Crosstalk-free simultaneous-source full waveform inversion with normalized seismic data

doi:10.1016/j.cageo.2020.104460

Computers & Geosciences

Volume 138, May 2020, 104460

https://doi.org/10.1016/j.cageo.2020.104460 Get rights and content

Abstract

Simultaneous-source algorithms can increase the efficiency of full waveform inversion (FWI) dramatically through reducing the number of times of wavefield simulations. However, the multiple sources induce the crosstalk artifacts, which severely contaminate the inversion results. To solve this problem, we provide a crosstalk-free simultaneous-source algorithm with the normalized seismic data. Sine harmonic functions with arbitrary phases are used as different wavelets in a super shot and as the encoding operator. Based on this algorithm, the crosstalk artifacts are eliminated by deblending the simultaneous-source wavefield with little additional computation. Moreover, the estimation or inversion of source wavelets at each iteration for simultaneous-source data, which is crucial for successful FWI but would severely reduce the efficiency of simultaneous-source algorithms, are avoided by normalizing the seismic data with deconvolution. Since the simultaneous-source data are deblended, the proposed algorithm is naturally applicable to the marine mobile streamer seismic data. Furthermore, it is convenient to select the reference traces for deblended data, instead of simultaneous-source data, to eliminate or unify the wavelet information by deconvolution. Finally, we verify the proposed algorithm with the synthetic data.

Introduction

Full waveform inversion (FWI) constructs the medium parameters (Tarantola, 1984) by minimizing the misfit between the observed and simulated data. Its high resolution has attracted a great attention (Mora, 1987, Plessix, 2006, Guitton and Díaz, 2012, Operto et al., 2013, Xu and McMechan, 2014, Chen et al., 2016) since it was proposed. However, compared to the conventional ray-based travel-time tomography, the extremely low efficiency of FWI caused by the great computation amount is still a challenge for its wide application. The parallel algorithms (Brossier, 2011, Kim et al., 2013, Liu et al., 2013, Shin et al., 2014, Yang et al., 2014, Zhang et al., 2014, Liu et al., 2015, Fabien-Ouellet et al., 2017, Gui et al., 2017, Li et al., 2017, Xu et al., 2018, Wu et al., 2019, Gu et al., 2019, Wang et al., 2019, Fang et al., 2020) are usually used to improve its efficiency, but these algorithms are based on the high-performance-computing ability of computer devices and do not essentially reduce the computation amount.

To reduce the amount of computation, the simultaneous-source algorithms (Romero et al., 1999, Bansal et al., 2013) are the crucial strategies. Unfortunately, the conventional simultaneous-source method has two drawbacks: one is the crosstalk artifacts, which severely contaminates the inversion results; the other is the fixed acquisition assumption (Krebs et al., 2009) for all sources in a super shot, which is inapplicable to mobile streamer seismic data.

In order to overcome the false fixed-spread assumption, the global correlation-norm objective function (Choi and Alkhalifah, 2012) was proposed for simultaneous-source FWI. But Son et al. (2014) pointed out that the correlation operation (Choi and Alkhalifah, 2012) might distort the seismic data and developed an alternative approach by modifying the limited offset of observed data to the full offset. Nevertheless, when tens or hundreds of sources are encoded simultaneously, this alternative algorithm would be complicated and difficult to realize with little efficiency improvement.

As for the problem of crosstalk, Krebs et al. (2009) proposed to change the code sequence within a super shot at each iteration to attenuate the artifacts. Xue et al. (2017) and Zhang et al. (2018a) applied a shaping regularization constraint to the model parameter gradient to reduce the crosstalk influence, but the smoothing process would decrease the resolution of inversion results. Wu and Bai (2018) adopted a low-rank constraint to improve the resolution of simultaneous-source migration. Overall, the aforementioned strategies cannot eliminate the crosstalk artifacts essentially.

FWI can be considered as a data waveform matching process (Plessix, 2006) by iterative optimization algorithm. Therefore, the wavelet is crucial for a successful inversion because wrong wavelet would induce the waveform mismatching problem even the velocity is accurate (Zhang et al., 2016). However, the common-used direct arrival is not the true wavelet (Song et al., 1995) and the iterative source estimation (Xu et al., 2006) for each source within a super shot would increase the additional computation amount to counteract the efficiency of simultaneous-source method (Choi and Alkhalifah, 2011). In order to remove the inversion or estimation of source wavelet, two main strategies (Zhang et al., 2016) have been proposed, that is, the deconvolution (Zhou and Greenhalgh, 2003) and convolution (Choi and Alkhalifah, 2011, Zhang et al., 2016) methods. Both strategies need to choose a reference to eliminate or unify the source wavelet information. When using the conventional simultaneous-source algorithm and each source wavelet within a super shot having different signal functions, it is difficult to accomplish the source-independent FWI because of the simultaneous-source crosstalk and the acquisition mismatch between the simulated and encoded observed simultaneous-source data.

