Analytic formula and validation of the Frechet derivatives for 2-D/2.5-D seismic full-waveform inversion in viscoelastic TTI media

Analytic formula and validation of the Frechet derivatives for 2-D/2.5-D seismic full-waveform inversion in viscoelastic TTI media. Q. Yang, B. Z. & Alkhaleel, M. PAAG, 2022.

Paper doi abstract bibtex

The Frchet derivatives of the displacement vector with respect to the independent parameter of the subsurface, also called sensitivity kernels, are the key ingredient for the full-waveform inversion of seismic data. They quantitatively exhibit the sensitivity of seismograms to perturbation of the subsurface model parameters and give the analytic formula of the Jacobian matrix of seismic full-waveform data to all parameters of the model. Because of using a real point source in a 2-D geological model (2.5-D) rather than an unreal linear source, the 2.5-D wave modeling generates the synthetic data more close to the practical data compared to the common 2-D wave simulation. In this paper, we analytically deduce the explicit expressions of the Frchet derivatives for 2- D/2.5-D frequency-domain seismic full-waveform inversion in viscoelastic anisotropic media and demonstrate the numerical calculations of all the quantities of the Frchet derivatives. Two common cases Ñ viscoelastic isotropic and viscoelastic tilted transversely isotropic media are exhibited analytically. Four comparable 2-D and 2.5-D examples are demonstrated numerically. Furthermore, we validate the Frchet derivatives by carrying out the frequency-domain full-waveform inversion to individually recover twelve model parameters (density, dipping angle, five independent moduli and five corresponding quality factors) in a simple box model.

@ARTICLE{Riahi2022-3,
author={Q. Yang, B. Zhou, M. K.Riahi and M. Alkhaleel},
title={Analytic formula and validation of the Frechet derivatives for 2-D/2.5-D seismic full-waveform inversion in viscoelastic TTI media},
journal={PAAG},
year={2022},
volume={},
number={},
doi={https://www.dropbox.com/s/1vkolxufh92lzvt/PAAG-D-21-00147_R2.pdf?dl=0},
art_number={},
url={https://www.dropbox.com/s/1vkolxufh92lzvt/PAAG-D-21-00147_R2.pdf?dl=0},
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={The Frchet derivatives of the displacement vector with respect to the independent
parameter of the subsurface, also called sensitivity kernels, are the key ingredient for
the full-waveform inversion of seismic data. They quantitatively exhibit the sensitivity of
seismograms to perturbation of the subsurface model parameters and give the analytic
formula of the Jacobian matrix of seismic full-waveform data to all parameters of the
model. Because of using a real point source in a 2-D geological model (2.5-D) rather
than an unreal linear source, the 2.5-D wave modeling generates the synthetic data
more close to the practical data compared to the common 2-D wave simulation. In this
paper, we analytically deduce the explicit expressions of the Frchet derivatives for 2-
D/2.5-D frequency-domain seismic full-waveform inversion in viscoelastic anisotropic
media and demonstrate the numerical calculations of all the quantities of the Frchet
derivatives. Two common cases Ñ viscoelastic isotropic and viscoelastic tilted
transversely isotropic media are exhibited analytically. Four comparable 2-D and 2.5-D
examples are demonstrated numerically. Furthermore, we validate the Frchet
derivatives by carrying out the frequency-domain full-waveform inversion to individually
recover twelve model parameters (density, dipping angle, five independent moduli and
five corresponding quality factors) in a simple box model.},
author_keywords={Inverse problem, CI, nMCI, Convergence study, Damage quantification, Complex structures, Laminated composite, and noise},document_type={Article},
source={},
}

