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1

Elastic full waveform inversion based on equivalent staggered grid FDM and inter-parameter trade-off mitigation

Li Qingyang, Wu Guochen

Acta Geophysica

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2022

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Vol. 70, no 6

2555--2579

EN

Elastic full waveform inversion (EFWI) has increasingly been applied in seismic exploration as computer performance improves. EFWI significantly improves calculation efficiency, but requires very large computer storage space and suffers interparameter trade-off and local minima problems. Preconditioning the gradients based on elastic wave mode decomposition can effectively mitigate inter-parameter trade-offs, but the decomposition-based scheme may further increase the memory usage, which limits EFWI application. The equivalent staggered grid (ESG) scheme in acoustic medium requires less memory usage and generates results numerically equivalent to those using the standard staggered grid (SSG) scheme. In this paper, we extend the ESG scheme to second-order elastic wave equations in terms of velocity, producing results numerically equivalent to the SSG ones based on first-order velocity–stress wave equations while reducing memory usage by 45% compared with the SSG scheme. We then apply the ESG scheme to EFWI and derive the formula of the preconditioned gradient of the S-wave velocity. Finally, three numerical examples demonstrate that applying the ESG scheme to decomposition-based EFWI can significantly reduce computer memory usage and mitigate the trade-offs between the P- and S-wave velocities.

2

An efcient multiparameter acoustic anisotropic full-waveform inversion depending on parameterization

Shin Youngjae, Oh Ju Won, Min Dong Joo

Acta Geophysica

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2021

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Vol. 69, no. 4

1257--1267

EN

The pressure-based acoustic approximation of the elastic wave equations in anisotropic media has advantages corresponding to computational efciency and numerical stability. However, the numerical scattering potentials from the anisotropic parameter perturbations for the pressure wavefeld are not consistent with the elastic scattering theory. In multiparameter full-waveform inversion (FWI), choosing a suitable parameterization, considering the acquisition parameters (e.g., the ofsetto-depth ratio and frequency band) and the accuracy of the anisotropy information in the background initial velocity model, is an important component to a successful anisotropic parameter estimation, because the parameterization determines the trade-of between inverted model parameters and their resolution power. However, because it is difcult to perform multiparameter FWI with various types of parameterization using the pressure-based acoustic wave equation, inaccurate scattered wavefelds cause the gradient direction to lose its unique properties with respect to each model parameter. To overcome these issues, we adopt the combination of pressure- and vector-based acoustic wave equations converted vector virtual sources, which preserves the computational efciency and the angular dependency of the partial derivative wavefelds in elastic media. With the proposed method, we generate the numerical PP scattering patterns for various parameterizations, which are consistent with the elastic scattering theory. Through the numerical tests using the synthetic anisotropic Marmousi-II models and a real ocean bottom cable dataset from the North Sea, we conduct acoustic FWI with three diferent parameterizations using the proposed method and verify that the modifed scattering patterns accurately refect the characteristics of the anisotropic parameter perturbations.

3

Syntetyczne testy inwersji pełnego pola falowego w warunkach rzeczywistej sieci monitoringu sejsmicznego ZG Rudna

Caputa Alicja, Rudziński Łukasz

Przegląd Geofizyczny

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2020

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Z. 3-4

123--138

PL

Sejsmiczność indukowana działalnością górniczą jest stale monitorowana i analizowana w celu zwiększenia bezpieczeństwa wydobycia kopalin. Jedną z procedur, chociaż niestosowanych rutynowo w polskim górnictwie węgla i miedzi, jest wyznaczanie mechanizmów ogniskowych silniejszych wstrząsów. Najprostszą i jak dotąd jedyną stosowaną metodą ich obliczania jest inwersja pierwszych wstąpień fali P w domenie czasu. Metoda ta pomimo swojej prostoty i możliwości bezpośredniej kontroli analizowanego wejścia fali sejsmicznej, jest procedurą bardzo czułą na geometrię sieci pomiarowej. Jest to szczególnie kłopotliwe w przypadku dołowych sieci kopalnianych, gdzie geometria sieci ograniczona jest istniejącą infrastrukturą podziemną. W niniejszym opracowaniu proponujemy i testujemy metodę inwersji pełnego pola falowego, przeprowadzaną w domenie częstotliwości oraz czasu, która do tej pory nie była powszechnie stosowana w polskim górnictwie. W oparciu o sejsmogramy syntetyczne obliczone dla lokalnego modelu prędkościowego oraz z wykorzystaniem geometrii rzeczywistej sieci monitoringu sejsmicznego, przeprowadziliśmy badanie przydatności inwersji pełnego pola falowego do obliczeń w warunkach górniczych. W pracy prezentujemy analizy 10 różnych modeli mechanizmów ogniskowych testowanych w różnych lokalizacjach kopalni dla zmiennej siły wstrząsu oraz z dodatkowym rzeczywistym szumem sejsmicznym. Na podstawie otrzymanych wyników możemy stwierdzić, iż głównym czynnikiem warunkującym jakość rozwiązania jest siła wstrząsu i wynikająca z niego zależność amplituda/szum. Natomiast metoda ta nie jest czuła na geometrię sieci pomiarowej.

