Implicit Finite-Difference Plane Wave Migration in TTI Media

2011 ◽  
Vol 54 (2) ◽  
pp. 254-263
Author(s):  
Li HAN ◽  
Li-Guo HAN ◽  
Xiang-Bo GONG ◽  
Gang-Yi SHAN ◽  
Jie CUI
Keyword(s):  
Finite Difference ◽  
Plane Wave ◽  
Implicit Finite Difference ◽  
Tti Media ◽  
Wave Migration

scholarly journals Applications of plane‐wave destruction filters

Geophysics ◽  
2002 ◽  
Vol 67 (6) ◽  
pp. 1946-1960 ◽  
Author(s):  
Sergey Fomel
Keyword(s):  
Finite Difference ◽  
Plane Wave ◽  
Prediction Error ◽  
Real Data ◽  
Wave Model ◽  
Implicit Finite Difference Scheme ◽  
Time Distance ◽  
Implicit Finite Difference ◽  
Local Plane ◽  
Frequency Distance

Plane‐wave destruction filters originate from a local plane‐wave model for characterizing seismic data. These filters can be thought of as a time–distance (T‐X) analog of frequency‐distance (F‐X) prediction‐error filters and as an alternative to T‐X prediction‐error filters. The filters are constructed with the help of an implicit finite‐difference scheme for the local plane‐wave equation. Several synthetic and real data examples show that finite‐difference plane‐wave destruction filters perform well in applications such as fault detection, data interpolation, and noise attenuation.

A comparison of common‐midpoint, single‐shot, and plane‐wave depth migration

Geophysics ◽  
1984 ◽  
Vol 49 (11) ◽  
pp. 1896-1907 ◽  
Author(s):  
P. Temme
Keyword(s):  
Reflection Coefficient ◽  
Finite Difference ◽  
Plane Wave ◽  
Wave Field ◽  
Single Shot ◽  
Imaging Condition ◽  
Depth Migration ◽  
Finite Aperture ◽  
Wave Migration ◽  
Slant Stacking

A comparison of common‐midpoint (CMP), single‐shot, and plane‐wave migration was made for simple two‐dimensional structures such as a syncline and a horizontal reflector with a laterally variable reflection coefficient by using synthetic seismograms. The seismograms were calculated employing the finite‐difference technique. CMP sections were simulated by 18-fold stacking and plane‐wave sections by slant stacking. By applying a finite‐difference scheme, the synthetic wave field was continued downward. The usual imaging condition of CMP migration was extended in order to carry out migration of single‐shot and plane‐wave sections. The reflection coefficient was reconstructed by comparing the migrated wave field with the incident wave field at the reflector. The results are: (1) all three migration techniques succeeded in reconstructing the reflector position; (2) as a consequence of the finite aperture of the geophone spread, only segments of the reflector could be reconstructed by single‐shot and plane‐wave migration; (3) for single‐shot and plane‐wave migration the reflection coefficient could be obtained; and (4) CMP migration may lead to incorrect conclusions regarding the reflection coefficient.

scholarly journals A robust numerical solution to a time-fractional Black–Scholes equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. M. Nuugulu ◽  
F. Gideon ◽  
K. C. Patidar
Keyword(s):  
Finite Difference ◽  
Stock Options ◽  
Stochastic Dynamics ◽  
European Options ◽  
Numerical Convergence ◽  
Put Option ◽  
Implicit Finite Difference Scheme ◽  
Black Scholes ◽  
Implicit Finite Difference ◽  
Rigorous Mathematical Analysis

AbstractDividend paying European stock options are modeled using a time-fractional Black–Scholes (tfBS) partial differential equation (PDE). The underlying fractional stochastic dynamics explored in this work are appropriate for capturing market fluctuations in which random fractional white noise has the potential to accurately estimate European put option premiums while providing a good numerical convergence. The aim of this paper is two fold: firstly, to construct a time-fractional (tfBS) PDE for pricing European options on continuous dividend paying stocks, and, secondly, to propose an implicit finite difference method for solving the constructed tfBS PDE. Through rigorous mathematical analysis it is established that the implicit finite difference scheme is unconditionally stable. To support these theoretical observations, two numerical examples are presented under the proposed fractional framework. Results indicate that the tfBS and its proposed numerical method are very effective mathematical tools for pricing European options.

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