The vertical image projection method for migration stretch compensation

True amplitude inversion is often carried out without taking into account migration distortions to the wavelet. Seismic migration leaves a dip-dependent effect on the wavelet that can cause significant inaccuracies in the inverted impedances obtained from conventional inversion approaches based on 1D vertical convolutional modelling. Neglecting this effect causes misleading inversion results and leakage of dipping noise and migration artifacts from higher frequency bands to the lower frequencies. I have observed that despite dip-dependency of this effect, low-dip and flat events may also suffer if they are contaminated with cross-cutting noise, steep migration artifacts, and smiles. In this paper I propose an efficient, effective and reversible data pre-conditioning approach that accounts for dip-dependency of the wavelet and is applied to migrated images prior to inversion. My proposed method consists of integrating data with respect to the total wavenumber followed by the differentiation with respect to the vertical wavenumber. This process is equivalent to applying a deterministic dip-consistent pre-conditioning that projects the data from the total wavenumber to the vertical wavenumber axis. This preconditioning can be applied to both pre- and post-stack data as well as to amplitude variation with offset (AVO) attributes such as intercept and gradient before inversion. The vertical image projection methodology that I propose here reduces the impact of migration artifacts such as cross-cutting noise and migration smiles and improves inverted impedances in both synthetic and real data examples. In particular I show that neglecting the proposed pre-conditioning leads to anomalously higher impedance values along the steeply dipping structures.

Analisis Bahassa ditinjau dari Karakteristik, Isu Belajar dan Teori Bahasa

This article discusses language in terms of children, issues and theories of language learning. Language is the special capacity that exists in humans to obtain and use complex communication systems, and a language is a specific example of such a system. Issues in language include language development, language and thought processes, language and animals, cultural differences in language and the relationship between the brain and language. Then the two theories of language learning approaches, namely the conditioning approach in language learning, have a basic assumption that language is studied in accordance with the principles of conditioning and a psycholinguistic approach.

Spectral Properties of Effective Dynamics from Conditional Expectations

The reduction of high-dimensional systems to effective models on a smaller set of variables is an essential task in many areas of science. For stochastic dynamics governed by diffusion processes, a general procedure to find effective equations is the conditioning approach. In this paper, we are interested in the spectrum of the generator of the resulting effective dynamics, and how it compares to the spectrum of the full generator. We prove a new relative error bound in terms of the eigenfunction approximation error for reversible systems. We also present numerical examples indicating that, if Kramers–Moyal (KM) type approximations are used to compute the spectrum of the reduced generator, it seems largely insensitive to the time window used for the KM estimators. We analyze the implications of these observations for systems driven by underdamped Langevin dynamics, and show how meaningful effective dynamics can be defined in this setting.