An improved gradient computation for adjoint wave‐equation reflection tomography

2011 ◽  
Author(s):  
Uwe Albertin
Keyword(s):  
Wave Equation ◽  
Gradient Computation ◽  
Reflection Tomography

Multi‐scale aspects of wave‐equation reflection tomography

2006 ◽  
Author(s):  
Maarten V. de Hoop ◽  
Robert D. van der Hilst ◽  
Peng Shen
Keyword(s):  
Wave Equation ◽  
Multi Scale ◽  
Reflection Tomography

Use of refraction, reflection, and wave-equation-based tomography for imaging beneath shallow gas: A Trinidad field data example

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE281-VE289 ◽  
Author(s):  
Nurul Kabir ◽  
Uwe Albertin ◽  
Min Zhou ◽  
Vishal Nagassar ◽  
Einar Kjos ◽  
...  
Keyword(s):  
Wave Equation ◽  
Velocity Field ◽  
Velocity Model ◽  
Surface Velocity ◽  
Low Velocity ◽  
Shallow Gas ◽  
Near Surface ◽  
Velocity Anomaly ◽  
Refraction Tomography ◽  
Reflection Tomography

Shallow localized gas pockets cause challenging problems in seismic imaging because of sags and wipe-out zones they produce on imaged reflectors deep in the section. In addition, the presence of shallow gas generates strong surface-related and interbed multiples, making velocity updating very difficult. When localized gas pockets are very shallow, we have limited information to build a near-surface velocity model using ray-based reflection tomography alone. Diving-wave refraction tomography successfully builds a starting model for the very shallow part. Usual ray-based reflection tomography using single-parameter hyperbolic moveout might need many iterations to update the deeper part of the velocity model. In addition, the method generates a low-velocity anomaly in the deeper part of the model. We present an innovative method for building the final velocity model by combining refraction, reflection, and wave-equation-based tomography. Wave-equation-based tomography effectively generates a detailed update of a shallow velocity field, resolving the gas-sag problem. When applied as the last step, following the refraction and reflection tomography, it resolves the gas-sag problem but fails to remove the low-velocity anomaly generated by the reflection tomography in the deeper part of the model. To improve the methodology, we update the shallow velocity field using refraction tomography followed by wave-equation tomography before updating the deeper part of the model. This step avoids generating the low-velocity anomaly. Refraction and wave-equation-based tomography followed by reflection tomography generates a simpler velocity model, giving better focusing in the deeper part of the image. We illustrate how the methodology successfully improves resolution of gas anomalies and significantly reduces gas sag from an imaged section in the Greater Cassia area, Trinidad.

scholarly journals Wave-equation reflection tomography: annihilators and sensitivity kernels

2006 ◽  
Vol 167 (3) ◽  
pp. 1332-1352 ◽  
Author(s):  
Maarten V. de Hoop ◽  
Robert D. van der Hilst ◽  
Peng Shen
Keyword(s):  
Wave Equation ◽  
Reflection Tomography

scholarly journals Wave equation-based reflection tomography of the 1992 Landers earthquake area

2016 ◽  
Vol 43 (5) ◽  
pp. 1884-1892 ◽  
Author(s):  
Xueyuan Huang ◽  
Dinghui Yang ◽  
Ping Tong ◽  
José Badal ◽  
Qinya Liu
Keyword(s):  
Wave Equation ◽  
Landers Earthquake ◽  
1992 Landers Earthquake ◽  
Reflection Tomography ◽  
Earthquake Area

Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

2020 ◽  
Vol 11 (1) ◽  
pp. 93-100
Author(s):  
Vina Apriliani ◽  
Ikhsan Maulidi ◽  
Budi Azhari
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Internal Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Mkdv Equation ◽  
Innovative Methods ◽  
De Vries

One of the phenomenon in marine science that is often encountered is the phenomenon of water waves. Waves that occur below the surface of seawater are called internal waves. One of the mathematical models that can represent solitary internal waves is the modified Korteweg-de Vries (mKdV) equation. Many methods can be used to construct the solution of the mKdV wave equation, one of which is the extended F-expansion method. The purpose of this study is to determine the solution of the mKdV wave equation using the extended F-expansion method. The result of solving the mKdV wave equation is the exact solutions. The exact solutions of the mKdV wave equation are expressed in the Jacobi elliptic functions, trigonometric functions, and hyperbolic functions. From this research, it is expected to be able to add insight and knowledge about the implementation of the innovative methods for solving wave equations. 

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