Fundamentals of geophysical data processing (Blackwell by Jon F. Claerbout

Mathematics

By Jon F. Claerbout

This e-book is set using computing device courses for the research of geophysical information to attempt to figure out the structure of the Earth's inside, a method which permits a geophysicist to find petroleum and mineral clients. conventional options of information processing are completely mentioned to supply an excellent beginning at the topic. the overall thought of mathematical-physical computations in stratified media ends up in computational options for 2- and three-dimensionally heterogeneous media. A function of the booklet is using partial differential equations for mirrored image seismic info processing in petroleum prospecting. Professor Claerbout and his scholars have originated loads of this fabric, which hence can't be present in the other booklet.

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Then we have Λ1 ×Λ2 |ϕ (r, t)| drdt = r ≤ 1 σk σm (k) (m) |∇y u (y, z) · y| Λ1 ×Λ2 1 σ k σ m λk−1 λm−1 1 2 k m−1 |y| |z| (k) (m) Λ1 ×Λ2 dx |∇y u (y, z)| dx < ∞ . (k) Finally, letting φ ∈ Cc∞ (Λ1 × Λ2 ) and setting Φ (x) := φ (|y| , |z|) ∈ Cc∞ (Λ1 × (m) Λ2 ), we get u ˜ (r, t) Λ1 ×Λ2 ∂φ (r, t) drdt = ∂r 1 σk σm = 1 σk σm ∂u ˜ ∂t u ˜ (|y| , |z|) ∂φ (|y| , |z|) dx |y|k−1 |z|m−1 ∂r k u (x) (k) (m) Λ1 ×Λ2 = − 1 σk σm = − 1 σk σm = − 1 σk σm = − Similarly one obtains complete. (k) (m) Λ1 ×Λ2 k−1 |y| k j=1 (k) (m) Λ1 ×Λ2 (k) (m) Λ1 ×Λ2 (k) (m) Λ1 ×Λ2 Λ1 ×Λ2 m−1 |z| j=1 yj ∂Φ (x) dx ∂yj |y| yj ∂u (x) k m−1 Φ (x) dx ∂yj |y| |z| ∇y u (x) · y k m−1 k m−1 |y| |z| ϕ (|y| , |z|) |y| |z| Φ (x) dx φ (|y| , |z|) dx ϕ (r, t) φ (r, t) drdt .

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