢɟ ɧɟɥɢɧɟɣɧɨɫɬɢ ɦɨɪɫɤɢɯ ɜɨɥɧ ɧɚ ɪɟɡɭɥɶɬɚɬɵ
ɪɚɞɢɨɚɥɶɬɢɦɟɬɪɢɱɟɫɤɢɯ ɢɡɦɟɪɟɧɢɣ
Ⱥ.ɋ. Ɂɚɩɟɜɚɥɨɜ, ȼ.ȼ. ɉɭɫɬɨɜɨɣɬɟɧɤɨ
Ɇɨɪɫɤɨɣ ɝɢɞɪɨɮɢɡɢɱɟɫɤɢɣ ɢɧɫɬɢɬɭɬ ɇȺɇ ɍɤɪɚɢɧɵ
99000, ɍɤɪɚɢɧɚ, ɋɟɜɚɫɬɨɩɨɥɶ, ɭɥ. Ʉɚɩɢɬɚɧɫɤɚɹ, 2
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Ɋɚɫɫɦɨɬɪɟɧɨ ɜɥɢɹɧɢɟ ɧɚ ɮɨɪɦɭ ɷɯɨ-ɫɢɝɧɚɥɚ ɚɥɶɬɢɦɟɬɪɚ ɧɟɥɢɧɟɣɧɵɯ ɷɮɮɟɤɬɨɜ ɜ ɩɨɥɟ ɦɨɪɫɤɢɯ ɩɨɜɟɪɯɧɨɫɬɧɵɯ
ɜɨɥɧ, ɩɪɢɜɨɞɹɳɢɯ ɤ ɨɬɤɥɨɧɟɧɢɸ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɜɨɡɜɵɲɟɧɢɣ ɩɨɜɟɪɯɧɨɫɬɢ ɨɬ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ƚɚɭɫɫɚ. ɉɨɤɚɡɚɧɵ ɨɝɪɚɧɢɱɟɧɢɹ ɫɭɳɟɫɬɜɭɸɳɢɯ ɦɨɞɟɥɟɣ ɪɚɫɩɪɟɞɟɥɟɧɢɣ (ɜ ɬɨɦ ɱɢɫɥɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ƚɪɚɦɚ-ɒɚɪɥɶɟ) ɩɪɢ
ɚɧɚɥɢɡɟ ɞɚɧɧɵɯ ɚɥɶɬɢɦɟɬɪɢɱɟɫɤɢɯ ɢɡɦɟɪɟɧɢɣ. Ɉɬɦɟɱɟɧɨ, ɱɬɨ ɨɞɧɨɣ ɢɡ ɩɪɨɛɥɟɦ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɷɯɨ-ɫɢɝɧɚɥɚ
ɚɥɶɬɢɦɟɬɪɚ ɹɜɥɹɟɬɫɹ ɨɬɫɭɬɫɬɜɢɟ ɦɨɞɟɥɢ, ɨɩɢɫɵɜɚɸɳɟɣ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɜɨɡɜɵɲɟɧɢɣ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ
ɧɚ ɦɚɫɲɬɚɛɚɯ ɛɨɥɟɟ ɱɟɦ ɜ ɩɨɥɬɨɪɚ ɪɚɡɚ, ɩɪɟɜɨɫɯɨɞɹɳɢɯ ɡɧɚɱɢɦɭɸ ɜɵɫɨɬɭ ɜɨɥɧ.
Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɫɩɭɬɧɢɤɨɜɚɹ ɚɥɶɬɢɦɟɬɪɢɹ, ɫɨɫɬɨɹɧɢɟ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɜɨɡɜɵɲɟɧɢɣ;
ɧɟɥɢɧɟɣɧɨɫɬɶ ɦɨɪɫɤɢɯ ɜɨɥɧ.
ȼɜɟɞɟɧɢɟ
Ⱦɨɫɬɢɝɧɭɬɚɹ ɤ ɧɚɫɬɨɹɳɟɦɭ ɜɪɟɦɟɧɢ ɬɨɱɧɨɫɬɶ ɚɥɶɬɢɦɟɬɪɢɱɟɫɤɢɯ ɢɡɦɟɪɟɧɢɣ ɭɪɨɜɧɹ
ɦɨɪɹ ɡɧɚɱɢɬɟɥɶɧɨ ɨɝɪɚɧɢɱɢɜɚɟɬ ɤɪɭɝ ɨɤɟɚɧɨɝɪɚɮɢɱɟɫɤɢɯ ɡɚɞɚɱ, ɤɨɬɨɪɵɟ ɪɟɲɚɸɬɫɹ ɧɚ ɨɫɧɨɜɟ ɞɚɧɧɵɯ, ɩɨɥɭɱɚɟɦɵɯ ɫ ɤɨɫɦɢɱɟɫɤɢɯ ɚɩɩɚɪɚɬɨɜ (ɄȺ). ɉɨɝɪɟɲɧɨɫɬɶ ɦɨɠɟɬ ɞɨɫɬɢɝɚɬɶ
10 ɫɦ, ɚ ɜ ɧɟɤɨɬɨɪɵɯ ɫɢɬɭɚɰɢɹɯ ɢ ɩɪɟɜɵɲɚɬɶ ɷɬɨɬ ɭɪɨɜɟɧɶ (Rodriguez, 1988). ɉɨɜɵɲɟɧɢɟ
ɬɨɱɧɨɫɬɢ ɚɥɶɬɢɦɟɬɪɢɱɟɫɤɢɯ ɢɡɦɟɪɟɧɢɣ ɢɞɟɬ ɩɭɬɟɦ ɭɥɭɱɲɟɧɢɹ ɬɟɯɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɭɫɬɚɧɨɜɥɟɧɧɵɯ ɧɚ ɄȺ ɚɥɶɬɢɦɟɬɪɨɜ (ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɦɧɨɝɨɱɚɫɬɨɬɧɵɯ ɚɥɶɬɢɦɟɬɪɨɜ,
ɫɨɜɟɪɲɟɧɫɬɜɨɜɚɧɢɟ ɦɨɞɟɥɟɣ ɢɨɧɨɫɮɟɪɵ ɢ ɬɪɨɩɨɫɮɟɪɵ, ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɫɢɫɬɟɦɵ ɬɨɱɧɨɝɨ
ɩɨɡɢɰɢɨɧɢɪɨɜɚɧɢɹ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ GPS ɢ ɬ.ɞ.) ɢ ɫɨɜɟɪɲɟɧɫɬɜɨɜɚɧɢɹ ɚɥɝɨɪɢɬɦɨɜ ɨɛɪɚɛɨɬɤɢ
ɢɧɮɨɪɦɚɰɢɢ (ȿɝɨɪɨɜ, Ɇɢɧ-ɏɨ, 2005; Ɇɢɧ-ɏɨ, ȿɝɨɪɨɜ, 2005; Ȼɚɫɤɚɤɨɜ, ȿɝɨɪɨɜ, 2008; Ʌɚɜɪɨɜɚ ɢ ɞɪ., 2011; Ginzburg et al., 2011). ɉɨɫɥɟɞɧɟɟ ɫɜɹɡɚɧɨ ɫ ɭɝɥɭɛɥɟɧɢɟɦ ɩɨɧɢɦɚɧɢɹ ɩɪɨɰɟɫɫɨɜ ɮɨɪɦɢɪɨɜɚɧɢɹ ɩɪɟɨɛɪɚɡɨɜɚɧɧɨɝɨ ɷɯɨ-ɫɢɝɧɚɥɚ (ɉɭɫɬɨɜɨɣɬɟɧɤɨ, Ɂɚɩɟɜɚɥɨɜ, 2012),
ɤɨɬɨɪɵɣ ɞɚɥɟɟ ɛɭɞɟɦ ɧɚɡɵɜɚɬɶ ɷɯɨ-ɫɢɝɧɚɥɨɦ.
ȼɫɸ ɢɧɮɨɪɦɚɰɢɸ ɨɛ ɭɪɨɜɧɟ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɜɞɨɥɶ ɬɪɚɫɫɵ ɄȺ ɢ ɨ ɟɟ ɥɨɤɚɥɶɧɵɯ ɩɚɪɚɦɟɬɪɚɯ ɧɟɫɟɬ ɩɟɪɟɞɧɢɣ ɮɪɨɧɬ ɷɯɨ-ɫɢɝɧɚɥɚ (Barrick, Lipa, 1985; Callahan, Rodriguez,
2004). ɇɚɪɹɞɭ ɫ ɢɡɦɟɪɟɧɢɹɦɢ ɭɪɨɜɧɹ ɦɨɪɹ ɩɨ ɞɚɧɧɵɦ ɚɥɶɬɢɦɟɬɪɢɱɟɫɤɢɯ ɢɡɦɟɪɟɧɢɣ ɨɩɪɟɞɟɥɹɸɬɫɹ ɟɳɟ ɞɜɚ ɩɚɪɚɦɟɬɪɚ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ: ɩɨ ɧɚɤɥɨɧɭ ɩɟɪɟɞɧɟɝɨ ɮɪɨɧɬɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɡɧɚɱɢɦɚɹ ɜɵɫɨɬɚ ɜɨɥɧ (Queffeulou, 2004), ɩɨ ɟɝɨ ɚɦɩɥɢɬɭɞɟ – ɭɪɨɜɟɧɶ ɲɟɪɨɯɨɜɚɬɨɫɬɢ
ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɩɨ ɤɨɬɨɪɨɦɭ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɫɤɨɪɨɫɬɶ ɩɪɢɜɨɞɧɨɝɨ ɜɟɬɪɚ (Glazman,
Greysukh, 1993). ɂɫɫɥɟɞɭɟɬɫɹ ɜɨɡɦɨɠɧɨɫɬɶ ɩɨ ɢɡɦɟɧɟɧɢɹɦ ɧɚɤɥɨɧɚ ɪɚɡɧɵɯ ɭɱɚɫɬɤɨɜ ɩɟɪɟɞɧɟɝɨ ɮɪɨɧɬɚ ɨɩɪɟɞɟɥɹɬɶ ɚɫɢɦɦɟɬɪɢɸ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɨɡɜɵɲɟɧɢɣ ɜɡɜɨɥɧɨɜɚɧɧɨɣ ɦɨɪɫɤɨɣ
ɩɨɜɟɪɯɧɨɫɬɢ (Gómez-Enri et al., 2007; Ɂɚɩɟɜɚɥɨɜ, ɉɭɫɬɨɜɨɣɬɟɧɤɨ, 2012).
ɉɪɨɛɥɟɦɚ ɩɨɜɵɲɟɧɢɹ ɬɨɱɧɨɫɬɢ ɚɥɶɬɢɦɟɬɪɢɱɟɫɤɢɯ ɢɡɦɟɪɟɧɢɣ ɫɜɹɡɚɧɚ ɫ ɬɟɦ, ɱɬɨ
ɚɩɪɢɨɪɢ ɧɟ ɢɡɜɟɫɬɧɵ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɨɬɪɚɠɚɸɳɟɣ ɩɨɜɟɪɯɧɨɫɬɢ (Ȼɚɫɫ ɢ ɞɪ., 1975). ɂɡɦɟɧɟɧɢɟ ɟɟ ɫɨɫɬɨɹɧɢɹ ɹɜɥɹɟɬɫɹ ɨɞɧɢɦ ɢɡ ɨɫɧɨɜɧɵɯ ɮɚɤɬɨɪɨɜ, ɨɩɪɟɞɟɥɹɸɳɢɯ ɨɲɢɛɤɢ
34
ɨɩɪɟɞɟɥɟɧɢɹ ɪɚɫɫɬɨɹɧɢɹ ɨɬ ɄȺ ɞɨ ɭɪɨɜɧɹ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ (Fu, Cazenave, 2001). ɗɬɨɬ
ɮɚɤɬɨɪ, ɩɨɥɭɱɢɜɲɢɣ ɜ ɚɧɝɥɨɹɡɵɱɧɨɣ ɥɢɬɟɪɚɬɭɪɟ ɧɚɡɜɚɧɢɟ «sea-state bias» (SSB), ɢɦɟɟɬ ɬɪɢ
ɫɨɫɬɚɜɥɹɸɳɢɟ.
ɉɟɪɜɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ SB («skewness bias») – ɷɬɨ ɨɲɢɛɤɢ, ɨɛɭɫɥɨɜɥɟɧɧɵɟ ɨɬɤɥɨɧɟɧɢɟɦ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɜɨɡɜɵɲɟɧɢɣ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɨɬ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ƚɚɭɫɫɚ (GómezEnri et al., 2006; Tran et al., 2006). Ⱥɫɢɦɦɟɬɪɢɹ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɨɡɜɵɲɟɧɢɣ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɩɪɢɜɨɞɢɬ ɤ ɬɨɦɭ, ɱɬɨ ɦɟɞɢɚɧɚ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɪɚɫɫɟɢɜɚɸɳɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɥɟɠɢɬ ɧɢɠɟ
