Source-independent full waveform inversion of seismic data
First Claim
1. An iterative method of normalized waveform invasion to obtain a model parameter describing one or more physical properties of a medium, the method comprising the steps of:
- a) inputting a time domain measurement data set Djid(t), (j=1~NG;
i=1~NS),where d denotes a data tensor, NG is the number of receivers and NS is the number of sources;
b) means for minimizing a model parameter m below an error bound in the process of creating a normalized waveform inversion, wherein said minimizing step further comprises;
i) Fourier transforming the time domain measurement data set Djid(t) to create a measurement spectral data set Djid(ω
);
ii) normalizing the measurement spectral data set Djid(ω
) to create a normalized data wavefield Tjid(ω
);
iii) modeling a medium by iterating the model parameter m describing one or more physical properties of the medium;
by(1) minimizing a weighted error, between the normalized data wavefield Tjid(ω
) and the normalized modeled wavefield Tjim(ω
) of the response of the medium, to a level below the error bound;
(2) outputting the iterated model parameter m corresponding to the weighted error below the error bound, as a minimized model parameter.
1 Assignment
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Accused Products
Abstract
A set of seismic trace data is collected in an input data set that is first Fourier transformed in its entirety into the frequency domain. A normalized wavefield is obtained for each trace of the input data set in the frequency domain. Normalization is done with respect to the frequency response of a reference trace selected from the set of seismic trace data. The normalized wavefield is source independent, complex, and dimensionless. The normalized wavefield is shown to be uniquely defined as the normalized impulse response, provided that a certain condition is met for the source. This property allows construction of the inversion algorithm disclosed herein, without any source or source coupling information. The algorithm minimizes the error between data normalized wavefield and the model normalized wavefield. The methodology is applicable to any 3-D seismic problem, and damping may be easily included in the process.
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Citations
18 Claims
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1. An iterative method of normalized waveform invasion to obtain a model parameter describing one or more physical properties of a medium, the method comprising the steps of:
-
a) inputting a time domain measurement data set Djid(t), (j=1~NG;
i=1~NS),where d denotes a data tensor, NG is the number of receivers and NS is the number of sources; b) means for minimizing a model parameter m below an error bound in the process of creating a normalized waveform inversion, wherein said minimizing step further comprises; i) Fourier transforming the time domain measurement data set Djid(t) to create a measurement spectral data set Djid(ω
);ii) normalizing the measurement spectral data set Djid(ω
) to create a normalized data wavefield Tjid(ω
);iii) modeling a medium by iterating the model parameter m describing one or more physical properties of the medium;
by(1) minimizing a weighted error, between the normalized data wavefield Tjid(ω
) and the normalized modeled wavefield Tjim(ω
) of the response of the medium, to a level below the error bound;(2) outputting the iterated model parameter m corresponding to the weighted error below the error bound, as a minimized model parameter. - View Dependent Claims (2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 14, 17, 18)
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4. An iterative method of using normalized waveform inversion to obtain a model parameter describing one or more physical properties of a medium, the method comprising the steps of:
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a) inputting one or more each of NS source and NG measurement spatial locations; b) measuring time domain data at each of the NG measurement locations resulting from an input waveform at one of the NS source locations propagating through a medium, i) for each of the NS source locations, ii) thereby forming a time domain measurement data set Djid(t), (j=1~NG;
i=1~NS), where d denotes a data tensor;c) Fourier transforming the time domain measurement data set Djid(t) to create a measurement spectral data set Djid(ω
) having frequency and amplitude information for each of the NG measurement locations;d) normalizing the measurement spectral data set Djid(ω
) to create a normalized data wavefield Tjid(ω
);e) modeling the medium using an iterated model parameter m describing one or more physical properties of the medium, (1) the NS source and the NG measurement spatial locations used as respective model input and model response spatial locations contained within the model of the medium, (2) and initializing the iterated model parameter in with corresponding one or more known bulk properties or the medium being modeled, ii) said modeling step comprising; iii) creating a measurement model by; (1) applying a delta function source collocated with the ith NS source, (2) modeling the response at the NG measurement locations, using a time domain modeling method, to create a synthetic medium response at the jth receiver due to the ith source, Pjim(t), m denoting the model response, (3) repeating the applying and modeling steps at each of the NS source locations and NG measurement locations until the measurement model is full, and iv) Fourier transforming the model response Pjim(t), to obtain a frequency domain synthetic response Pjim(ω
);v) forming a normalized modeled wavefield using the frequency domain synthetic response Tjim(ω
)=Pjim(ω
)[P1im(ω
)]−
1; andf) minimizing a weighted error, between the normalized data wavefield Tjid(ω
) and the normalized modeled wavefield Tjim(ω
) of the response of the medium, to a level below an error bound,i) said weighted error met by using the iterated model parameter m, known as the a minimized model parameter m.