EN

In order to improve the safety procedures of georesources exploitation, the induced seismicity is constantly monitored and examined. One of the procedures method, although even though not routinely used in Polish coal and copper mining mines, is the calculation of focal mechanisms of strong seismic events. The simplest and so far the only used method for source mechanisms estimation is the inversion of the first P wave onsets in the time domain. Despite its simplicity and the ability to direct control of analyzed seismic waves used during inversion, it is a procedure very sensitive to the geometry of the monitoring seismic network. This is particularly troublesome in the case of underground seismic monitoring system, where the geometry of the network is limited by the existing underground infrastructure. In this study, we propose and test the full waveform inversion method, performed both in the frequency and time domain. This kind of method has not been widely used in Polish miningmines. Basing on synthetic seismograms prepared for the local velocity model and using geometry of the real seismic monitoring network, we conducted a study of the suitability of the full waveform inversion for calculations in underground mining conditions. In this paper, we present analyzes of 10 different source models of focal mechanisms tested in various mine locations within mining area. The tests were performed for variable events strength and with additional real seismic noise. On the grounds of obtained results, we can conclude that the main factor determining the solution quality is the strength of mining tremor and amplitude/noise relationship resulting from it. However, this method is not sensitive to the geometry of the measurement network.

4

Full waveform inversion based on a local traveltime correction and zero-mean cross-correlation-based misft function

Dong Shiqi, Han Liguo, Hu Yong, Yin Yuchen

Acta Geophysica

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2020

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Vol. 68, no. 1

29--50

EN

Full waveform inversion (FWI) sufers from the cycle skipping problem, because the observed data usually lack low-frequency components or due to errors in the wavelet estimation. In addition, the strong low-frequency non-zero-mean noise can have a large impact on FWI results. Thus, we propose a local waveform traveltime correction scheme to solve the situations when the observed data lack low-frequency components or when the estimation for the wavelet is incorrect. We use a sliding time window, which is used to decrease the traveltime diferences between the calculated and observed data to increase the cross-correlation between them. Besides, we propose a zero-mean normalized cross-correlation misft function to reduce the interference of the low-frequency non-zero-mean noise. Therefore, we propose new approaches to improve FWI results whether the observed data lack low-frequency components or the observed data are contaminated by the non-zero-mean lowfrequency noise. Numerical examples on Marmousi model show the feasibility of a FWI based on the zero-mean normalized cross-correlation misft function and a FWI based on the local traveltime correction method.

5

Frequency extension and robust full waveform inversion based on nth power operation

Zhang Pan, Han Liguo, Gao Rui, Zhang Fengjiao, Xing Zhenzhen

Acta Geophysica

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2020

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Vol. 68, no. 5

1317--1333

EN

The conventional full-waveform inversion (FWI) often minimizes the objective function using some local optimization algorithms. As a result, when the initial model is not good enough, the inversion process will drop into a local minimum. The low-frequency components contained in seismic data are of vital importance for reducing the initial model dependence and mitigating the cycle-skipping phenomenon of FWI. In this research, a frequency extension method using the nth power operation is proposed, which compresses the seismic data in time domain and extends their frequency band. Based on this, we construct a new objective function using the nth power wavefeld and derive the corresponding gradient formula. The new objective function shows better property to overcome local minimum than the conventional one. When conduct inversion, we can invert from high-order to low-order successively, which is a new multiscale strategy. Since seismic data is more sensitive to source wavelet errors after high-order operation, we make the method more robust by proposing a source-independent method to mitigate the efects of source wavelet inaccuracy. After that, we extend the proposed method to encoded multisource waveform inversion. The numerical examples on the Marmousi model demonstrate that the proposed method can efectively mitigate the cycle-skipping of FWI, and it also has good anti-noise property.

6

Models of the Earth’s crust from controlled-source seismology – where we stand and where we go?

Malinowski M.

Acta Geophysica

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2013

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Vol. 61, no. 6

1437--1456

EN

Controlled-source seismology (CSS) is the primary source of information regarding the fine structure of the lithosphere. The aim of this paper is to provide an overview of the methods that are commonly used to derive Earth models from CSS data with the focus on the wide-angle reflection/refraction method. Some outlook on the future of the CSS is presented with the special emphasis on the full-wavefield based methods like full-waveform inversion, which brings high level of objectivity into modeling, as well as significantly increases spatial resolution. It is stressed that the researchers should be aware of the limitations of how the elastic parameters transcribe into the actual rock properties which should stimulate them to go beyond the simple P-wave modeling and to build multiparameter Earth models based either on the seismic data or constrained by additional geophysical fields in order to derive sound geological interpretation of their models.

7

Full waveform inversion of gas hydrate reflectors in Northern South China Sea

Huo Y., Zhang M.

Acta Geophysica

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2009

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Vol. 57, no. 3

716-727

EN

Bottom Simulating Reflectors (BSRs) are considered to be the bottom of gas hydrate bearing sediments; hence, BSRs are used to identify gas hydrate and free gas. In order to obtain accurate velocity structure of BSRs, this paper presents a full waveform inversion strategy based on Genetic Algorithm. Synthetic seismograms are calculated using the slowness technique. Through numerical experiments made with noisy synthetic data, the inversion algorithm shows stable performance, and genetic operators are defined. This method was applied to field data from the northern South China Sea. Inversion results show that obvious velocity anomaly of BSRs can be detected, which indicates the existence of gas hydrate and free gas.