ɫɪɟɞɧɟɝɨ ɡɧɚɱɟɧɢɹ. ȼɬɨɪɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ EB («electromagnetic bias») ɫɜɹɡɚɧɚ ɫ ɬɟɦ, ɱɬɨ ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɪɚɫɫɟɹɧɢɹ ɪɚɞɢɨɜɨɥɧ ɦɟɧɹɟɬɫɹ ɜɞɨɥɶ ɩɪɨɮɢɥɹ ɞɨɦɢɧɚɧɬɧɨɣ ɜɨɥɧɵ (Rodriguez,
Martin, 1994; Kumar et al., 2003), ɱɬɨ ɬɚɤɠɟ ɨɛɭɫɥɨɜɥɟɧɨ ɧɟɥɢɧɟɣɧɨɫɬɶɸ ɩɨɜɟɪɯɧɨɫɬɧɵɯ
ɜɨɥɧ (Bar, Agnon, 1997). Ⱦɢɫɩɟɪɫɢɹ ɭɤɥɨɧɨɜ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɜ ɨɤɪɟɫɬɧɨɫɬɢ ɝɪɟɛɧɹ
ɜɵɲɟ, ɱɟɦ ɜɨ ɜɩɚɞɢɧɟ, ɱɬɨ ɩɪɢɜɨɞɢɬ ɤ ɛɨɥɟɟ ɜɵɫɨɤɨɣ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɪɚɫɫɟɹɧɢɹ ɨɬ ɭɱɚɫɬɤɨɜ ɩɨɜɟɪɯɧɨɫɬɢ, ɪɚɫɩɨɥɨɠɟɧɧɵɯ ɜɨ ɜɩɚɞɢɧɟ, ɱɟɦ ɨɬ ɭɱɚɫɬɤɨɜ, ɪɚɫɩɨɥɨɠɟɧɧɵɯ ɧɚ ɝɪɟɛɧɟ
(Yaplee et al., 1971; Ƚɚɥɚɟɜ ɢ ɞɪ., 1978). Ɍɪɟɬɶɹ ɫɨɫɬɚɜɥɹɸɳɚɹ TB («tracker bias») ɫɜɹɡɚɧɚ
ɫ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɣ ɨɛɪɚɛɨɬɤɨɣ ɞɚɧɧɵɯ ɚɥɶɬɢɦɟɬɪɚ ɧɚ ɛɨɪɬɭ ɄȺ (Gómez-Enri et al., 2006).
ȼ ɧɚɫɬɨɹɳɟɦ ɨɛɡɨɪɟ ɦɵ ɨɝɪɚɧɢɱɢɦɫɹ ɚɧɚɥɢɡɨɦ ɬɟɯ ɷɮɮɟɤɬɨɜ, ɤɨɬɨɪɵɟ ɫɨɡɞɚɸɬ SB
ɩɨɝɪɟɲɧɨɫɬɶ. ȿɫɥɢ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɜɨɡɜɵɲɟɧɢɣ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɹɜɥɹɟɬɫɹ Ƚɚɭɫɫɨɜɵɦ,
ɬɨ ɜɪɟɦɹ ɩɪɨɯɨɠɞɟɧɢɹ ɪɚɞɢɨɢɦɩɭɥɶɫɚ ɞɨ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɢ ɨɛɪɚɬɧɨ t0 ɫɨɨɬɜɟɬɫɬɜɭɟɬ
ɜɪɟɦɟɧɢ ɦɟɠɞɭ ɩɨɫɵɥɤɨɣ ɡɨɧɞɢɪɭɸɳɟɝɨ ɢɦɩɭɥɶɫɚ ɢ ɦɨɦɟɧɬɨɦ ɪɟɝɢɫɬɪɚɰɢɢ ɧɚ ɩɟɪɟɞɧɟɦ
ɮɪɨɧɬɟ ɷɯɨ-ɫɢɝɧɚɥɚ ɬɨɱɤɢ, ɝɞɟ ɞɨɫɬɢɝɚɟɬɫɹ ɟɝɨ ɩɨɥɨɜɢɧɧɚɹ ɦɨɳɧɨɫɬɶ. Ɉɬɤɥɨɧɟɧɢɹ ɨɬ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ƚɚɭɫɫɚ ɩɪɢɜɨɞɹɬ ɤ ɢɡɦɟɧɟɧɢɸ ɮɨɪɦɵ ɷɯɨ-ɫɢɝɧɚɥɚ ɢ ɤ ɫɦɟɳɟɧɢɸ ɬɨɱɤɢ t0, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɭɪɨɜɧɸ ɧɟɜɨɡɦɭɳɟɧɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ (Hayne, 1980; Ɂɚɩɟɜɚɥɨɜ, 2012ɚ).
ɐɟɥɶɸ ɧɚɫɬɨɹɳɟɣ ɪɚɛɨɬɵ ɹɜɥɹɟɬɫɹ ɚɧɚɥɢɡ ɜɥɢɹɧɢɹ ɨɬɤɥɨɧɟɧɢɣ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɨɡɜɵɲɟɧɢɣ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɨɬ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ƚɚɭɫɫɚ ɧɚ ɮɨɪɦɭ ɷɯɨ-ɫɢɝɧɚɥɚ ɫɩɭɬɧɢɤɨɜɨɝɨ ɪɚɞɢɨɚɥɶɬɢɦɟɬɪɚ, ɚ ɬɚɤɠɟ ɚɧɚɥɢɡ ɜɨɡɦɨɠɧɨɫɬɢ ɨɩɢɫɚɬɶ ɷɬɨɬ ɷɮɮɟɤɬ ɧɚ ɨɫɧɨɜɟ ɫɭɳɟɫɬɜɭɸɳɢɯ ɦɨɞɟɥɟɣ ɜɨɡɜɵɲɟɧɢɣ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ.
Ɏɨɪɦɢɪɨɜɚɧɢɟ ɷɯɨ-ɫɢɝɧɚɥɚ ɪɚɞɢɨɚɥɶɬɢɦɟɬɪɚ
Ɉɞɧɨɣ ɢɡ ɩɟɪɜɵɯ ɪɚɛɨɬ, ɩɨɫɜɹɳɟɧɧɵɯ ɢɡɭɱɟɧɢɸ ɩɪɨɰɟɫɫɚ ɮɨɪɦɢɪɨɜɚɧɢɹ ɢɦɩɭɥɶɫɚ
ɊɅ-ɫɢɝɧɚɥɚ ɩɪɢ ɡɨɧɞɢɪɨɜɚɧɢɢ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɫ ɩɨɦɨɳɶɸ ɚɥɶɬɢɦɟɬɪɚ ɤɨɫɦɢɱɟɫɤɨɝɨ
ɛɚɡɢɪɨɜɚɧɢɹ, ɹɜɥɹɟɬɫɹ, ɩɨ-ɜɢɞɢɦɨɦɭ, ɪɚɛɨɬɚ (Moore, Williams, 1957), ɜ ɤɨɬɨɪɨɣ ɚɧɚɥɢɡɢɪɨɜɚɥɨɫɶ ɧɟɤɨɝɟɪɟɧɬɧɨɟ (ɩɨ ɦɨɳɧɨɫɬɢ) ɪɚɫɫɟɹɧɢɟ ɪɚɞɢɨɜɨɥɧ ɲɟɪɨɯɨɜɚɬɨɣ ɩɨɜɟɪɯɧɨɫɬɶɸ.
ɉɨɫɥɟɞɨɜɚɜɲɟɟ ɡɚ ɷɬɨɣ ɪɚɛɨɬɨɣ ɪɚɡɜɢɬɢɟ ɪɚɞɢɨɜɵɫɨɬɨɦɟɬɪɢɢ ɩɨɡɜɨɥɢɥɨ ɜ 70-ɟ ɝɨɞɵ ɫɮɨɪɦɭɥɢɪɨɜɚɬɶ ɟɟ ɨɫɧɨɜɧɵɟ ɩɨɥɨɠɟɧɢɹ (ɫɦ. ɦɨɧɨɝɪɚɮɢɢ (Ȼɚɤɭɬ ɢ ɞɪ., 1964; ɀɭɤɨɜɫɤɢɣ ɢ ɞɪ.,
1979) ɢ ɢɯ ɛɢɛɥɢɨɝɪɚɮɢɸ).
ȼ ɪɚɛɨɬɟ (Brown, 1977) ɛɵɥɚ ɩɨɫɬɪɨɟɧɚ ɦɨɞɟɥɶ, ɧɚɡɜɚɧɧɚɹ ɩɨ ɢɦɟɧɢ ɟɟ ɚɜɬɨɪɚ ɦɨɞɟɥɶɸ Ȼɪɚɭɧɚ, ɤɨɬɨɪɚɹ ɨɩɢɫɵɜɚɥɚ ɫɪɟɞɧɸɸ ɮɨɪɦɭ ɷɯɨ-ɫɢɝɧɚɥɚ ɩɪɢ ɤɜɚɡɢɜɟɪɬɢɤɚɥɶɧɨɦ
ɡɨɧɞɢɪɨɜɚɧɢɢ. Ɇɨɞɟɥɶ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɜɟɪɬɤɭ ɬɪɟɯ ɮɭɧɤɰɢɣ
V (t ) = χ (t ) ∗ s (t ) ∗ q(t ) ,
(1)
35
ɝɞɟ Ȥ(t) – ɮɨɪɦɚ ɪɚɞɢɨɢɦɩɭɥɶɫɚ, ɨɬɪɚɠɟɧɧɨɝɨ ɨɬ ɩɥɨɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ; s(t) – ɮɨɪɦɚ ɡɨɧɞɢɪɭɸɳɟɝɨ ɪɚɞɢɨɢɦɩɭɥɶɫɚ; q(t) – ɮɭɧɤɰɢɹ, ɫɜɹɡɚɧɧɚɹ ɫ ɩɥɨɬɧɨɫɬɶɸ ɜɟɪɨɹɬɧɨɫɬɟɣ ɜɵɫɨɬ ɬɨɱɟɤ
ɡɟɪɤɚɥɶɧɨɝɨ ɨɬɪɚɠɟɧɢɹ; ɫɢɦɜɨɥ * ɨɡɧɚɱɚɟɬ ɫɜɟɪɬɤɭ; t – ɜɪɟɦɹ.
ȼ ɪɚɦɤɚɯ ɦɨɞɟɥɢ (1) ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɬɨɱɤɢ ɡɟɪɤɚɥɶɧɨɝɨ ɨɬɪɚɠɟɧɢɹ ɪɚɜɧɨɦɟɪɧɨ
ɪɚɫɩɪɟɞɟɥɟɧɵ ɜɞɨɥɶ ɩɪɨɮɢɥɹ ɜɨɥɧɵ, ɬ.ɟ. ɮɭɧɤɰɢɹ qs(t) ɨɞɧɨɡɧɚɱɧɨ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɥɨɬɧɨɫɬɶɸ ɜɟɪɨɹɬɧɨɫɬɟɣ ɜɨɡɜɵɲɟɧɢɣ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ P(Ș). Ɉɬɫɸɞɚ ɫɥɟɞɭɟɬ
q (t ) =
dη
P(η (t ) ) ,
dt
ɝɞɟ ɫɜɹɡɶ ɦɟɠɞɭ ɜɪɟɦɟɧɧɨɣ ɢ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɣ ɩɟɪɟɦɟɧɧɵɦɢ ɡɚɞɚɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ
Ș = (c/2)t . Ɉɬɤɥɨɧɟɧɢɹ ɨɬ ɩɪɟɞɩɨɥɨɠɟɧɢɹ ɨ ɪɚɜɧɨɦɟɪɧɨɫɬɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɡɟɪɤɚɥɶɧɵɯ ɬɨɱɟɤ
ɫɨɡɞɚɸɬ ɭɤɚɡɚɧɧɭɸ ɜɵɲɟ EB ɫɨɫɬɚɜɥɹɸɳɭɸ ɩɨɝɪɟɲɧɨɫɬɢ ɨɩɪɟɞɟɥɟɧɢɹ ɭɪɨɜɧɹ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ (Bar, Agnon, 1997), ɚɧɚɥɢɡ ɤɨɬɨɪɨɣ ɜɵɯɨɞɢɬ ɡɚ ɪɚɦɤɢ ɧɚɫɬɨɹɳɟɣ ɪɚɛɨɬɵ.
Ɇɨɞɟɥɢ ɩɥɨɬɧɨɫɬɢ ɜɟɪɨɹɬɧɨɫɬɟɣ ɜɨɡɜɵɲɟɧɢɣ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ
ɇɟɥɢɧɟɣɧɨɫɬɶ ɦɨɪɫɤɢɯ ɩɨɜɟɪɯɧɨɫɬɧɵɯ ɜɨɥɧ
Ɋɚɡɥɢɱɧɵɦ ɚɫɩɟɤɬɚɦ ɧɟɥɢɧɟɣɧɵɯ ɷɮɮɟɤɬɨɜ ɜ ɩɨɥɟ ɦɨɪɫɤɢɯ ɩɨɜɟɪɯɧɨɫɬɧɵɯ ɜɨɥɧ ɩɨɫɜɹɳɟɧɨ ɛɨɥɶɲɨɟ ɤɨɥɢɱɟɫɬɜɨ ɪɚɛɨɬ. Ɂɞɟɫɶ ɦɵ ɨɝɪɚɧɢɱɢɦɫɹ ɪɚɫɫɦɨɬɪɟɧɢɟɦ ɨɬɤɥɨɧɟɧɢɣ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɜɨɡɜɵɲɟɧɢɣ ɨɬ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ƚɚɭɫɫɚ, ɤɨɬɨɪɵɟ ɜɥɢɹɸɬ ɧɚ ɮɨɪɦɭ ɷɯɨ-ɫɢɝɧɚɥɚ
ɩɪɢ ɤɜɚɡɢɜɟɪɬɢɤɚɥɶɧɨɦ ɡɨɧɞɢɪɨɜɚɧɢɢ ɲɟɪɨɯɨɜɚɬɨɣ ɩɨɜɟɪɯɧɨɫɬɢ.
