Abstract
Two analytical models of gravity field and geological medium have been suggested for the horizontally layered medium with several density interfaces present in the lower semi-space. The first model is acquired from the equation of gravity derived from 2D consideration of normal gravity potential in a local neighborhood of the measurement points. In addition to well-known in the theory of potential fields interpretation the main classes of contact surfaces a new medium model is introduced named a Chorny contact surfaces class. The examples of field separation theorems for a case of several one-coherent volumes and several non-crossed layers (two most popular initial approximations of a medium) are given in the model studied. A new numerical approach for definition of the start approximation of density interface and its asymptotes in the multilayered geological medium by means of several "contact" algorithms is given.
Highlights
Ðàññìîòðèì òåïåðü ðåøåíèÿ íåëèíåéíîãî èíòåãðàëüíîãî óðàâíåíèÿÅãî ìîæíî ðàññìàòðèâàòü êàê ôóíêöèîíàë íà íåêîòîðîì ëèíåàëå
Òåõíîëîãèÿ îöèôðîâêè êàðò ôàêòè÷åñêîãî ìàòåðèàëà íà îñíîâå ïðîãðàììíîãî îáåñïå÷åíèÿ MapInfo Professional è CorelDraw // Ãåîôèç. æóðí. 2010. 32, 1 3. Ñ. 112124
Summary
Åãî ìîæíî ðàññìàòðèâàòü êàê ôóíêöèîíàë íà íåêîòîðîì ëèíåàëå. Îòêóäà î÷åâèäíî: àëãîðèòìû Íüþòîíà è êîíòàêò 1 ôîðìàëüíî ñîâïàäàþò òîëüêî íà ïåðâîì øàãå, òàê êàê 3. Ïîëàãàÿ â ýòîì óðàâíåíèè z n+1 ( ξ ) = z n ( ξ ) + h n ( ξ ) , H n+1 = H n + τ n , n = 0 , 1, 2, K , è h 0 ( ξ ) ≡ 0 , τ 0 ≡ 0 , a ≤ ξ ≤ b , (22) è çàäàâàÿ H 0 , z 0 ( ξ ) , a ≤ ξ ≤ b , ïîëó÷àåì. Ñëîæèì âåëè÷èíû (14) è (21) ñ òî÷íîñòüþ äî h 3 ( ξ ) è ïîëó÷èì b (ξ− x) 2 + (H + τ) 2 τdξ = ln dξ− g (x) −.
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