In the following context, we provide a novel crosstalk-free and source-independent simultaneous-source inversion algorithm with the normalized seismic data by deconvolution. The proposed algorithm uses the harmonic sine functions (Nihei and Li, 2007) as the source wavelet signals and encoding operators to conduct the time-domain simultaneous-source wavefield simulation, by which we can deblend the simultaneous-source wavefield. Therefore, the proposed algorithm can be naturally suitable for marine mobile streamer data. Likewise, it is easy to eliminate or unify the wavelet information for every source data without simultaneous-source crosstalk. The adjoint wavefield calculated by backward propagating the simultaneous-source residuals are also deblended so that the gradient can be calculated without the contamination of crosstalk artifacts. The whole deblending processes take only little time of the inversion.

In the following context, we first introduce the generation of crosstalk artifacts and make a detailed description for the proposed simultaneous-source algorithm to avoid this problem. Then we implement the source-independent simultaneous-source inversion with the normalized data by deconvolution. Next, we provide the deblending strategy to ensure the accuracy and adopt the Graphics Processing Unit (GPU) device to further enhance the efficiency of our algorithm. Finally, we use the synthetic examples to perform the feasibility analysis to our algorithm, and then give the corresponding discussion and conclusions.

Section snippets

Simultaneous-source crosstalk artifacts

The object function of FWI is built based on the following equation, $χ (m) = \frac{1}{2} \sum_{i s = 1}^{N S} {‖ d^{s y n} (m, γ_{i s} (t), t) - d_{i s}^{o b s} (t) ‖}^{2},$ where the superscripts of $o b s$ and $s y n$ represent the observed and simulated data, $m$ means the medium parameter, $γ_{i s}$ denotes the wavelet signal of the $i s$ th source, $N S$ is the total source number.

In order to enhance the inversion efficiency, the simultaneous-source algorithm is one crucial strategy. The corresponding objective function (Krebs et al., 2009) is expressed as $χ (m) = \frac{1}{2} \sum_{i s = 1}^{N N} ‖ d^{s y n} (m, \sum s s = 1)$

Examples

The Overthrust model is used to perform the simultaneous-source inversion tests. One hundred sources are set evenly at the surface. The temporal sampling interval is 1.0 ms and the length of recording seismogram is 8.0 s. The true velocity shown in Fig. 2(a) and the Ricker wavelet with 15.0 Hz dominant frequency are used to generate the unblended observed data. Fig. 2(b) shows the initial velocity for FWI, which is generated by the true velocity (Fig. 2(a)) after smoothing with a square spatial

Discussions

As for the frequency selection within a super shot for each source wavelet, one can choose $2 Δ ω$ as Eqs. (15)–(17), or $Δ ω$ by padding to double simulation time. It should be noted that different-frequency harmonic wavelets composes a band-limited super wavelet, so the number of encoded sources $E N$ are restricted to assure the merit of multi-scale inversion scheme. In this paper, we do not perform analysis to quantitatively choose the optimal number of encoding sources. A suggestion is that one can

Conclusions

We provide a novel simultaneous-source algorithm with normalized seismic data for FWI. Sine harmonic functions are used as the wavelets and encoding operators. Based on the trigonometric orthogonality, the blended wavefield are deblended so that the proposed encoding algorithm can avoid the crosstalk artifacts and unrealistic fixed-spread assumption. Combining with the deconvolution-based objective function, the encoding algorithm can be implemented successfully without the true wavelet

CRediT authorship contribution statement

Qingchen Zhang: Methodology, Writing - original draft, Writing - review & editing. Weijian Mao: Supervision, Validation. Jinwei Fang: Software.

Acknowledgments

This work was jointly supported by State Key Research Development Program of China (2016YFC0601100, 2018YFC0310104), National Natural Science Foundation of China (U1562216) and Hubei Provincial Natural Science Foundation of China (2018CFB355).

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Research paperCrosstalk-free simultaneous-source full waveform inversion with normalized seismic data

Abstract

Introduction

Section snippets

Simultaneous-source crosstalk artifacts

Examples

Discussions

Conclusions

CRediT authorship contribution statement

Acknowledgments

Comput. Geosci.

Comput. Geosci.

Comput. Geosci.

Comput. Geosci.

Comput. Geosci.

Comput. Geosci.

Comput. Geosci.

Comput. Geosci.

Comput. Geosci.

Comput. Geosci.

Comput. Geosci.

Comput. Geosci.

Comput. Geosci.

Comput. Geosci.

Comput. Geosci.

A recipe for practical full-waveform inversion in anisotropic media: An analytical parameter resolution study

Geophysics

Simultaneous-source full-wavefield inversion

Lead. Edge

An efficient multiscale method for time-domain waveform tomography

Geophysics

Geological structure guided well log interpolation for high-fidelity full waveform inversion

Geophys. J. Int.

A matrix-transform numerical solver for fractional Laplacian viscoacoustic wave equation

Geophysics

Source-independent time-domain waveform inversion using convolved wavefields: Application to the encoded multisource waveform inversion

Geophysics

Application of multi-source waveform inversion to marine streamer data using the global correlation norm

Geophys. Prospect.

Multi-source least-squares reverse time migration

Geophys. Prospect.

Simplified hybrid domain FWI method and GPU acceleration

Geophys. Prospect. Petrol.

Research paper
Crosstalk-free simultaneous-source full waveform inversion with normalized seismic data