ɇɟɫɦɨɬɪɹ ɧɚ ɬɨ ɱɬɨ ɟɳɟ ɜ 1849 ɝ. ɋɬɨɤɫ ɨɩɭɛɥɢɤɨɜɚɥ ɪɚɛɨɬɭ (Stokes, 1849), ɜ ɤɨɬɨɪɨɣ
ɩɨɤɚɡɚɥ ɤɢɧɟɦɚɬɢɱɟɫɤɭɸ ɧɟɥɢɧɟɣɧɨɫɬɶ ɩɪɨɮɢɥɹ ɜɨɥɧ ɤɨɧɟɱɧɨɣ ɚɦɩɥɢɬɭɞɵ, ɞɥɢɬɟɥɶɧɨɟ ɜɪɟɦɹ
ɢɦɟɧɧɨ ɥɢɧɟɣɧɚɹ ɦɨɞɟɥɶ ɨɫɬɚɜɚɥɚɫɶ ɨɫɧɨɜɧɨɣ ɦɨɞɟɥɶɸ, ɨɩɢɫɵɜɚɸɳɟɣ ɩɨɥɟ ɦɨɪɫɤɢɯ ɩɨɜɟɪɯɧɨɫɬɧɵɯ ɜɨɥɧ. ȼ ɟɟ ɪɚɦɤɚɯ ɩɨɥɟ ɦɨɪɫɤɢɯ ɜɨɥɧ ɩɪɟɞɫɬɚɜɥɹɸɬ ɜ ɜɢɞɟ ɫɭɦɦɵ ɛɨɥɶɲɨɝɨ ɱɢɫɥɚ
ɧɟɡɚɜɢɫɢɦɵɯ ɫɢɧɭɫɨɢɞɚɥɶɧɵɯ ɫɨɫɬɚɜɥɹɸɳɢɯ, ɚɦɩɥɢɬɭɞɵ ɤɨɬɨɪɵɯ ɹɜɥɹɸɬɫɹ ɫɥɭɱɚɣɧɵɦɢ
ɩɟɪɟɦɟɧɧɵɦɢ, ɚ ɮɚɡɵ ɫɥɭɱɚɣɧɨ ɪɚɫɩɪɟɞɟɥɟɧɵ ɫ ɪɚɜɧɨɣ ɜɟɪɨɹɬɧɨɫɬɶɸ ɜ ɢɧɬɟɪɜɚɥɟ (0, 2ʌ).
ȼ ɫɢɥɭ ɰɟɧɬɪɚɥɶɧɨɣ ɩɪɟɞɟɥɶɧɨɣ ɬɟɨɪɟɦɵ ɩɨɞɨɛɧɚɹ ɦɨɞɟɥɶ ɩɪɟɞɩɨɥɚɝɚɟɬ, ɱɬɨ ɜɨɡɜɵɲɟɧɢɟ ɩɨɜɟɪɯɧɨɫɬɢ ɩɨɞɱɢɧɹɟɬɫɹ ɪɚɫɩɪɟɞɟɥɟɧɢɸ Ƚɚɭɫɫɚ (Ʌɨɧɝɟ-ɏɢɝɝɢɧɫ, 1962).
Ⱥɤɬɢɜɧɵɟ ɢɫɫɥɟɞɨɜɚɧɢɹ ɧɟɥɢɧɟɣɧɵɯ ɷɮɮɟɤɬɨɜ ɜ ɩɨɥɟ ɦɨɪɫɤɢɯ ɜɨɥɧ ɧɚɱɚɥɢ ɩɪɨɜɨɞɢɬɶ ɜ ɧɚɱɚɥɟ ɜɬɨɪɨɣ ɩɨɥɨɜɢɧɵ ɩɪɨɲɥɨɝɨ ɫɬɨɥɟɬɢɹ. ɋɬɢɦɭɥɨɦ ɩɨɫɥɭɠɢɥɢ ɪɚɛɨɬɵ, ɜ ɤɨɬɨɪɵɯ
ɩɨɤɚɡɚɧɨ, ɱɬɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɦɟɠɞɭ ɜɨɥɧɨɜɵɦɢ ɫɨɫɬɚɜɥɹɸɳɢɦɢ ɩɪɢɜɨɞɢɬ ɤ ɨɬɤɥɨɧɟɧɢɹɦ
ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɟɝɨ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɨɬ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ƚɚɭɫɫɚ (Phillips, 1961; Longuet-Higgins,
1963). ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɢɫɫɥɟɞɨɜɚɧɢɹ ɩɨɤɚɡɚɥɢ, ɱɬɨ ɩɨɥɟ ɦɨɪɫɤɢɯ ɩɨɜɟɪɯɧɨɫɬɧɵɯ ɜɨɥɧ
ɹɜɥɹɟɬɫɹ ɫɥɚɛɨ ɧɟɥɢɧɟɣɧɵɦ, ɢ ɨɬɤɥɨɧɟɧɢɹ ɨɬ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ƚɚɭɫɫɚ ɹɜɥɹɸɬɫɹ ɧɟɛɨɥɶɲɢɦɢ
(Kinsman, 1965; Jha, Winterstein, 2000; Ɂɚɩɟɜɚɥɨɜ ɢ ɞɪ., 2011). ɗɬɨ ɩɨɡɜɨɥɹɟɬ ɨɬɧɟɫɬɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɨɡɜɵɲɟɧɢɣ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɤ ɤɥɚɫɫɭ ɤɜɚɡɢɝɚɭɫɫɨɜɵɯ ɪɚɫɩɪɟɞɟɥɟɧɢɣ,
ɤɨɬɨɪɵɟ ɨɛɵɱɧɨ ɨɩɢɫɵɜɚɸɬɫɹ ɪɚɫɩɪɟɞɟɥɟɧɢɹɦɢ Ƚɪɚɦɚ-ɒɚɪɥɶɟ (Ʉɟɧɞɚɥɥ, ɋɬɶɸɚɪɬ, 1966).
Ɍɟɨɪɟɬɢɱɟɫɤɢ ɩɨɤɚɡɚɧɨ (Phillips, 1961; Longuet-Higgins, 1963), ɱɬɨ ɜɨɡɧɢɤɚɸɳɢɟ
ɜ ɪɟɡɭɥɶɬɚɬɟ ɦɟɠɜɨɥɧɨɜɵɯ ɜɡɚɢɦɨɞɟɣɫɬɜɢɣ ɨɬɤɥɨɧɟɧɢɹ ɨɬ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ƚɚɭɫɫɚ ɩɪɨɩɨɪ36
ɰɢɨɧɚɥɶɧɵ ɫɪɟɞɧɟɦɭ ɭɤɥɨɧɭ ɜɨɥɧ, ε = λ2 L0 , ɝɞɟ Ȝ2 – ɞɢɫɩɟɪɫɢɹ ɜɨɡɜɵɲɟɧɢɣ ɦɨɪɫɤɨɣ
ɩɨɜɟɪɯɧɨɫɬɢ; L0 – ɞɥɢɧɚ ɞɨɦɢɧɚɧɬɧɵɯ ɜɨɥɧ.
ɐɢɤɥ ɥɚɛɨɪɚɬɨɪɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɩɨɞɬɜɟɪɞɢɥ, ɱɬɨ ɤɭɦɭɥɹɧɬɵ ɜɨɡɜɵɲɟɧɢɣ ɩɨɜɟɪɯɧɨɫɬɢ ɞɨ ɜɨɫɶɦɨɝɨ ɩɨɪɹɞɤɚ ɜɤɥɸɱɢɬɟɥɶɧɨ ɞɟɣɫɬɜɢɬɟɥɶɧɨ ɡɚɜɢɫɹɬ ɨɬ ɫɪɟɞɧɟɝɨ ɭɤɥɨɧɚ
(Huang, Long, 1980). ɂɫɤɥɸɱɟɧɢɟ ɫɨɫɬɚɜɢɥ ɤɭɦɭɥɹɧɬ ɱɟɬɜɟɪɬɨɝɨ ɩɨɪɹɞɤɚ (ɷɤɫɰɟɫɫ), ɞɥɹ
ɤɨɬɨɪɨɝɨ ɡɚɜɢɫɢɦɨɫɬɶ ɨɬ İ ɧɟ ɛɵɥɚ ɜɵɹɜɥɟɧɚ. ȼ ɧɚɬɭɪɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɚɯ (Ɂɚɩɟɜɚɥɨɜ, 2011)
ɬɚɤɠɟ ɛɵɥɚ ɨɛɧɚɪɭɠɟɧɚ ɯɨɪɨɲɨ ɜɵɪɚɠɟɧɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɚɫɢɦɦɟɬɪɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɨɡɜɵɲɟɧɢɣ ɩɨɜɟɪɯɧɨɫɬɢ ɨɬ ɫɪɟɞɧɟɝɨ ɭɤɥɨɧɚ. Ʉɨɷɮɮɢɰɢɟɧɬ ɤɨɪɪɟɥɹɰɢɢ ɦɟɠɞɭ ɩɚɪɚɦɟɬɪɚɦɢ
~
~
λ3 ɢ İ ɪɚɜɟɧ 0,43. ɋɬɚɬɢɫɬɢɱɟɫɤɚɹ ɫɜɹɡɶ ɦɟɠɞɭ ɩɚɪɚɦɟɬɪɚɦɢ λ4 ɢ İ ɜɵɪɚɠɟɧɚ ɯɭɠɟ, ɤɨɷɮɮɢɰɢɟɧɬ ɤɨɪɪɟɥɹɰɢɢ ɪɚɜɟɧ 0,24.
Ɋɚɫɩɪɟɞɟɥɟɧɢɟ Ƚɪɚɦɚ-ɒɚɪɥɶɟ
Ɉɫɧɨɜɧɵɦ ɪɚɫɩɪɟɞɟɥɟɧɢɟɦ ɜɨɡɜɵɲɟɧɢɣ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɜ ɩɪɢɥɨɠɟɧɢɹɯ, ɫɜɹɡɚɧɧɵɯ ɫ ɪɚɫɫɟɹɧɢɟɦ ɪɚɞɢɨɜɨɥɧ ɧɚ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɹɜɥɹɟɬɫɹ ɪɚɫɩɪɟɞɟɥɟɧɢɟ Ƚɪɚɦɚɒɚɪɥɶɟ. ɇɚ ɨɫɧɨɜɟ ɪɹɞɨɜ Ƚɪɚɦɚ-ɒɚɪɥɶɟ ɩɥɨɬɧɨɫɬɶ ɜɟɪɨɹɬɧɨɫɬɟɣ ɤɜɚɡɢɝɚɭɫɫɨɜɚ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɫɥɭɱɚɣɧɨɣ ɜɟɥɢɱɢɧɵ x ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ (Ʉɟɧɞɚɥɥ, ɋɬɶɸɚɪɬ, 1966)
∞
PG −C ( x) = ∑ an H n ( x)
n =0
1
 1 
exp − x 2  ,
2π
 2 
ɝɞɟ an – ɤɨɷɮɮɢɰɢɟɧɬɵ ɪɹɞɚ; Hn(x) – ɩɨɥɢɧɨɦ ɑɟɛɵɲɟɜɚ-ɗɪɦɢɬɚ ɩɨɪɹɞɤɚ n.
Ʉɨɷɮɮɢɰɢɟɧɬɵ ɪɹɞɚ ɜɵɪɚɠɚɸɬ ɱɟɪɟɡ ɫɬɚɬɢɫɬɢɱɟɫɤɢɟ ɦɨɦɟɧɬɵ ɫɥɭɱɚɣɧɨɣ ɜɟɥɢɱɢɧɵ
x ɢɥɢ ɟɟ ɤɭɦɭɥɹɧɬɵ Ȝn. ȿɫɥɢ ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɫɥɭɱɚɣɧɨɣ ɜɟɥɢɱɢɧɵ x ɪɚɜɧɨ ɧɭɥɸ, ɬɨ ɩɟɪɜɵɟ
ɱɟɬɵɪɟ ɤɭɦɭɥɹɧɬɚ ɟɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɨɩɢɫɵɜɚɸɬɫɹ ɜɵɪɚɠɟɧɢɹɦɢ
λ1 = 0 , λ2 = µ 2 , λ3 = µ3 , λ4 = µ 4 − 3 µ 22,
∞
ɝɞɟ µ n = ∫ x n P( x ) dx – ɦɨɦɟɧɬɵ ɪɚɫɩɪɟɞɟɥɟɧɢɹ; P(x) – ɩɥɨɬɧɨɫɬɶ ɜɟɪɨɹɬɧɨɫɬɟɣ ɫɥɭɱɚɣɧɨɣ
ɜɟɥɢɱɢɧɵ−∞x. Ʉɭɦɭɥɹɧɬɵ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ƚɚɭɫɫɚ ɫɬɚɪɲɟ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ ɪɚɜɧɵ ɧɭɥɸ, ɱɬɨ
ɞɟɥɚɟɬ ɢɯ ɷɮɮɟɤɬɢɜɧɵɦ ɢɧɫɬɪɭɦɟɧɬɨɦ ɞɥɹ ɚɧɚɥɢɡɚ ɧɟɥɢɧɟɣɧɵɯ ɷɮɮɟɤɬɨɜ.
~
ȼɜɟɞɟɦ ɧɨɪɦɢɪɨɜɚɧɢɟ η~ = η λ2 , ɬɨɝɞɚ ɤɭɦɭɥɹɧɬ λ3 ɹɜɥɹɟɬɫɹ ɚɫɢɦɦɟɬɪɢɟɣ ɪɚɫɩɪɟ~
ɞɟɥɟɧɢɹ, λ4 – ɷɤɫɰɟɫɫɨɦ. Ɉɛɵɱɧɨ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɩɥɨɬɧɨɫɬɢ ɜɟɪɨɹɬɧɨɫɬɟɣ ɜɨɡɜɵɲɟɧɢɣ
ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɢɫɩɨɥɶɡɭɟɬɫɹ ɗɞɠɜɨɪɬɨɜɚ ɮɨɪɦɚ ɬɢɩɚ Ⱥ ɪɹɞɨɜ Ƚɪɚɦɚ-ɒɚɪɥɶɟ (Huang,
Long, 1980)
(
)
~
~
~
exp − η~ 2 2  λ3
λ4
λ5
~
~
~
PG −C (η ) =
H 3 (η ) +
H 4 (η ) +
H 5 (η~ ) +
1 +
120
24
6
2π