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13. An iterative method of using normalized waveform inversion to obtain a model parameter describing one or more physical properties of a medium, the method comprising the steps of:
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a) inputting one or more each of NS source and NG measurement spatial locations; b) measuring time domain data at each of the NG measurement locations resulting from an input waveform at one of the NS source locations propagating through a medium, i) for each of the 195 source locations, ii) thereby forming a time domain measurement data set Djid(t), (j=1~NG;
i=1~NT), where d denotes a data tensor;c) Fourier transforming the time domain measurement data set Djid(t) to create a measurement spectral data set Djid(ω
) having frequency and amplitude information for each of the NG measurement locations;d) normalizing the measurement spectral data set Djid(ω
) to create a normalized data wavefield Tjid(ω
);e) modeling the medium using an iterated model parameter m describing one or more physical properties of the medium, the NS source and the NG measurement spatial locations used as respective model input and model response spatial locations contained within the model of the medium, and initializing the iterated model parameter m with corresponding one or more known bulk properties of the medium being modeled,
said modeling step comprising;i) creating a measurement model by; (1) applying a delta function source collocated with the ith NS source, (2) modeling the response at the NG measurement locations, using a time domain modeling method, to create a synthetic medium response at the jth receiver due to the ith source, Pjim(t), m denoting the model response, (3) repeating the applying and modeling steps at each of the NS source locations and NG measurement locations until the measurement model is full, and ii) Fourier transforming the model response Pjim(t), to obtain a frequency domain synthetic response Pjim(t); iii) forming a normalized modeled wavefield using the frequency domain synthetic response Tjim(ω
)=Pjim(ω
)[P1im(ω
)]−
1; andf) minimizing a weighted error, between the normalized data wavefield Tjid(ω
) and the normalized modeled wavefield Tjim(ω
) of the response of the medium, to a level below an error bound,g) said weighted error met by using the iterated model parameter m, known as the a minimized model parameter m.
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15. An article of manufacture for normalized waveform inversion using a computer, said article comprising:
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a computer readable medium comprising instructions for a computer to execute, said execution comprising the steps of; a) inputting one or more each of NS source and NG measurement spatial locations; b) measuring time domain data at each of the NG measurement locations resulting from an input waveform at one of the NS source locations propagating through a medium, i) for each of the NS source locations, ii) thereby forming a time domain measurement data set Djid(t), (j=1~NG;
i=1~NS), where d denotes a data tensor;c) Fourier transforming the time domain measurement data set Djid(t) to create a measurement spectral data set Djid(ω
) having frequency and amplitude information for each of the NG measurement locations;d) normalizing the measurement spectral data set Djid(ω
) to create a normalized data wavefield Tjid(ω
);e) modeling the medium using an iterated model parameter m describing one or more physical properties of the medium, the ATS source and the NG measurement spatial locations used as respective model input and model response spatial locations contained within the model of the medium. and initializing the iterated model parameter m with corresponding one or more known bulk properties of the medium being modeled,
said modeling step comprising;i) creating a measurement model by; (1) applying a delta function source collocated with the ith NS source, (2) modeling the response at the NG measurement locations, using a time domain modeling method, to create a synthetic medium response at the jth receiver due to the ith source, Pjim(ω
), m denoting the model response,(3) repeating the applying and modeling steps at each of the NS source locations and NG measurement locations until the measurement model is full, and ii) Fourier transforming the model response Pjim(ω
), to obtain a frequency domain synthetic response Pjim(ω
);iii) forming a normalized modeled wavefield using the frequency domain synthetic response Tjim(ω
)=Pjim(ω
)[P1im(ω
)]−
1; andf) minimizing a weighted error, between the normalized data wavefield Tjid(ω
) and the normalized modeled wavefield Tjim(ω
) of the response of the medium, to a level below an error bound,i) said weighted error met by using the iterated model parameter m, known as the a minimized model parameter m.
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16. An iterative method of using normalized waveform inversion to obtain a model parameter describing one or more physical properties of a medium, the method comprising the steps of:
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a) inputting one or more each of NS source and NG measurement spatial locations; b) measuring time domain data at each of the NG measurement locations resulting from an input waveform at one of the NS source locations propagating through a medium, i) for each of the NS source locations, ii) thereby forming a time domain measurement data set Djid(ω
), (j=1~NG;
i=1~NS) where d denotes a data tensor;c) Fourier transforming the time domain measurement data set Djid(t) to create a measurement spectral data set Djid(ω
) having frequency and amplitude information for each of the NG measurement locations;d) normalizing the measurement spectral data set Djid(ω
) to create a normalized data wavefield Tjid(ω
);e) modeling the medium using an iterated model parameter m describing one or more physical properties of the medium. the NS source and the NG measurement spatial locations used as respective model input and model response spatial locations contained within the model of the medium, and initializing the iterated model parameter m in with corresponding one or more known bulk properties of the medium being modeled,
said modeling step comprising;i) creating a measurement model by; (1) applying a delta function source collocated with the ith source, (2) modeling the response at the NG measurement locations, using a frequency domain modeling method, to create a frequency domain synthetic response at the jth receiver due to the ith source, Pjim(ω
), m denoting the model response,(3) repeating the applying and modeling steps at each of the NS source locations and NG measurement locations until the frequency domain synthetic response is full, and ii) forming a normalized modeled wavefield using the frequency domain synthetic response Tjim(ω
)=Pjim(ω
)[P1im(ω
)]−
1; andf) minimizing a weighted error, between the normalized data wavefield Tjid(ω
) and the normalized modeled wavefield Tjim(ω
) of the response of the medium, to a level below an error bound,i) said weighted error met by using the iterated model parameter m, known as the a minimized model parameter m.
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Specification