Downloads: 0

{"_id":"XCaGMBXHjxNCr7ftv","bibbaseid":"qyang-alkhaleel-analyticformulaandvalidationofthefrechetderivativesfor2d25dseismicfullwaveforminversioninviscoelasticttimedia-2022","author_short":["Q. Yang, B. Z.","Alkhaleel, M."],"bibdata":{"bibtype":"article","type":"article","author":[{"propositions":[],"lastnames":["Q.","Yang"],"firstnames":["B.","Zhou"],"suffixes":["M.","K.Riahi"]},{"firstnames":["M."],"propositions":[],"lastnames":["Alkhaleel"],"suffixes":[]}],"title":"Analytic formula and validation of the Frechet derivatives for 2-D/2.5-D seismic full-waveform inversion in viscoelastic TTI media","journal":"PAAG","year":"2022","volume":"","number":"","doi":"https://www.dropbox.com/s/1vkolxufh92lzvt/PAAG-D-21-00147_R2.pdf?dl=0","art_number":"","url":"https://www.dropbox.com/s/1vkolxufh92lzvt/PAAG-D-21-00147_R2.pdf?dl=0","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":"The Frchet derivatives of the displacement vector with respect to the independent parameter of the subsurface, also called sensitivity kernels, are the key ingredient for the full-waveform inversion of seismic data. They quantitatively exhibit the sensitivity of seismograms to perturbation of the subsurface model parameters and give the analytic formula of the Jacobian matrix of seismic full-waveform data to all parameters of the model. Because of using a real point source in a 2-D geological model (2.5-D) rather than an unreal linear source, the 2.5-D wave modeling generates the synthetic data more close to the practical data compared to the common 2-D wave simulation. In this paper, we analytically deduce the explicit expressions of the Frchet derivatives for 2- D/2.5-D frequency-domain seismic full-waveform inversion in viscoelastic anisotropic media and demonstrate the numerical calculations of all the quantities of the Frchet derivatives. Two common cases Ñ viscoelastic isotropic and viscoelastic tilted transversely isotropic media are exhibited analytically. Four comparable 2-D and 2.5-D examples are demonstrated numerically. Furthermore, we validate the Frchet derivatives by carrying out the frequency-domain full-waveform inversion to individually recover twelve model parameters (density, dipping angle, five independent moduli and five corresponding quality factors) in a simple box model.","author_keywords":"Inverse problem, CI, nMCI, Convergence study, Damage quantification, Complex structures, Laminated composite, and noise","document_type":"Article","source":"","bibtex":"@ARTICLE{Riahi2022-3,\nauthor={Q. Yang, B. Zhou, M. K.Riahi and M. Alkhaleel},\ntitle={Analytic formula and validation of the Frechet derivatives for 2-D/2.5-D seismic full-waveform inversion in viscoelastic TTI media},\njournal={PAAG},\nyear={2022},\nvolume={},\nnumber={},\ndoi={https://www.dropbox.com/s/1vkolxufh92lzvt/PAAG-D-21-00147_R2.pdf?dl=0},\nart_number={},\nurl={https://www.dropbox.com/s/1vkolxufh92lzvt/PAAG-D-21-00147_R2.pdf?dl=0},\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={The Frchet derivatives of the displacement vector with respect to the independent\nparameter of the subsurface, also called sensitivity kernels, are the key ingredient for\nthe full-waveform inversion of seismic data. They quantitatively exhibit the sensitivity of\nseismograms to perturbation of the subsurface model parameters and give the analytic\nformula of the Jacobian matrix of seismic full-waveform data to all parameters of the\nmodel. Because of using a real point source in a 2-D geological model (2.5-D) rather\nthan an unreal linear source, the 2.5-D wave modeling generates the synthetic data\nmore close to the practical data compared to the common 2-D wave simulation. In this\npaper, we analytically deduce the explicit expressions of the Frchet derivatives for 2-\nD/2.5-D frequency-domain seismic full-waveform inversion in viscoelastic anisotropic\nmedia and demonstrate the numerical calculations of all the quantities of the Frchet\nderivatives. Two common cases Ñ viscoelastic isotropic and viscoelastic tilted\ntransversely isotropic media are exhibited analytically. Four comparable 2-D and 2.5-D\nexamples are demonstrated numerically. Furthermore, we validate the Frchet\nderivatives by carrying out the frequency-domain full-waveform inversion to individually\nrecover twelve model parameters (density, dipping angle, five independent moduli and\nfive corresponding quality factors) in a simple box model.},\nauthor_keywords={Inverse problem, CI, nMCI, Convergence study, Damage quantification, Complex structures, Laminated composite, and noise},document_type={Article},\nsource={},\n}\n","author_short":["Q. Yang, B. Z.","Alkhaleel, M."],"key":"Riahi2022-3","id":"Riahi2022-3","bibbaseid":"qyang-alkhaleel-analyticformulaandvalidationofthefrechetderivativesfor2d25dseismicfullwaveforminversioninviscoelasticttimedia-2022","role":"author","urls":{"Paper":"https://www.dropbox.com/s/1vkolxufh92lzvt/PAAG-D-21-00147_R2.pdf?dl=0"},"metadata":{"authorlinks":{}}},"bibtype":"article","biburl":"https://docs.google.com/uc?export=download&id=1GhoAKJBee1PlLyIx6KepRvIg2UrLVBRg","dataSources":["EebkmJjgLhgSZMFtf"],"keywords":[],"search_terms":["analytic","formula","validation","frechet","derivatives","seismic","full","waveform","inversion","viscoelastic","tti","media","q. yang","alkhaleel"],"title":"Analytic formula and validation of the Frechet derivatives for 2-D/2.5-D seismic full-waveform inversion in viscoelastic TTI media","year":2022}