~
+
~
λ6 + 10 λ32
720
~
~~
~
~~
~

λ7 + 35 λ4 λ3
λ8 + 56 λ5λ3 + 35 λ42
~
~
H 6 (η ) +
H 7 (η ) +
H 8 (η~ ) + ... .
5040
40320

(2)
37
ȿɫɥɢ ɜɡɹɬɶ ɜ (2) ɩɟɪɜɵɟ ɲɟɫɬɶ ɱɥɟɧɨɜ ɢ ɩɨɥɨɠɢɬɶ, ɱɬɨ Ȝn = 0, ɩɪɢ n • 5, ɬɨ ɜɵɪɚɠɟɧɢɟ (2) ɫɨɜɩɚɞɚɟɬ ɫ ɜɵɪɚɠɟɧɢɟɦ ɞɥɹ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɨɡɜɵɲɟɧɢɣ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɜ ɩɪɢɛɥɢɠɟɧɢɢ ɫɥɚɛɨɣ ɧɟɥɢɧɟɣɧɨɫɬɢ, ɩɨɥɭɱɟɧɧɵɦ Ʌɨɧɝɟ-ɏɢɝɝɢɧɫɨɦ (Longuet-Higgins, 1963).
ɉɪɢ ɨɩɢɫɚɧɢɢ ɩɥɨɬɧɨɫɬɢ ɜɟɪɨɹɬɧɨɫɬɟɣ ɜɨɡɜɵɲɟɧɢɣ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɫ ɩɨɦɨɳɶɸ ɪɹɞɨɜ Ƚɪɚɦɚ-ɒɚɪɥɶɟ ɱɚɳɟ ɞɪɭɝɢɯ ɢɫɩɨɥɶɡɭɟɬɫɹ ɚɩɩɪɨɤɫɢɦɚɰɢɹ ɜ ɮɨɪɦɟ
PG −C (η~ ) =
~
~

 η~ 2   λ3
1
λ
 1 + H 3 (η~ ) + 4 H 4 (η~ ) .
exp −

24
6
2π

 2 
(3)
Ⱥɩɩɪɨɤɫɢɦɚɰɢɹ (3) ɩɨɡɜɨɥɹɟɬ ɨɩɢɫɚɬɶ ɩɥɨɬɧɨɫɬɶ ɜɟɪɨɹɬɧɨɫɬɟɣ ɦɨɞɟɥɢɪɭɟɦɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɬɨɥɶɤɨ ɜ ɨɝɪɚɧɢɱɟɧɧɨɦ ɞɢɚɩɚɡɨɧɟ ɟɟ ɢɡɦɟɧɟɧɢɣ (Ɂɚɩɟɜɚɥɨɜ, 2011; Ɂɚɩɟɜɚɥɨɜ
ɢ ɞɪ., 2011). ɇɚɝɥɹɞɧɵɦ ɩɪɢɦɟɪɨɦ ɨɝɪɚɧɢɱɟɧɢɣ ɜ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɞɚɧɧɨɣ ɚɩɩɪɨɤɫɢɦɚɰɢɢ
ɹɜɥɹɟɬɫɹ ɩɨɹɜɥɟɧɢɟ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɡɧɚɱɟɧɢɣ ɮɭɧɤɰɢɢ PG −C (η~ ) (ɪɢɫ. 1). Ɉɬɪɢɰɚɬɟɥɶɧɵɟ
ɡɧɚɱɟɧɢɹ ɜ ɚɩɩɪɨɤɫɢɦɚɰɢɢ (3) ɩɨɹɜɥɹɸɬɫɹ ɩɪɢ η~ ≥ 3 . Ƚɪɚɧɢɰɚ ɩɨɹɜɥɟɧɢɹ ɨɬɪɢɰɚɬɟɥɶɧɵɯ
ɡɧɚɱɟɧɢɣ (ɧɚɢɦɟɧɶɲɢɣ ɩɨ ɦɨɞɭɥɸ ɤɨɪɟɧɶ ɭɪɚɜɧɟɧɢɹ PG −C (η~ ) = 0 ) ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɜɟɥɢɱɢɧɵ
ɫɪɟɞɧɟɝɨ ɭɤɥɨɧɚ ɢ ɫɬɚɞɢɢ ɪɚɡɜɢɬɢɹ ɜɨɥɧɨɜɨɝɨ ɩɨɥɹ (Ɂɚɩɟɜɚɥɨɜ, 2012ɛ).
P (η~ )
P (η~ )× 10 4
10
4
10-1
2
10-2
0
10-3
-2
10-4
-6
-3
0
3
η~
6
-6
-3
η~
0
3
6
-4
Ɋɢɫ. 1. Ɇɨɞɟɥɢ ɩɥɨɬɧɨɫɬɢ ɜɟɪɨɹɬɧɨɫɬɟɣ P (η~ ) :
~
~
ɫɩɥɨɲɧɚɹ ɥɢɧɢɹ – PG −C (η~ ) ( λ3 = −0,05 , λ4 = −0,3 );
~
~
ɩɭɧɤɬɢɪɧɚɹ ɥɢɧɢɹ PG −C (η~ ) ( λ3 = 0,3 , λ4 = −0,1 ); ɲɬɪɢɯɨɜɚɹ ɥɢɧɢɹ – PG (η~ )
Ƚɢɩɨɬɟɡɚ ɨ ɫɨɨɬɜɟɬɫɬɜɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɨɡɜɵɲɟɧɢɣ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɦɨɞɟɥɢ (3)
ɩɨ ɤɪɢɬɟɪɢɸ ɫɨɝɥɚɫɢɹ Ʉɨɥɦɨɝɨɪɨɜɚ ɧɟ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɞɚɧɧɵɦ ɢɡɦɟɪɟɧɢɣ ɢ ɞɨɥɠɧɚ ɛɵɬɶ
ɨɬɜɟɪɝɧɭɬɚ (Ɂɚɩɟɜɚɥɨɜ ɢ ɞɪ., 2011). ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɞɚɧɧɨɣ ɦɨɞɟɥɢ ɩɪɢɜɨɞɢɬ ɤ ɨɲɢɛɤɚɦ,
ɤɨɬɨɪɵɟ ɚɧɚɥɢɡɢɪɨɜɚɥɢɫɶ ɫ ɩɨɦɨɳɶɸ ɞɜɭɯ ɫɬɚɬɢɫɬɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ: ɨɬɧɨɫɢɬɟɥɶɧɨɣ
ɩɨɝɪɟɲɧɨɫɬɢ ɢ ɨɰɟɧɤɢ ɪɚɡɛɪɨɫɚ ɟɟ ɡɧɚɱɟɧɢɣ
~
P (η~ ) − P (η~ )
,
R(η~ ) = E ~ G~−C
PG −C (η )
38
δ R(η~ ) =
(R(η~) − R(η~))
2
.
~
ɉɪɢ ɢɡɦɟɧɟɧɢɢ η~ ɜ ɞɢɚɩɚɡɨɧɟ − 3 < η < 3 ɡɧɚɱɟɧɢɹ ɮɭɧɤɰɢɢ R(η~ ) ɥɟɠɚɬ ɜ ɞɢɚɩɚɡɨɧɟ ɨɬ –0,02 ɞɨ 0,07 (ɪɢɫ. 2). Ɂɚ ɩɪɟɞɟɥɚɦɢ ɭɤɚɡɚɧɧɨɝɨ ɞɢɚɩɚɡɨɧɚ ɡɧɚɱɟɧɢɹ ɮɭɧɤɰɢɢ R(η~ )
ɪɟɡɤɨ ɜɨɡɪɚɫɬɚɸɬ. ȼ ɨɛɥɚɫɬɢ − 1 < η~ < 1 ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɟɫɤɨɟ ɨɬɤɥɨɧɟɧɢɟ δ R (η~ ) <0,08.
Ɂɚ ɩɪɟɞɟɥɚɦɢ ɭɤɚɡɚɧɧɨɣ ɨɛɥɚɫɬɢ ɫ ɪɨɫɬɨɦ η~ ɮɭɧɤɰɢɹ δ R (η~ ) ɛɵɫɬɪɨ ɪɚɫɬɟɬ, ɱɬɨ ɨɩɪɟɞɟɥɹɟɬ ɨɝɪɚɧɢɱɟɧɢɹ ɜ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɦɨɞɟɥɢ (7).
2
10
δ R(η~ )
R (η~ )
1
1
0
0,1
-1
-4
-2
0
2
η~
0,01
4
-4
-2
0
2
η~
4
Ɋɢɫ. 2. Ɉɬɤɥɨɧɟɧɢɹ ɦɨɞɟɥɶɧɵɯ ɮɭɧɤɰɢɣ ɩɥɨɬɧɨɫɬɢ ɜɟɪɨɹɬɧɨɫɬɟɣ
ɨɬ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ: R(η~ ) – ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɨɲɢɛɤɢ;
δ R(η~ ) – ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɟɫɤɨɟ ɡɧɚɱɟɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɨɲɢɛɤɢ
ɍɱɟɬ ɤɭɦɭɥɹɧɬɨɜ ɩɹɬɨɝɨ Ȝ5 ɢ ɲɟɫɬɨɝɨ Ȝ6 ɩɨɪɹɞɤɨɜ ɧɟ ɭɥɭɱɲɚɟɬ ɫɢɬɭɚɰɢɸ. ɉɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɩɥɨɬɧɨɫɬɢ ɜɟɪɨɹɬɧɨɫɬɟɣ ɜɨɡɜɵɲɟɧɢɣ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɪɹɞɚɦɢ Ƚɪɚɦɚɒɚɪɥɶɟ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɨɝɪɚɧɢɱɢɬɶɫɹ ɱɥɟɧɚɦɢ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵɦɢ ɩɨɥɢɧɨɦɚɦ ɑɟɛɵɲɟɜɚɗɪɦɢɬɚ ɞɨ ɱɟɬɜɟɪɬɨɝɨ ɩɨɪɹɞɤɚ ɜɤɥɸɱɢɬɟɥɶɧɨ, ɞɚɠɟ ɩɪɢ ɧɚɥɢɱɢɢ ɨɰɟɧɨɤ ɤɭɦɭɥɹɧɬɨɜ Ȝ5 ɢ Ȝ6.
ɗɬɨɬ ɜɵɜɨɞ ɩɨɞɬɜɟɪɠɞɚɸɬ ɪɟɡɭɥɶɬɚɬɵ ɥɚɛɨɪɚɬɨɪɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɨɜ (Sun, Ping-Xing, 1994).
Ʉɨɦɛɢɧɢɪɨɜɚɧɧɚɹ ɦɨɞɟɥɶ
ɑɬɨ ɛɵ ɢɫɤɥɸɱɢɬɶ ɨɬɦɟɱɟɧɧɵɟ ɜɵɲɟ ɧɟɞɨɫɬɚɬɤɢ ɦɨɞɟɥɢ (3) ɛɵɥɚ ɩɪɟɞɥɨɠɟɧɚ ɤɨɦɛɢɧɢɪɨɜɚɧɧɚɹ ɦɨɞɟɥɶ, ɤɨɬɨɪɚɹ ɜ ɨɛɥɚɫɬɢ ɦɚɥɵɯ ɡɧɚɱɟɧɢɣ ɜɨɡɜɵɲɟɧɢɣ ( η~ < 2,5 ) ɛɥɢɡɤɚ
ɤ ɦɨɞɟɥɢ Ƚɪɚɦɚ-ɒɚɪɥɶɟ, ɡɚ ɩɪɟɞɟɥɚɦɢ ɭɤɚɡɚɧɧɨɣ ɨɛɥɚɫɬɢ ɛɥɢɡɤɚ ɤ ɪɚɫɩɪɟɞɟɥɟɧɢɸ Ƚɚɭɫɫɚ
(Ɂɚɩɟɜɚɥɨɜ, ɉɭɫɬɨɜɨɣɬɟɧɤɨ, 2010). Ʉɨɦɛɢɧɢɪɨɜɚɧɧɭɸ ɦɨɞɟɥɶ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ
PC (η~ ) =
~
~

