Laplace-domain full-waveform inversion of seismic data lacking low-frequency information

Geophysics ◽  
2012 ◽  
Vol 77 (5) ◽  
pp. R199-R206 ◽  
Author(s):  
Wansoo Ha ◽  
Changsoo Shin
Keyword(s):  
Seismic Data ◽  
Field Data ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Single Frequency ◽  
Frequency Content ◽  
Laplace Domain ◽  
Frequency Information ◽  
Velocity Models ◽  
Gaussian Source

The lack of the low-frequency information in field data prohibits the time- or frequency-domain waveform inversions from recovering large-scale background velocity models. On the other hand, Laplace-domain waveform inversion is less sensitive to the lack of the low frequencies than conventional inversions. In theory, frequency filtering of the seismic signal in the time domain is equivalent to a constant multiplication of the wavefield in the Laplace domain. Because the constant can be retrieved using the source estimation process, the frequency content of the seismic data does not affect the gradient direction of the Laplace-domain waveform inversion. We obtained inversion results of the frequency-filtered field data acquired in the Gulf of Mexico and two synthetic data sets obtained using a first-derivative Gaussian source wavelet and a single-frequency causal sine function. They demonstrated that Laplace-domain inversion yielded consistent results regardless of the frequency content within the seismic data.

Reflection intensity waveform inversion

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. R263-R273 ◽  
Author(s):  
Yike Liu ◽  
Bin He ◽  
Zhendong Zhang ◽  
Yingcai Zheng ◽  
Peng Li
Keyword(s):  
Frequency Band ◽  
Field Data ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Velocity Model ◽  
Inversion Method ◽  
Frequency Content ◽  
Frequency Information ◽  
Long Offset ◽  
Reflection Intensity

Traditional iteration-based full-waveform inversion (FWI) methods encounter serious challenges if the initial velocity model is far from the true model or if the observed data are lacking low-frequency content. As such, the optimization algorithm may be trapped in local minima and fail to go to a global optimal model. In addition, the traditional FWI method requires long-offset data to update the deep structure of a velocity model with diving waves. To overcome the disadvantages of traditional FWI under these circumstances, we have developed a reflection intensity waveform inversion method. This method aims to minimize the seismic intensity differences between the modeled reflection data and field data. Our method is less dependent on the starting model, and long-offset data are no longer required. The wave intensity, proportional to the square of the original data amplitude, can have a low-frequency band and a higher frequency band, even for waveforms without initial low-frequency content. Our multiscale intensity inversion starts from the low-frequency information in the intensity data, and it can largely avoid the cycle-skipping problem. Synthetic and field data examples demonstrate that our method is able to overcome cycle skipping in handling data with no low-frequency information.

3D Laplace-domain waveform inversion using a low-frequency time-domain modeling algorithm

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. R1-R13 ◽  
Author(s):  
Wansoo Ha ◽  
Seung-Goo Kang ◽  
Changsoo Shin
Keyword(s):  
Time Domain ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Domain Modeling ◽  
Laplace Domain ◽  
Long Wavelength ◽  
Velocity Models ◽  
Time Domain Modeling ◽  
The Time Domain ◽  
Domain Inversion

We have developed a Laplace-domain full-waveform inversion technique based on a time-domain finite-difference modeling algorithm for efficient 3D inversions. Theoretically, the Laplace-domain Green’s function multiplied by a constant can be obtained regardless of the frequency content in the time-domain source wavelet. Therefore, we can use low-frequency sources and large grids for efficient modeling in the time domain. We Laplace-transform time-domain seismograms to the Laplace domain and calculate the residuals in the Laplace domain. Then, we back-propagate the Laplace-domain residuals in the time domain using a predefined time-domain source wavelet with the amplitude of the residuals. The back-propagated wavefields are transformed to the Laplace domain again to update the velocity model. The inversion results are long-wavelength velocity models on large grids similar to those obtained by the original approach based on Laplace-domain modeling. Inversion examples with 2D Gulf of Mexico field data revealed that the method yielded long-wavelength velocity models comparable with the results of the original Laplace-domain inversion methods. A 3D SEG/EAGE salt model example revealed that the 3D Laplace-domain inversion based on time-domain modeling method can be more efficient than the inversion based on Laplace-domain modeling using an iterative linear system solver.

scholarly journals Multi-scale time-frequency domain full waveform inversion with a weighted local correlation-phase misfit function

2019 ◽  
Vol 16 (6) ◽  
pp. 1017-1031 ◽  
Author(s):  
Yong Hu ◽  
Liguo Han ◽  
Rushan Wu ◽  
Yongzhong Xu
Keyword(s):  
Frequency Domain ◽  
Seismic Data ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Full Waveform Inversion ◽  
Local Correlation ◽  
Time Frequency ◽  
Model Dependence ◽  
Full Waveform ◽  
Frequency Components

Abstract Full Waveform Inversion (FWI) is based on the least squares algorithm to minimize the difference between the synthetic and observed data, which is a promising technique for high-resolution velocity inversion. However, the FWI method is characterized by strong model dependence, because the ultra-low-frequency components in the field seismic data are usually not available. In this work, to reduce the model dependence of the FWI method, we introduce a Weighted Local Correlation-phase based FWI method (WLCFWI), which emphasizes the correlation phase between the synthetic and observed data in the time-frequency domain. The local correlation-phase misfit function combines the advantages of phase and normalized correlation function, and has an enormous potential for reducing the model dependence and improving FWI results. Besides, in the correlation-phase misfit function, the amplitude information is treated as a weighting factor, which emphasizes the phase similarity between synthetic and observed data. Numerical examples and the analysis of the misfit function show that the WLCFWI method has a strong ability to reduce model dependence, even if the seismic data are devoid of low-frequency components and contain strong Gaussian noise.

