@ARTICLE{Riahi2022-2,
author={Chao Jin, Bing Zhou, Moosoo Won, Mohamed Riahi, Mohamed Jamal Zemerly},
title={Recursive convolution method to solve the first-order
viscoacoustic and viscoelastic wave equations},
journal={Geophysics},
year={2022},
volume={x},
number={under review},
doi={},
art_number={},
url={},
affiliation={Department of Applied Mathematics, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates; Emirates Nuclear Technology Center, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates; Department of Nuclear Engineering, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates; Department of Mechanical Engineering, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates},
abstract={Seismic wave modeling in anelastic medium is a fundamental tool for seismic data processing
and interpretation in exploration geophysics. To compute the convolutions in the constitutive
equation of an anelastic medium, we propose a new semi-analytical method, called the Ôrecursive
convolution methodÕ to replace solving the auxiliary partial differential equations of the memory
variables. New sets of the first-order viscoacoustic and viscoelastic wave equations in the time
domain are established, and show the new method does not require solving the auxiliary partial
different equations of the memory variables like the traditional methods do. The new method
may accurately simulate the viscoacoustic and viscoelastic waves with a standard grid finite
difference method without any additional computational costs compared to the traditional
method, and its accuracy may reach the satisfactory levels as a high-order time-stepping formula
and the staggered grid are applied to the traditional method. Our numerical experiments verify
the feasibility and accuracy of the new method to solve the first-order viscoacoustic and
viscoelastic wave equations, as well as the validation of the staggered grid finite-difference
method.},
author_keywords={},document_type={Article}
}

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R."],"bibdata":{"bibtype":"article","type":"article","author":[{"propositions":[],"lastnames":["Chao","Jin"],"firstnames":["Bing","Zhou"],"suffixes":[]},{"propositions":[],"lastnames":["Moosoo","Won"],"firstnames":["Mohamed","Riahi"],"suffixes":[]}],"title":"Recursive convolution method to solve the first-order viscoacoustic and viscoelastic wave equations","journal":"Geophysics","year":"2022","volume":"x","number":"under review","doi":"","art_number":"","url":"","affiliation":"Department of Applied Mathematics, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates; Emirates Nuclear Technology Center, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates; Department of Nuclear Engineering, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates; Department of Mechanical Engineering, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates","abstract":"Seismic wave modeling in anelastic medium is a fundamental tool for seismic data processing and interpretation in exploration geophysics. To compute the convolutions in the constitutive equation of an anelastic medium, we propose a new semi-analytical method, called the Ôrecursive convolution methodÕ to replace solving the auxiliary partial differential equations of the memory variables. New sets of the first-order viscoacoustic and viscoelastic wave equations in the time domain are established, and show the new method does not require solving the auxiliary partial different equations of the memory variables like the traditional methods do. The new method may accurately simulate the viscoacoustic and viscoelastic waves with a standard grid finite difference method without any additional computational costs compared to the traditional method, and its accuracy may reach the satisfactory levels as a high-order time-stepping formula and the staggered grid are applied to the traditional method. Our numerical experiments verify the feasibility and accuracy of the new method to solve the first-order viscoacoustic and viscoelastic wave equations, as well as the validation of the staggered grid finite-difference method.","author_keywords":"","document_type":"Article","bibtex":"@ARTICLE{Riahi2022-2,\nauthor={Chao Jin, Bing Zhou, Moosoo Won, Mohamed Riahi, Mohamed Jamal Zemerly},\ntitle={Recursive convolution method to solve the first-order\nviscoacoustic and viscoelastic wave equations},\njournal={Geophysics},\nyear={2022},\nvolume={x},\nnumber={under review},\ndoi={},\nart_number={},\nurl={},\naffiliation={Department of Applied Mathematics, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates; Emirates Nuclear Technology Center, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates; Department of Nuclear Engineering, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates; Department of Mechanical Engineering, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates},\nabstract={Seismic wave modeling in anelastic medium is a fundamental tool for seismic data processing\nand interpretation in exploration geophysics. To compute the convolutions in the constitutive\nequation of an anelastic medium, we propose a new semi-analytical method, called the Ôrecursive\nconvolution methodÕ to replace solving the auxiliary partial differential equations of the memory\nvariables. New sets of the first-order viscoacoustic and viscoelastic wave equations in the time\ndomain are established, and show the new method does not require solving the auxiliary partial\ndifferent equations of the memory variables like the traditional methods do. The new method\nmay accurately simulate the viscoacoustic and viscoelastic waves with a standard grid finite\ndifference method without any additional computational costs compared to the traditional\nmethod, and its accuracy may reach the satisfactory levels as a high-order time-stepping formula\nand the staggered grid are applied to the traditional method. Our numerical experiments verify\nthe feasibility and accuracy of the new method to solve the first-order viscoacoustic and\nviscoelastic wave equations, as well as the validation of the staggered grid finite-difference\nmethod.},\nauthor_keywords={},document_type={Article}\n}\n\n%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n","author_short":["Chao Jin, B. Z.","Moosoo Won, M. 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