 η~ 2    λ3
λ
1
~
~
 1 +  H 3 (η ) + 4 H 4 ξ  F (η~ ) ,
exp −

24
2π


 2    6
()
(4)
ɝɞɟ ɮɭɧɤɰɢɹ F ɜɵɩɨɥɧɹɟɬ ɪɨɥɶ ɮɢɥɶɬɪɚ. ȼ ɤɚɱɟɫɬɜɟ ɮɢɥɶɬɪɚ F ɢɫɩɨɥɶɡɭɟɬɫɹ ɞɜɭɯɩɚɪɚɦɟɬɪɢɱɟɫɤɚɹ ɮɭɧɤɰɢɹ, F (η~ ) = exp − ( η~ d ) n , ɝɞɟ ɩɚɪɚɦɟɬɪ d ɨɩɪɟɞɟɥɹɟɬ ɨɛɥɚɫɬɶ, ɜɧɭɬɪɢ
ɤɨɬɨɪɨɣ F (η~ ) ≈ 1 , ɩɚɪɚɦɟɬɪ n ɨɩɪɟɞɟɥɹɟɬ ɫɤɨɪɨɫɬɶ, ɫ ɤɨɬɨɪɨɣ ɮɭɧɤɰɢɹ F ɫɬɪɟɦɢɬɫɹ ɤ ɧɭɥɸ
[
]
39
ɡɚ ɩɪɟɞɟɥɚɦɢ ɷɬɨɣ ɨɛɥɚɫɬɢ. Ɂɚɞɚɱɚ ɜɵɛɨɪɚ ɱɢɫɥɟɧɧɵɯ ɡɧɚɱɟɧɢɣ ɩɚɪɚɦɟɬɪɨɜ n ɢ d ɪɚɫɫɦɨɬɪɟɧɚ ɜ ɪɚɛɨɬɟ (Ɂɚɩɟɜɚɥɨɜ, 2012ɛ), ɪɟɤɨɦɟɧɞɭɟɬɫɹ n = 3,5, d – 3,4.
Ɇɨɞɟɥɶ ɏɨɭ
Ɇɨɞɟɥɶ ɏɨɭ ɩɪɟɞɥɨɠɟɧɚ ɜ ɪɚɛɨɬɟ (Hou, 2006) ɢ ɧɚɡɜɚɧɚ ɡɞɟɫɶ ɬɚɤ ɩɨ ɮɚɦɢɥɢɢ ɩɟɪɜɨɝɨ ɚɜɬɨɪɚ. ɉɪɢ ɟɟ ɩɨɫɬɪɨɟɧɢɢ ɢɫɩɨɥɶɡɨɜɚɥɫɹ ɩɨɞɯɨɞ, ɜ ɪɚɦɤɚɯ ɤɨɬɨɪɨɝɨ ɫɬɚɬɢɫɬɢɱɟɫɤɨɟ
ɨɩɢɫɚɧɢɟ ɫɥɭɱɚɣɧɨɝɨ ɩɪɨɰɟɫɫɚ ɫɨɱɟɬɚɟɬɫɹ ɫ ɪɟɲɟɧɢɟɦ ɞɢɧɚɦɢɱɟɫɤɢɯ ɭɪɚɜɧɟɧɢɣ. Ɇɨɞɟɥɶ
ɏɨɭ ɢɦɟɟɬ ɜɢɞ
PH (η~ ) =
1
 1

1 − δ η~ exp(− δ η~ ) exp − η~ 2 exp(− 2δ η~ ) ,
2π
 2

ɝɞɟ ɩɚɪɚɦɟɬɪ į ɫɜɹɡɚɧ ɫɨ ɫɪɟɞɧɢɦ ɭɤɥɨɧɨɦ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ İ ɫɨɨɬɧɨɲɟɧɢɟɦ į = 2 ʌ İ.
ɉɪɢ ɫɬɪɟɦɥɟɧɢɢ ɩɚɪɚɦɟɬɪɚ į ɤ ɧɭɥɸ ɦɨɞɟɥɶ ɏɨɭ ɩɪɢɛɥɢɠɚɟɬɫɹ ɤ ɪɚɫɩɪɟɞɟɥɟɧɢɸ Ƚɚɭɫɫɚ.
Ɋɢɫ. 3 ɩɨɡɜɨɥɹɟɬ ɫɪɚɜɧɢɬɶ ɩɨɜɟɞɟɧɢɟ ɦɨɞɟɥɢ ɏɨɭ ɩɪɢ ɪɚɡɧɵɯ ɡɧɚɱɟɧɢɹɯ ɫɪɟɞɧɟɝɨ ɭɤɥɨɧɚ İ
ɜ ɞɜɭɯ ɨɛɥɚɫɬɹɯ ɢɡɦɟɧɟɧɢɹ ɩɚɪɚɦɟɬɪɚ η~ .
Плотность вероятностей
0,5
0,4
0,3
0,2
0,1
-2
0
η~
2
-2
0
η~
2
Плотность вероятностей
10
10-2
10-4
ε=0
ε=0,005
ε=0,015
10-6
10-8 -6
ε=0
ε=0,005
ε=0,015
ε=0,005
ε=0,015
-3
0
3
η~
6
-6
-3
0
3
η~
Ɋɢɫ. 3. Ɇɨɞɟɥɢ ɩɥɨɬɧɨɫɬɢ ɜɟɪɨɹɬɧɨɫɬɟɣ ɜɨɡɜɵɲɟɧɢɣ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ.
~
Ʌɟɜɵɣ ɫɬɨɥɛɟɰ – PH (η ) , ɩɪɚɜɵɣ ɫɬɨɥɛɟɰ – PS1 (η~ ) (ɫɩɥɨɲɧɚɹ ɥɢɧɢɹ)
ɢ PS 2 (η~ ) (ɩɭɧɤɬɢɪɧɚɹ ɥɢɧɢɹ)
40
6
Ɇɨɞɟɥɢ, ɩɨɫɬɪɨɟɧɧɵɟ ɧɚ ɨɫɧɨɜɟ ɜɨɥɧɵ ɋɬɨɤɫɚ
Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɞɥɹ ɭɡɤɨɩɨɥɨɫɧɨɝɨ ɜɨɥɧɨɜɨɝɨ ɫɩɟɤɬɪɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ ɚɦɩɥɢɬɭɞɧɨ-ɦɨɞɭɥɢɪɨɜɚɧɧɨɣ ɜɨɥɧɟ ɋɬɨɤɫɚ ɫ ɩɨɩɪɚɜɤɨɣ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ, ɫ ɡɚɞɚɧɧɨɣ ɫɪɟɞɧɟɣ ɱɚɫɬɨɬɨɣ ɢ ɫɥɭɱɚɣɧɵɦ ɪɚɫɩɪɟɞɟɥɟɧɢɟɦ ɮɚɡɵ ɛɵɥɨ ɩɨɫɬɪɨɟɧɨ ɜ ɪɚɛɨɬɟ (Tayfun, 1980). Ⱦɚɧɧɵɣ
ɩɨɞɯɨɞ ɪɚɡɜɢɬ ɜ ɪɚɛɨɬɟ (Huang, 1983), ɝɞɟ ɩɨɫɬɪɨɟɧɨ ɪɚɫɩɪɟɞɟɥɟɧɢɟ, ɨɫɧɨɜɚɧɧɨɟ ɧɚ ɩɪɢɛɥɢɠɟɧɢɢ ɋɬɨɤɫɚ ɬɪɟɬɶɟɝɨ ɩɨɪɹɞɤɚ. ɗɬɨ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɨɛɨɡɧɚɱɢɦ ɤɚɤ PS.
ȼ ɩɪɢɛɥɢɠɟɧɢɢ ɬɪɟɬɶɟɝɨ ɩɨɪɹɞɤɚ ɜɨɡɜɵɲɟɧɢɟ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɜ ɬɨɱɤɟ x, ɫɨɡɞɚɜɚɟɦɨɟ ɤɚɠɞɨɣ ɤɨɦɩɨɧɟɧɬɨɣ ɜɨɥɧɨɜɨɝɨ ɩɨɥɹ, ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ
1
2
η (x, t ) = a 2 k + a cos X +
3a 3k 2
a 2k
cos 2 X +
cos 3 X ,
2
2
(5)
ɝɞɟ a – ɚɦɩɥɢɬɭɞɚ; t – ɜɪɟɦɹ; X = kx − ωt + ϕ ; k ɢ Ȧ – ɜɨɥɧɨɜɨɟ ɱɢɫɥɨ ɢ ɰɢɤɥɢɱɟɫɤɚɹ ɱɚɫɬɨɬɚ;
ij – ɮɚɡɚ. Ⱥɦɩɥɢɬɭɞɵ ɤɨɦɩɨɧɟɧɬ ɩɟɪɜɨɝɨ ɩɨɪɹɞɤɚ ɩɪɟɞɩɨɥɚɝɚɸɬɫɹ ɪɚɫɩɪɟɞɟɥɟɧɧɵɦɢ ɩɨ ɡɚɤɨɧɭ Ɋɷɥɟɹ, ɮɚɡɵ ɢɦɟɸɬ ɪɚɜɧɨɦɟɪɧɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ.
ɉɨɫɬɪɨɟɧɵ ɞɜɟ ɦɨɞɟɥɢ PS1 (η~ ) ɢ PS 2 (η~ ) , ɨɬɥɢɱɚɸɳɢɟɫɹ ɬɟɦ, ɱɬɨ ɜɨ ɜɬɨɪɨɣ ɧɟ ɭɱɢɬɵɜɚɟɬɫɹ ɩɨɫɬɨɹɧɧɵɣ ɱɥɟɧ (1 2) a 2 k ɜ (5). Ɋɚɫɩɪɟɞɟɥɟɧɢɟ PS1 (η~ ) ɨɩɢɫɵɜɚɟɬɫɹ ɜɵɪɚɠɟɧɢɟɦ
exp(− h1 2 )  f1
9 δ 2 −3 2 
~
+
PS1 (η ) =
R1  ,

2π
 R1 8 N1


9
 39

ɝɞɟ N1 = 1 + δ 2 ; R1 = 1 + δ 2 η~ 2 ; f1 = N1 1 − 2δ η~ + δ 2  η~ 2 − 2  ;
4
 8


h1 =

N12 η~ − δ

(
2
)

 13
η~ 2 − 1 + δ 2  η~ 3 − 2η~  .