scholarly journals Normalized nonzero-lag crosscorrelation elastic full-waveform inversion

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. R1-R10 ◽  
Author(s):  
Zhendong Zhang ◽  
Tariq Alkhalifah ◽  
Zedong Wu ◽  
Yike Liu ◽  
Bin He ◽  
...  
Keyword(s):  
Field Data ◽  
Extreme Values ◽  
Time Lag ◽  
Waveform Inversion ◽  
Optimal Time ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Velocity Models ◽  
Full Waveform ◽  
The Earth

Full-waveform inversion (FWI) is an attractive technique due to its ability to build high-resolution velocity models. Conventional amplitude-matching FWI approaches remain challenging because the simplified computational physics used does not fully represent all wave phenomena in the earth. Because the earth is attenuating, a sample-by-sample fitting of the amplitude may not be feasible in practice. We have developed a normalized nonzero-lag crosscorrelataion-based elastic FWI algorithm to maximize the similarity of the calculated and observed data. We use the first-order elastic-wave equation to simulate the propagation of seismic waves in the earth. Our proposed objective function emphasizes the matching of the phases of the events in the calculated and observed data, and thus, it is more immune to inaccuracies in the initial model and the difference between the true and modeled physics. The normalization term can compensate the energy loss in the far offsets because of geometric spreading and avoid a bias in estimation toward extreme values in the observed data. We develop a polynomial-type weighting function and evaluate an approach to determine the optimal time lag. We use a synthetic elastic Marmousi model and the BigSky field data set to verify the effectiveness of the proposed method. To suppress the short-wavelength artifacts in the estimated S-wave velocity and noise in the field data, we apply a Laplacian regularization and a total variation constraint on the synthetic and field data examples, respectively.

2D Laplace-Domain Waveform Inversion of Field Data Using a Power Objective Function

2013 ◽  
Vol 170 (12) ◽  
pp. 2075-2085 ◽  
Author(s):  
Eunjin Park ◽  
Wansoo Ha ◽  
Wookeen Chung ◽  
Changsoo Shin ◽  
Dong-Joo Min
Keyword(s):  
Objective Function ◽  
Field Data ◽  
Waveform Inversion ◽  
Laplace Domain

scholarly journals Passive seismic event estimation using multiscattering waveform inversion

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. KS59-KS69 ◽  
Author(s):  
Chao Song ◽  
Zedong Wu ◽  
Tariq Alkhalifah
Keyword(s):  
Seismic Data ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Source Image ◽  
Time Inversion ◽  
Multiple Sources ◽  
Origin Time ◽  
Secondary Sources ◽  
Velocity Models ◽  
Passive Seismic

Passive seismic monitoring has become an effective method to understand underground processes. Time-reversal-based methods are often used to locate passive seismic events directly. However, these kinds of methods are strongly dependent on the accuracy of the velocity model. Full-waveform inversion (FWI) has been used on passive seismic data to invert the velocity model and source image, simultaneously. However, waveform inversion of passive seismic data uses mainly the transmission energy, which results in poor illumination and low resolution. We developed a waveform inversion using multiscattered energy for passive seismic to extract more information from the data than conventional FWI. Using transmission wavepath information from single- and double-scattering, computed from a predicted scatterer field acting as secondary sources, our method provides better illumination of the velocity model than conventional FWI. Using a new objective function, we optimized the source image and velocity model, including multiscattered energy, simultaneously. Because we conducted our method in the frequency domain with a complex source function including spatial and wavelet information, we mitigate the uncertainties of the source wavelet and source origin time. Inversion results from the Marmousi model indicate that by taking advantage of multiscattered energy and starting from a reasonably acceptable frequency (a single source at 3 Hz and multiple sources at 5 Hz), our method yields better inverted velocity models and source images compared with conventional FWI.

Broadband seismic over/under sources and their designature-deghosting

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. P61-P73 ◽  
Author(s):  
Lasse Amundsen ◽  
Ørjan Pedersen ◽  
Are Osen ◽  
Johan O. A. Robertsson ◽  
Martin Landrø
Keyword(s):  
Seismic Data ◽  
High Frequency ◽  
Low Frequency ◽  
Point Sources ◽  
High Frequency Side ◽  
Frequency Content ◽  
Source Depth ◽  
Deep Sources ◽  
The Cost ◽  
High Frequency Content

The source depth influences the frequency band of seismic data. Due to the source ghost effect, it is advantageous to deploy sources deep to enhance the low-frequency content of seismic data. But, for a given source volume, the bubble period decreases with the source depth, thereby degrading the low-frequency content. At the same time, deep sources reduce the seismic bandwidth. Deploying sources at shallower depths has the opposite effects. A shallow source provides improved high-frequency content at the cost of degraded low-frequency content due to the ghosting effect, whereas the bubble period increases with a lesser source depth, thereby slightly improving the low-frequency content. A solution to the challenge of extending the bandwidth on the low- and high-frequency side is to deploy over/under sources, in which sources are towed at two depths. We have developed a mathematical ghost model for over/under point sources fired in sequential and simultaneous modes, and we have found an inverse model, which on common receiver gathers can jointly perform designature and deghosting of the over/under source measurements. We relate the model for simultaneous mode shooting to recent work on general multidepth level array sources, with previous known solutions. Two numerical examples related to over/under sequential shooting develop the main principles and the viability of the method.

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