Innovative improvements of the parabolic wave equation method for radiowave propagation modeling

2003 ◽  
Author(s):  
V. Fabbro
Keyword(s):  
Wave Equation ◽  
Radiowave Propagation ◽  
Equation Method ◽  
Propagation Modeling

Migration Velocity Modeling for Common Imaging Point Gathers by the Wave Equation Method

2003 ◽  
Vol 46 (1) ◽  
pp. 110-123 ◽  
Author(s):  
Zhenchun LI ◽  
Yunxia YAO ◽  
Zaitian MA ◽  
Huazhong WANG
Keyword(s):  
Wave Equation ◽  
Migration Velocity ◽  
Equation Method ◽  
Velocity Modeling ◽  
Imaging Point

Optical solitons for paraxial wave equation in Kerr media

2019 ◽  
Vol 33 (03) ◽  
pp. 1950020 ◽  
Author(s):  
Kashif Ali ◽  
Syed Tahir Raza Rizvi ◽  
Badar Nawaz ◽  
Muhammad Younis
Keyword(s):  
Wave Equation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Optical Solitons ◽  
Equation Method ◽  
Kerr Media ◽  
Extended Trial Equation Method ◽  
Trial Equation Method ◽  
Paraxial Wave Equation ◽  
Extended Trial

This paper retrieves Jacobi elliptic, periodic, bright and singular solitons for paraxial nonlinear Schrödinger equation (NLSE) in Kerr media. We use extended trial equation method to obtain these solitons solutions. For the existence of the soliton solutions, constraint conditions are also presented.

scholarly journals Exact Solutions for a New Nonlinear KdV-Like Wave Equation Using Simplest Equation Method and Its Variants

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yinghui He ◽  
Yun-Mei Zhao ◽  
Yao Long
Keyword(s):  
Thin Film ◽  
Wave Equation ◽  
Exact Solutions ◽  
Wave Motion ◽  
Wave Equations ◽  
Equation Method ◽  
Nonlinear Wave Equations ◽  
New Exact Solutions ◽  
Simplest Equation Method ◽  
Film Mass Transfer

The simplest equation method presents wide applicability to the handling of nonlinear wave equations. In this paper, we focus on the exact solution of a new nonlinear KdV-like wave equation by means of the simplest equation method, the modified simplest equation method and, the extended simplest equation method. The KdV-like wave equation was derived for solitary waves propagating on an interface (liquid-air) with wave motion induced by a harmonic forcing which is more appropriate for the study of thin film mass transfer. Thus finding the exact solutions of this equation is of great importance and interest. By these three methods, many new exact solutions of this equation are obtained.

Deep‐water peg legs and multiples: Emulation and suppression

Geophysics ◽  
1986 ◽  
Vol 51 (12) ◽  
pp. 2177-2184 ◽  
Author(s):  
J. R. Berryhill ◽  
Y. C. Kim
Keyword(s):  
Wave Equation ◽  
Seismic Data ◽  
Water Layer ◽  
Original Data ◽  
Equation Method ◽  
Multiple Reflections ◽  
Step Method ◽  
Arrival Times ◽  
Sea Floor ◽  
Water Bottom

This paper discusses a two‐step method for predicting and attenuating multiple and peg‐leg reflections in unstacked seismic data. In the first step, an (observed) seismic record is extrapolated through a round‐trip traversal of the water layer, thus creating an accurate prediction of all possible multiples. In the second step, the record containing the predicted multiples is compared with and subtracted from the original. The wave‐equation method employed to predict the multiples takes accurate account of sea‐floor topography and so requires a precise water‐bottom profile as part of the input. Information about the subsurface below the sea floor is not required. The arrival times of multiple reflections are reproduced precisely, although the amplitudes are not accurate, and the sea floor is treated as a perfect reflector. The comparison step detects the similarities between the computed multiples and the original data, and estimates a transfer function to equalize the amplitudes and account for any change in waveform caused by the sea‐floor reflector. This two‐step wave‐equation method is effective even for dipping sea floors and dipping subsurface reflectors. It does not depend upon any assumed periodicity in the data or upon any difference in stacking velocity between primaries and multiples. Thus it is complementary to the less specialized methods of multiple suppression.

Combining wave‐equation imaging with traveltime tomography to form high‐resolution images from crosshole data

Geophysics ◽  
1991 ◽  
Vol 56 (2) ◽  
pp. 208-224 ◽  
Author(s):  
R. Gerhard Pratt ◽  
Neil R. Goulty
Keyword(s):  
Wave Equation ◽  
High Resolution ◽  
Acoustic Wave ◽  
Equation Method ◽  
Single Frequency ◽  
Acoustic Wave Equation ◽  
Elastic Wave Equation ◽  
Traveltime Tomography ◽  
Combined Use ◽  
Frequency Components

Traveltime tomography is an appropriate method for estimating seismic velocity structure from arrival times. However, tomography fails to resolve discontinuities in the velocities. Wave‐equation techniques provide images using the full wave field that complement the results of traveltime tomography. We use the velocity estimates from tomography as a reference model for a numerical propagation of the time reversed data. These “backpropagated” wave fields are used to provide images of the discontinuities in the velocity field. The combined use of traveltime tomography and wave‐equation imaging is particularly suitable for forming high‐resolution geologic images from multiple‐source/multiple‐receiver data acquired in borehole‐to‐borehole seismic surveying. In the context of crosshole imaging, an effective implementation of wave‐equation imaging is obtained by transforming the data and the algorithms into the frequency domain. This transformation allows the use of efficient frequency‐domain numerical propagation methods. Experiments with computer‐generated data demonstrate the quality of the images that can be obtained from only a single frequency component of the data. Images of both compressional [Formula: see text] and shear wave [Formula: see text] velocity anomalies can be obtained by applying acoustic wave‐equation imaging in two passes. An imaging technique derived from the full elastic wave‐equation method yields superior images of both anomalies in a single pass. To demonstrate the combined use of traveltime tomography and wave‐equation imaging, a scale model experiment was carried out to simulate a crosshole seismic survey in the presence of strong velocity contrasts. Following the application of traveltime tomography, wave‐equation methods were used to form images from single frequency components of the data. The images were further enhanced by summing the results from several frequency components. The elastic wave‐equation method provided slightly better images of the [Formula: see text] discontinuities than the acoustic wave‐equation method. Errors in picking shear‐wave arrivals and uncertainties in the source radiation pattern prevented us from obtaining satisfactory images of the [Formula: see text] discontinuities.

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