8
ȼɬɨɪɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ PS 2 (η~ ) ɨɩɢɫɵɜɚɟɬɫɹ ɜɵɪɚɠɟɧɢɟɦ,
f
exp(− h2 2 )  f 2
9
5δ 2 
+ δ 2 −25 2 +
PS 2 (η~ ) =

,
8 N 2 R23 2 
2π
 R2 8 R2
ɝɞɟ N 2 = 1 +
1 2
3
3
δ ; R2 = 1 + δ η~ + δ 2η~ 2 ; f 2 = N 2 1 − 2 δ η~ + δ 2 η~ 2 ;
4
8


2
1


h2 = N 22 η~ 2 − δ η~ 3 + δ 2η~ 4  .
2


Ɉɛɚ ɪɚɫɩɪɟɞɟɥɟɧɢɹ PS1 (η~ ) ɢ PS 2 (η~ ) ɹɜɥɹɸɬɫɹ ɨɞɧɨɩɚɪɚɦɟɬɪɢɱɟɫɤɢɦɢ. Ʉɚɤ ɢ ɦɨɞɟɥɶ
ɏɨɭ, ɢɯ ɦɨɠɧɨ ɨɩɢɫɚɬɶ, ɡɚɞɚɜ ɬɨɥɶɤɨ ɫɪɟɞɧɢɣ ɭɤɥɨɧ ɩɨɜɟɪɯɧɨɫɬɢ İ. ɉɪɢ İ ĺ 0 ɨɧɢ ɩɪɢɛɥɢɠɚɸɬɫɹ ɤ ɪɚɫɩɪɟɞɟɥɟɧɢɸ Ƚɚɭɫɫɚ. ɂɡ ɪɢɫ. 3 ɜɢɞɧɨ, ɱɬɨ ɭɱɟɬ ɩɨɫɬɨɹɧɧɨɝɨ ɱɥɟɧɚ (1/2) a2k
ɜ ɜɵɪɚɠɟɧɢɢ (5) ɫɭɳɟɫɬɜɟɧɧɨ ɜɥɢɹɟɬ ɧɚ ɯɚɪɚɤɬɟɪ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɨɡɜɵɲɟɧɢɣ ɩɨɜɟɪɯɧɨɫɬɢ.
ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɦɨɞɟɥɢ PH (η ) , PS1 (η ) и PS 2 (η ) ɩɨɡɜɨɥɹɸɬ ɨɩɢɫɚɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɜɨɡɜɵɲɟɧɢɣ ɩɨɜɟɪɯɧɨɫɬɢ ɜ ɨɝɪɚɧɢɱɟɧɧɨɦ ɞɢɚɩɚɡɨɧɟ ɡɧɚɱɟɧɢɣ η~ . ɉɪɢ ɜɵɯɨɞɟ ɡɚ
41
ɩɪɟɞɟɥɵ ɷɬɨɝɨ ɞɢɚɩɚɡɨɧɚ ɚɫɢɦɦɟɬɪɢɹ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɢ ɷɤɫɰɟɫɫ ɫɭɳɟɫɬɜɟɧɧɨ ɨɬɥɢɱɚɸɬɫɹ
ɨɬ ɡɧɚɱɟɧɢɣ ɷɬɢɦ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦ, ɩɨɥɭɱɟɧɧɵɦ ɩɨ ɞɚɧɧɵɦ ɩɪɹɦɵɯ ɜɨɥɧɨɝɪɚɮɢɱɟɫɤɢɯ
ɢɡɦɟɪɟɧɢɣ (Ɂɚɩɟɜɚɥɨɜ, 2012ɛ).
Ɂɚɜɢɫɢɦɨɫɬɶ ɮɨɪɦɵ ɷɯɨ-ɫɢɝɧɚɥɚ ɨɬ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɨɡɜɵɲɟɧɢɣ
ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ
ɋ ɩɨɦɨɳɶɸ ɦɨɞɟɥɢ Ȼɪɚɭɧɚ (1) ɩɨɫɬɪɨɢɦ ɷɯɨ-ɫɢɝɧɚɥ ɞɥɹ ɫɢɬɭɚɰɢɣ, ɤɨɝɞɚ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɨɡɜɵɲɟɧɢɣ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɨɩɢɫɵɜɚɟɬɫɹ ɨɞɧɨɣ ɢɡ ɪɚɫɫɦɨɬɪɟɧɧɵɯ ɜɵɲɟ
ɦɨɞɟɥɟɣ. Ⱦɥɹ ɪɚɡɦɟɳɟɧɧɵɯ ɧɚ ɤɨɫɦɢɱɟɫɤɢɯ ɚɩɩɚɪɚɬɚɯ ɚɥɶɬɢɦɟɬɪɨɜ ɮɨɪɦɚ ɨɬɪɚɠɟɧɧɨɝɨ ɨɬ
ɩɥɨɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɢɦɩɭɥɶɫɚ ɢɦɟɟɬ ɜɢɞ (Brown, 1977):
 
 4c
4c
cos(2 ξ )t  I 0  2 2 sin 2 (2 ξ )t
Fr (t ) = a exp −

  γ h
 γh

 H (t ) ,


ɝɞɟ a – ɚɦɩɥɢɬɭɞɚ; c – ɫɤɨɪɨɫɬɶ ɫɜɟɬɚ; Ȗ – ɲɢɪɢɧɚ ɥɭɱɚ ɚɧɬɟɧɧɵ; h – ɜɵɫɨɬɚ ɨɪɛɢɬɵ ɤɨɫɦɢɱɟɫɤɨɝɨ ɚɩɩɚɪɚɬɚ; ȟ – ɚɛɫɨɥɸɬɧɨɟ ɡɧɚɱɟɧɢɟ ɭɝɥɚ ɩɚɞɟɧɢɹ; I0 – ɦɨɞɢɮɢɰɢɪɨɜɚɧɧɚɹ ɮɭɧɤɰɢɹ
Ȼɟɫɫɟɥɹ ɩɟɪɜɨɝɨ ɪɨɞɚ; H (t) – ɟɞɢɧɢɱɧɚɹ ɮɭɧɤɰɢɹ ɏɟɜɢɫɚɣɞɚ. Ȼɭɞɟɦ ɩɨɥɚɝɚɬɶ, ɱɬɨ ɮɨɪɦɚ
ɡɨɧɞɢɪɭɸɳɟɝɨ ɪɚɞɢɨɢɦɩɭɥɶɫɚ ɹɜɥɹɟɬɫɹ ɝɚɭɫɫɨɜɨɣ
sr (t ) =
 t2
exp −
2 π Dr
 2 Dr
1

,


ɝɞɟ ɩɚɪɚɦɟɬɪ Dr ɨɩɪɟɞɟɥɹɟɬ ɲɢɪɢɧɭ ɪɚɞɢɨɢɦɩɭɥɶɫɚ.
ɉɪɢ ɪɚɫɱɟɬɚɯ ɡɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ șw, ¥Dr ɢ h, ɤɚɤ ɜ ɪɚɛɨɬɟ (Hayne, 1980), ɩɪɢɦɟɦ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɩɚɪɚɦɟɬɪɚɦ ɚɥɶɬɢɦɟɬɪɚ, ɭɫɬɚɧɨɜɥɟɧɧɨɝɨ ɧɚ SEASAT-1: șw = 1,6°,
¥Dr = 1,327 ɧɫɟɤ ɢ h = 8 × 105 ɦ. Ɉɬɦɟɬɢɦ, ɱɬɨ ɡɚɦɟɧɚ ɡɧɚɱɟɧɢɣ ɭɤɚɡɚɧɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɧɚ
ɡɧɚɱɟɧɢɹ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɫɨɜɪɟɦɟɧɧɵɦ ɚɥɶɬɢɦɟɬɪɚɦ ɧɟ ɜɧɨɫɢɬ ɩɪɢɧɰɢɩɢɚɥɶɧɵɯ ɢɡɦɟɧɟɧɢɣ. ɉɪɢɧɹɬɨ, ɱɬɨ ɚɦɩɥɢɬɭɞɧɵɣ ɦɧɨɠɢɬɟɥɶ ɜ ɜɵɪɚɠɟɧɢɢ (2) a = 100.
ɇɚ ɪɢɫ. 4 ɩɨɤɚɡɚɧɵ ɮɨɪɦɵ ɷɯɨ-ɫɢɝɧɚɥɨɜ, ɩɨɫɬɪɨɟɧɧɵɯ ɞɥɹ ɫɥɭɱɚɹ, ɤɨɝɞɚ ɩɥɨɬɧɨɫɬɶ
ɜɟɪɨɹɬɧɨɫɬɟɣ ɜɨɡɜɵɲɟɧɢɣ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɨɩɢɫɵɜɚɟɬɫɹ ɦɨɞɟɥɶɸ (3). ɍɱɬɟɧɨ, ɱɬɨ
ɩɪɢ ɡɧɚɱɢɦɨɣ ɜɵɫɨɬɟ ɜɨɥɧ ɛɨɥɶɲɟ 4,5 ɦ, ɡɧɚɱɟɧɢɹ ɚɫɢɦɦɟɬɪɢɢ ɢ ɷɤɫɰɟɫɫɚ ɜ ɨɫɧɨɜɧɨɦ
~
~
ɥɟɠɚɬ ɜ ɞɢɚɩɚɡɨɧɚɯ − 0,05 ≤ λ3 ≤ 0,4 и − 0,4 ≤ λ4 ≤ 0,4 (Jha, Winterstein, 2000). Ɋɟɡɭɥɶɬɚɬɵ
ɪɚɫɱɟɬɨɜ ɩɪɢ Hs = 5 ɦ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɝɪɚɧɢɰɚɦ ɭɤɚɡɚɧɧɵɯ ɞɢɚɩɚɡɨɧɨɜ, ɩɪɟɞɫɬɚɜɥɟɧɵ
ɧɚ ɪɢɫ. 4.
Ɉɬɦɟɬɢɦ ɩɨɹɜɥɟɧɢɟ ɜ ɧɟɤɨɬɨɪɵɯ ɫɢɬɭɚɰɢɹɯ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɡɧɚɱɟɧɢɣ ɜ ɦɨɞɟɥɢ V (t).
Ⱦɚɧɧɵɣ ɧɟɮɢɡɢɱɟɫɤɢɣ ɷɮɮɟɤɬ ɨɛɭɫɥɨɜɥɟɧ ɪɚɫɫɦɨɬɪɟɧɧɵɦɢ ɜɵɲɟ ɢɫɤɚɠɟɧɢɹɦɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ƚɪɚɦɚ-ɒɚɪɥɶɟ ɜ ɨɛɥɚɫɬɢ η~ > 2,5. ɏɨɬɹ ɨɬɪɢɰɚɬɟɥɶɧɵɟ ɡɧɚɱɟɧɢɹ V (t) ɦɚɥɵ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɚɦɩɥɢɬɭɞɨɣ ɷɯɨ-ɫɢɝɧɚɥɚ, ɢɯ ɩɨɹɜɥɟɧɢɟ ɭɤɚɡɵɜɚɟɬ ɧɚ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɩɨɫɬɪɨɟɧɢɹ ɦɨɞɟɥɢ, ɩɨɡɜɨɥɹɸɳɟɣ ɤɨɪɪɟɤɬɧɨ ɨɩɢɫɵɜɚɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɜɨɡɜɵɲɟɧɢɣ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ
ɜ ɛɨɥɟɟ ɲɢɪɨɤɨɦ ɞɢɚɩɚɡɨɧɟ ɢɡɦɟɧɟɧɢɹ η~ . ȼ ɱɚɫɬɧɨɫɬɢ, ɬɚɤɨɜɨɣ ɹɜɥɹɟɬɫɹ ɤɨɦɛɢɧɢɪɨɜɚɧɧɚɹ
ɦɨɞɟɥɶ (4).
42
100
V (t )
80
60
40
1
2
3
4
5
20
0
-30
-20
-10
0
10
20
t, нсек 30
Ɋɢɫ. 4. Ɏɨɪɦɵ ɷɯɨ-ɫɢɝɧɚɥɨɜ V (t) ɩɪɢ ɡɨɧɞɢɪɨɜɚɧɢɢ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ,
ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɜɨɡɜɵɲɟɧɢɣ ɤɨɬɨɪɨɣ ɨɩɢɫɵɜɚɟɬɫɹ ɪɚɫɩɪɟɞɟɥɟɧɢɟɦ Ƚɪɚɦɚ-ɒɚɪɥɶɟ (7).
~
~
~
~
~
~
1 – λ3 = 0 , λ4 = 0 ; 2 – λ3 = 0,4 , λ4 = 0,4 ; 3 – λ3 = 0,4 , λ4 = −0,4 ;
~
~
~
~
4 – λ3 = −0,05 , λ4 = 0,4 ; 5 – λ3 = −0,05 , λ4 = −0,4
Ɏɨɪɦɵ ɷɯɨ-ɫɢɝɧɚɥɨɜ, ɪɚɫɫɱɢɬɚɧɧɵɯ ɩɨ ɦɨɞɟɥɹɦ PH (η ) , PS1 (η ) и PS 2 (η ) ɩɪɢ Hs = 5 ɦ,
ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɚ ɪɢɫ. 5. ɍɱɢɬɵɜɚɹ, ɱɬɨ ɩɪɢ ɮɢɤɫɢɪɨɜɚɧɧɨɣ ɞɢɫɩɟɪɫɢɢ ɜɨɥɧɨɜɨɝɨ ɩɨɥɹ ɭɤɚɡɚɧɧɵɟ ɦɨɞɟɥɢ ɨɩɪɟɞɟɥɹɸɬɫɹ ɨɞɧɢɦ ɩɚɪɚɦɟɬɪɨɦ (ɫɪɟɞɧɢɦ ɭɤɥɨɧɨɦ İ), ɢɧɬɟɪɟɫɧɨ ɨɰɟɧɢɬɶ,
ɤɚɤ ɜɵɛɨɪ ɦɨɞɟɥɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɨɡɜɵɲɟɧɢɣ ɩɨɜɟɪɯɧɨɫɬɢ ɜɥɢɹɟɬ ɧɚ ɨɩɪɟɞɟɥɟɧɢɟ ɪɚɫɫɬɨɹɧɢɹ ɨɬ ɄȺ ɞɨ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ. ȼɢɞɧɨ, ɱɬɨ ɩɪɢ ɨɞɧɢɯ ɢ ɬɟɯ ɠɟ ɡɧɚɱɟɧɢɹɯ ɩɚɪɚɦɟɬɪɚ
İ ɫɦɟɳɟɧɢɹ ɮɪɨɧɬɚ ɢɦɩɭɥɶɫɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɢɦɩɭɥɶɫɚ ɪɚɫɫɱɢɬɚɧɧɨɝɨ ɞɥɹ ɝɚɭɫɫɨɜɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɪɚɡɥɢɱɧɨ, ɨɧɨ ɦɢɧɢɦɚɥɶɧɨ ɞɥɹ ɦɨɞɟɥɢ PH (Ș) ɢ ɦɚɤɫɢɦɚɥɶɧɨ ɞɥɹ ɦɨɞɟɥɢ PS2 (Ș).
100
V (t )
80
I
II
III
60
40
ε=0
ε=0,005
ε=0,015
20
0
-20
0
20
40
t , нсек
60
Ɋɢɫ. 5. Ɏɨɪɦɵ ɷɯɨ-ɫɢɝɧɚɥɨɜ V(t) ɩɪɢ ɡɨɧɞɢɪɨɜɚɧɢɢ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ,
~
ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɜɨɡɜɵɲɟɧɢɣ ɤɨɬɨɪɨɣ ɨɩɢɫɵɜɚɟɬɫɹ ɦɨɞɟɥɹɦɢ PH (η ) , PS1 (η~ ) ɢ PS 2 (η~ ) :
~
ɝɪɭɩɩɚ I – PH (η ) ; ɝɪɭɩɩɚ II – PS1 (η~ ) ; ɝɪɭɩɩɚ III – PS 2 (η~ )
43
ɋɦɟɳɟɧɢɟ ɮɪɨɧɬɚ ɷɯɨ-ɫɢɝɧɚɥɚ ɧɚ ɨɞɧɭ ɧɚɧɨɫɟɤɭɧɞɭ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɢɡɦɟɧɟɧɢɸ ɪɚɫɫɬɨɹɧɢɹ ɨɬ ɄȺ ɞɨ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɧɚ 15 ɫɦ. Ⱦɥɹ ɦɨɞɟɥɢ PH (Ș) ɢɡɦɟɧɟɧɢɟ ɪɚɫɫɬɨɹɧɢɹ
ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɪɚɫɫɬɨɹɧɢɟɦ, ɪɚɫɫɱɢɬɚɧɧɵɦ ɞɥɹ ɝɚɭɫɫɨɜɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɫɨɫɬɚɜɢɥɨ 2,1 ɫɦ
ɩɪɢ İ = 0,015 ɢ 0,5 ɫɦ ɩɪɢ İ = 0,005; ɞɥɹ ɦɨɞɟɥɢ PS1 (Ș) – 12,8 ɫɦ ɢ 4,4 ɫɦ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ;
ɞɥɹ ɦɨɞɟɥɢ PS2 (Ș) – 17,6 ɫɦ ɢ 6,1 ɫɦ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ.
Ɂɚɤɥɸɱɟɧɢɟ
ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɜɫɟ ɨɰɟɧɤɢ ɨɲɢɛɨɤ ɜ ɨɩɪɟɞɟɥɟɧɢɢ ɪɚɫɫɬɨɹɧɢɹ ɨɬ ɄȺ ɞɨ ɭɪɨɜɧɹ
ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɨɛɭɫɥɨɜɥɟɧɧɵɟ ɢɡɦɟɧɟɧɢɟɦ ɟɟ ɫɨɫɬɨɹɧɢɹ (SSB), ɹɜɥɹɸɬɫɹ ɷɦɩɢɪɢɱɟɫɤɢɦɢ (Hausman, Zlotnicki, 2010). ȼɨ ɦɧɨɝɨɦ ɷɬɨ ɨɛɭɫɥɨɜɥɟɧɨ ɧɟɞɨɫɬɚɬɤɨɦ ɢɧɮɨɪɦɚɰɢɢ
ɨɛ ɢɡɦɟɧɱɢɜɨɫɬɢ ɫɬɪɭɤɬɭɪɵ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɚ ɬɚɤɠɟ ɨɬɫɭɬɫɬɜɢɟɦ ɦɨɞɟɥɟɣ ɨɩɢɫɵɜɚɸɳɢɯ ɷɬɭ ɢɡɦɟɧɱɢɜɨɫɬɶ ɜ ɲɢɪɨɤɨɦ ɞɢɚɩɚɡɨɧɟ ɦɟɬɟɨɪɨɥɨɝɢɱɟɫɤɢɯ ɢ ɝɢɞɪɨɥɨɝɢɱɟɫɤɢɯ
ɭɫɥɨɜɢɣ.
ɇɟɫɦɨɬɪɹ ɧɚ ɜɫɸ ɚɤɬɭɚɥɶɧɨɫɬɶ ɢ ɦɧɨɝɨɥɟɬɧɸɸ ɢɫɬɨɪɢɸ, ɩɪɨɛɥɟɦɚ ɨɩɢɫɚɧɢɹ ɫɬɪɭɤɬɭɪɵ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɟɳɟ ɞɚɥɟɤɚ ɨɬ ɫɜɨɟɝɨ ɪɟɲɟɧɢɹ. ɋ ɨɞɧɨɣ ɫɬɨɪɨɧɵ, ɷɬɨ ɨɛɴɹɫɧɹɟɬɫɹ ɫɥɨɠɧɨɫɬɶɸ ɩɨɫɬɪɨɟɧɢɹ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɦɨɞɟɥɟɣ, ɜ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɭɱɢɬɵɜɚɬɶ
ɧɟɥɢɧɟɣɧɨɫɬɶ ɩɪɨɰɟɫɫɚ ɢ ɛɨɥɶɲɨɟ ɱɢɫɥɨ ɫɚɦɵɯ ɪɚɡɧɵɯ ɩɨ ɫɜɨɟɣ ɮɢɡɢɱɟɫɤɨɣ ɩɪɢɪɨɞɟ
ɮɚɤɬɨɪɨɜ, ɪɨɥɶ ɤɨɬɨɪɵɯ ɦɟɧɹɟɬɫɹ ɫ ɢɡɦɟɧɟɧɢɟɦ ɦɟɬɟɨɪɨɥɨɝɢɱɟɫɤɢɯ ɢ ɝɢɞɪɨɥɨɝɢɱɟɫɤɢɯ
ɭɫɥɨɜɢɣ (ɏɪɢɫɬɨɮɨɪɨɜ ɢ ɞɪ., 1991; ɒɚɪɤɨɜ, 2009; Ɇɟɥɶɧɢɤɨɜɚ, ɉɨɤɚɡɟɟɜ, 2009; Melnikova
et al., 2008). ɋ ɞɪɭɝɨɣ ɫɬɨɪɨɧɵ, ɷɬɨ ɬɪɭɞɧɨɫɬɶ ɧɚɬɭɪɧɵɯ ɢɫɫɥɟɞɨɜɚɧɢɣ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɜɨɡɜɵɲɟɧɢɣ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɧɚ ɦɚɫɲɬɚɛɚɯ η~ > 3 , ɤɨɬɨɪɵɟ ɨɤɚɡɵɜɚɸɬ ɡɚɦɟɬɧɨɟ ɜɥɢɹɧɢɟ
ɧɚ ɮɨɪɦɢɪɨɜɚɧɢɟ ɷɯɨ-ɫɢɝɧɚɥɚ ɪɚɞɢɨɚɥɶɬɢɦɟɬɪɚ.
ɋɭɳɟɫɬɜɭɟɬ ɛɨɥɶɲɨɟ ɱɢɫɥɨ ɦɨɞɟɥɟɣ, ɩɨɫɬɪɨɟɧɧɵɯ ɜ ɪɚɦɤɚɯ ɪɚɡɥɢɱɧɵɯ ɮɢɡɢɱɟɫɤɢɯ
ɝɢɩɨɬɟɡ ɢ ɩɨɞɯɨɞɨɜ, ɤɨɬɨɪɵɟ ɨɩɢɫɵɜɚɸɬ ɩɥɨɬɧɨɫɬɶ ɜɟɪɨɹɬɧɨɫɬɟɣ ɜɨɡɜɵɲɟɧɢɣ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ (Tayfun, 1980; CieĞlikiewicz, 1989; Srokosz, 1998; Dai, 2002; Ɂɚɩɟɜɚɥɨɜ, Ɋɚɬɧɟɪ,
2003; Hou, 2006). ɂɯ ɨɛɳɢɦ ɧɟɞɨɫɬɚɬɤɨɦ ɹɜɥɹɟɬɫɹ ɬɨ, ɱɬɨ ɨɧɢ ɭɱɢɬɵɜɚɸɬ ɬɨɥɶɤɨ ɤɚɤɨɣ-ɬɨ
ɨɞɢɧ ɮɢɡɢɱɟɫɤɢɣ ɦɟɯɚɧɢɡɦ, ɨɩɪɟɞɟɥɹɸɳɢɣ ɨɬɤɥɨɧɟɧɢɹ ɨɬ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ƚɚɭɫɫɚ, ɱɬɨ ɧɚɤɥɚɞɵɜɚɟɬ ɡɧɚɱɢɬɟɥɶɧɵɟ ɨɝɪɚɧɢɱɟɧɢɹ ɧɚ ɜɨɡɦɨɠɧɨɫɬɶ ɢɯ ɩɪɢɦɟɧɟɧɢɹ.
Ɉɫɧɨɜɧɵɦ ɩɪɢ ɨɩɢɫɚɧɢɢ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɜ ɩɪɢɥɨɠɟɧɢɹɯ, ɫɜɹɡɚɧɧɵɯ ɫ ɪɚɫɫɟɹɧɢɟɦ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɯ ɜɨɥɧ ɨɫɬɚɟɬɫɹ ɪɚɫɩɪɟɞɟɥɟɧɢɟ Ƚɪɚɦɚ-ɒɚɪɥɶɟ. Ɉɞɧɚɤɨ ɢ ɨɧɨ
ɢɦɟɟɬ ɪɹɞ ɫɭɳɟɫɬɜɟɧɧɵɯ ɧɟɞɨɫɬɚɬɤɨɜ. ɋɪɚɜɧɟɧɢɟ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɜɨɡɜɵɲɟɧɢɣ ɦɨɪɫɤɨɣ
ɩɨɜɟɪɯɧɨɫɬɢ, ɩɨɫɬɪɨɟɧɧɵɯ ɫ ɩɨɦɨɳɶɸ ɦɨɞɟɥɟɣ Ƚɪɚɦɚ-ɒɚɪɥɶɟ ɫ ɪɟɡɭɥɶɬɚɬɚɦɢ ɧɚɬɭɪɧɵɯ
ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɨɧɢ ɩɨɡɜɨɥɹɸɬ ɨɩɢɫɚɬɶ ɜɨɡɜɵɲɟɧɢɹ ɬɨɥɶɤɨ ɜ ɨɝɪɚɧɢɱɟɧɧɨɦ
ɞɢɚɩɚɡɨɧɟ η~ < 2.5 . ɋɥɟɞɫɬɜɢɣ ɢɫɤɚɠɟɧɢɣ ɧɚ ɤɪɵɥɶɹɯ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɨɡɜɵɲɟɧɢɣ ɩɨɜɟɪɯɧɨɫɬɢ ɹɜɥɹɟɬɫɹ ɩɨɹɜɥɟɧɢɟ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɡɧɚɱɟɧɢɣ ɜ ɪɚɫɱɟɬɧɨɣ ɮɨɪɦɟ ɷɯɨ-ɫɢɝɧɚɥɚ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɨɞɧɢɦ ɢɡ ɨɫɧɨɜɧɵɯ ɮɚɤɬɨɪɨɜ, ɩɪɟɩɹɬɫɬɜɭɸɳɢɯ
ɤɨɪɪɟɤɬɧɨɦɭ ɨɩɢɫɚɧɢɸ ɮɨɪɦɵ ɷɯɨ-ɫɢɝɧɚɥɚ ɭɫɬɚɧɨɜɥɟɧɧɨɝɨ ɧɚ ɫɩɭɬɧɢɤɟ ɪɚɞɢɨɚɥɶɬɢɦɟɬɪɚ,
ɹɜɥɹɟɬɫɹ ɨɬɫɭɬɫɬɜɢɟ ɦɨɞɟɥɟɣ, ɨɩɢɫɵɜɚɸɳɢɯ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɜɨɡɜɵɲɟɧɢɣ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɧɚ ɦɚɫɲɬɚɛɚɯ ɛɨɥɟɟ ɱɟɦ ɜ ɩɨɥɬɨɪɚ ɪɚɡɚ, ɩɪɟɜɨɫɯɨɞɹɳɢɯ ɡɧɚɱɢɦɭɸ ɜɵɫɨɬɭ ɜɨɥɧ.
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Ʌɢɬɟɪɚɬɭɪɚ
1. Ȼɚɤɭɬ ɉ.Ⱥ., Ȼɨɥɶɲɚɤɨɜ ɂ.Ⱥ., Ƚɟɪɚɫɢɦɨɜ Ȼ.Ɇ., Ʉɭɪɢɤɲɚ A.A., Ɋɟɩɢɧ ȼ.Ƚ., Ɍɚɪɬɚɤɨɜɫɤɢɣ Ƚ.ɉ.,
ɒɢɪɨɤɨɜ ȼ.ȼ. ȼɨɩɪɨɫɵ ɫɬɚɬɢɫɬɢɱɟɫɤɨɣ ɬɟɨɪɢɢ ɪɚɞɢɨɥɨɤɚɰɢɢ. Ɇ.: ɋɨɜ.ɪɚɞɢɨ, 1964. Ɍ. 2.
1087 ɫ.
2. Ȼɚɫɤɚɤɨɜ Ⱥ.ɂ., ȿɝɨɪɨɜ ȼ.ȼ. ɉɟɪɫɩɟɤɬɢɜɧɵɣ ɜɵɫɨɤɨɬɨɱɧɵɣ ɫɩɭɬɧɢɤɨɜɵɣ ɚɥɶɬɢɦɟɬɪ //
ɋɨɜɪɟɦɟɧɧɵɟ ɩɪɨɛɥɟɦɵ ɞɢɫɬɚɧɰɢɨɧɧɨɝɨ ɡɨɧɞɢɪɨɜɚɧɢɹ Ɂɟɦɥɢ ɢɡ ɤɨɫɦɨɫɚ. 2008. Ɍ. 5.
ʋ 1. ɋ. 225–228.
3. Ȼɚɫɫ Ɏ.Ƚ., Ȼɪɚɭɞɟ ɋ.ə., Ʉɚɥɦɵɤɨɜ Ⱥ.ɂ., Ɇɟɧɶ Ⱥ.ȼ., Ɉɫɬɪɨɜɫɤɢɣ ɂ.ȿ., ɉɭɫɬɨɜɨɣɬɟɧɤɨ ȼ.ȼ.,
Ɋɨɡɟɧɛɟɪɝ Ⱥ.Ⱦ., Ɏɭɤɫ ɂ.Ɇ. Ɇɟɬɨɞɵ ɪɚɞɢɨɥɨɤɚɰɢɨɧɧɵɯ ɢɫɫɥɟɞɨɜɚɧɢɣ ɦɨɪɫɤɨɝɨ ɜɨɥɧɟɧɢɹ
(ɪɚɞɢɨɨɤɟɚɧɨɝɪɚɮɢɹ) // ɍɫɩɟɯɢ ɮɢɡɢɱɟɫɤɢɯ ɧɚɭɤ. 1975. Ɍ. 116. ɋ. 741–743.
4. Ƚɚɥɚɟɜ ɘ.Ɇ., Ȼɨɥɶɲɚɤɨɜ Ⱥ.ɇ., ȿɮɢɦɨɜ ȼ.Ȼ., Ʉɚɥɦɵɤɨɜ Ⱥ.ɂ., Ʉɭɪɟɤɢɧ Ⱥ.ɋ., Ʌɟɦɟɧɬɚ ɘ.Ⱥ.,
ɇɟɥɟɩɨ Ȼ.Ⱥ., Ɉɫɬɪɨɜɫɤɢɣ ɂ.ȿ., ɉɢɱɭɝɢɧ Ⱥ.ɉ., ɉɭɫɬɨɜɨɣɬɟɧɤɨ ȼ.ȼ., Ɍɟɪɟɯɢɧ ɘ.ȼ. ɇɟɤɨɬɨɪɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɪɚɞɢɨɥɨɤɚɰɢɨɧɧɵɯ ɨɬɪɚɠɟɧɢɣ ɩɨɜɟɪɯɧɨɫɬɶɸ ɦɨɪɹ ɩɪɢ ɭɝɥɚɯ ɩɚɞɟɧɢɹ, ɛɥɢɡɤɢɯ ɤ ɜɟɪɬɢɤɚɥɶɧɵɦ // ɉɪɟɩɪɢɧɬ ʋ 1. ɋɟɜɚɫɬɨɩɨɥɶ: ɆȽɂ Ⱥɇ ɍɋɋɊ. 1978. 22 ɫ.
5. ȿɝɨɪɨɜ ȼ.ȼ., Ɇɢɧ-ɏɨ Ʉɚ. ȼɨɩɪɨɫɵ ɬɨɱɧɨɫɬɢ ɚɷɪɨɤɨɫɦɢɱɟɫɤɨɣ ɚɥɶɬɢɦɟɬɪɢɢ // ɂɫɫɥɟɞ.
Ɂɟɦɥɢ ɢɡ ɤɨɫɦɨɫɚ. 2005. ʋ 5. ɋ. 48–55.
6. ɀɭɤɨɜɫɤɢɣ Ⱥ.ɉ., Ɉɧɨɩɪɢɟɧɤɨ ȿ.ɂ., ɑɢɠɨɜ ȼ.ɂ. Ɍɟɨɪɟɬɢɱɟɫɤɢɟ ɨɫɧɨɜɵ ɪɚɞɢɨɜɵɫɨɬɨɦɟɬɪɢɢ / ɉɨɞ ɪɟɞ. Ⱥ.ɉ. ɀɭɤɨɜɫɤɨɝɨ. Ɇ.: ɋɨɜ ɪɚɞɢɨ, 1979. 320 ɫ.
7. Ɂɚɩɟɜɚɥɨɜ Ⱥ.ɋ. ȼɥɢɹɧɢɟ ɚɫɢɦɦɟɬɪɢɢ ɢ ɷɤɫɰɟɫɫɚ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɨɡɜɵɲɟɧɢɣ ɜɡɜɨɥɧɨɜɚɧɧɨɣ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɧɚ ɬɨɱɧɨɫɬɶ ɚɥɶɬɢɦɟɬɪɢɱɟɫɤɢɯ ɢɡɦɟɪɟɧɢɣ ɟɟ ɭɪɨɜɧɹ //
ɂɡɜ. ɊȺɇ. ɋɟɪ. Ɏɢɡɢɤɚ ɚɬɦɨɫɮɟɪɵ ɢ ɨɤɟɚɧɚ. 2012ɚ. T. 48. ʋ 2. ɋ. 224–231.
8. Ɂɚɩɟɜɚɥɨɜ Ⱥ.ɋ. ɋɬɚɪɲɢɟ ɤɭɦɭɥɹɧɬɵ ɜɨɡɜɵɲɟɧɢɣ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ // Ɇɟɬɟɨɪɨɥɨɝɢɹ
ɢ ɝɢɞɪɨɥɨɝɢɹ. 2011. ʋ 9. ɋ. 78–85.
9. Ɂɚɩɟɜɚɥɨɜ Ⱥ.ɋ. ɋɬɚɬɢɫɬɢɱɟɫɤɢɟ ɦɨɞɟɥɢ ɜɡɜɨɥɧɨɜɚɧɧɨɣ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ. Ⱦɥɹ ɡɚɞɚɱ
ɞɢɫɬɚɧɰɢɨɧɧɨɝɨ ɡɨɧɞɢɪɨɜɚɧɢɹ: LAP LAMBERT Academic Publishing, 2012ɛ. 69 ɫ.
10. Ɂɚɩɟɜɚɥɨɜ Ⱥ.ɋ., Ȼɨɥɶɲɚɤɨɜ Ⱥ.ɇ., ɋɦɨɥɨɜ ȼ.ȿ. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɩɥɨɬɧɨɫɬɢ ɜɟɪɨɹɬɧɨɫɬɟɣ
ɜɨɡɜɵɲɟɧɢɣ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɫ ɩɨɦɨɳɶɸ ɪɹɞɨɜ Ƚɪɚɦɚ-ɒɚɪɥɶɟ // Ɉɤɟɚɧɨɥɨɝɢɹ.
2011. Ɍ. 51. ʋ 3. ɋ. 432–439.
11. Ɂɚɩɟɜɚɥɨɜ Ⱥ.ɋ., ɉɭɫɬɨɜɨɣɬɟɧɤɨ ȼ.ȼ. Ʉ ɜɨɩɪɨɫɭ ɨɩɪɟɞɟɥɟɧɢɹ ɚɫɢɦɦɟɬɪɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ
ɜɨɡɜɵɲɟɧɢɣ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɩɨ ɞɚɧɧɵɦ ɚɥɶɬɢɦɟɬɪɢɱɟɫɤɢɯ ɢɡɦɟɪɟɧɢɣ // ɂɫɫɥɟɞɨɜɚɧɢɹ Ɂɟɦɥɢ ɢɡ ɤɨɫɦɨɫɚ. 2012. ʋ 5. ɋ. 12–21.
12. Ɂɚɩɟɜɚɥɨɜ Ⱥ.ɋ., ɉɭɫɬɨɜɨɣɬɟɧɤɨ ȼ.ȼ. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɩɥɨɬɧɨɫɬɢ ɜɟɪɨɹɬɧɨɫɬɟɣ ɭɤɥɨɧɨɜ
ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɜ ɡɚɞɚɱɚɯ ɪɚɫɫɟɹɧɢɹ ɪɚɞɢɨɜɨɥɧ // ɂɡɜɟɫɬɢɹ ɜɭɡɨɜ. Ɋɚɞɢɨɮɢɡɢɤɚ.
2010. Ɍ. 53. ʋ 2. ɋ. 110–121.
13. Ɂɚɩɟɜɚɥɨɜ Ⱥ.ɋ., Ɋɚɬɧɟɪ ɘ.Ȼ. Ⱥɧɚɥɢɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɩɥɨɬɧɨɫɬɢ ɜɟɪɨɹɬɧɨɫɬɟɣ ɭɤɥɨɧɨɜ
ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ // Ɇɨɪɫɤɨɣ ɝɢɞɪɨɮɢɡɢɱɟɫɤɢɣ ɠɭɪɧɚɥ. 2003. ʋ 1. ɋ. 3–17.
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16. Ʌɨɧɝɟ-ɏɢɝɝɢɧɫ Ɇ.ɋ. ɋɬɚɬɢɫɬɢɱɟɫɤɢɣ ɚɧɚɥɢɡ ɫɥɭɱɚɣɧɨɣ ɞɜɢɠɭɳɟɣɫɹ ɩɨɜɟɪɯɧɨɫɬɢ //
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Inßuence of non-linearity sea waves on the results
of radio altimetr measurements
A.S. Zapevalov, V.V. Pustovoitenko
Marine Hydrophysical Institute of the National Academy of Sciences of Ukraine
99000, Ukraine, Sevastopol, ul. Kapitanskaya, 2
E-mail: sevzepter@mail.ru
The inßuence on the return waveform pulse altimeter nonlinear effects of the sea surface waves that lead to deviation
of the distribution surface elevations from Gaussian. Demonstrated the limitations of existing models of distributions
(including the distribution of the Gram-Charlier) in the analysis of altimetry. It was noted that one of the problems of
the simulation of the return waveform pulse altimeter is no model describing the distribution of sea surface elevation
on a scale of more than one and a half times that exceed a signiÞcant wave height.
Keywords: satellite altimetry; state sea surface; distribution of elevations, nonlinearity of the sea waves.
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