Seismic envelope inversion and modulation signal model

We recognized that the envelope fluctuation and decay of seismic records carries ultra low-frequency (ULF, i.e., the frequency below the lowest frequency in the source spectrum) signals that can be used to estimate the long-wavelength velocity structure. We then developed envelope inversion for the recovery of low-wavenumber components of media (smooth background), so that the initial model dependence of waveform inversion can be reduced. We derived the misfit function and the corresponding gradient operator for envelope inversion. To understand the long-wavelength recovery by the envelope inversion, we developed a nonlinear seismic signal model, the modulation signal model, as the basis for retrieving the ULF data and studied the nonlinear scale separation by the envelope operator. To separate the envelope data from the wavefield data (envelope extraction), a demodulation operator (envelope operator) was applied to the waveform data. Numerical tests using synthetic data for the Marmousi model proved the validity and feasibility of the proposed approach. The final results of combined [Formula: see text] (envelope-inversion for smooth background plus waveform-inversion for high-resolution velocity structure) indicated that it can deliver much improved results compared with regular full-waveform inversion (FWI) alone. Furthermore, to test the independence of the envelope to the source frequency band, we used a low-cut source wavelet (cut from 5 Hz below) to generate the synthetic data. The envelope inversion and the combined [Formula: see text] showed no appreciable difference from the full-band source results. The proposed envelope inversion is also an efficient method with very little extra work compared with conventional FWI.

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Elastic envelope inversion using multicomponent seismic data without low frequency

Nonlinear Processes in Geophysics Discussions ◽

10.5194/npgd-1-1757-2014 ◽

2014 ◽

Vol 1 (2) ◽

pp. 1757-1802

Author(s):

C. Huang ◽

L. Dong ◽

Y. Liu ◽

B. Chi

Keyword(s):

Seismic Data ◽

Waveform Inversion ◽

Synthetic Data ◽

Low Frequency ◽

Velocity Model ◽

Inversion Method ◽

Full Waveform Inversion ◽

S Wave ◽

Full Waveform ◽

Multicomponent Data

Abstract. Low frequency is a key issue to reduce the nonlinearity of elastic full waveform inversion. Hence, the lack of low frequency in recorded seismic data is one of the most challenging problems in elastic full waveform inversion. Theoretical derivations and numerical analysis are presented in this paper to show that envelope operator can retrieve strong low frequency modulation signal demodulated in multicomponent data, no matter what the frequency bands of the data is. With the benefit of such low frequency information, we use elastic envelope of multicomponent data to construct the objective function and present an elastic envelope inversion method to recover the long-wavelength components of the subsurface model, especially for the S-wave velocity model. Numerical tests using synthetic data for the Marmousi-II model prove the effectiveness of the proposed elastic envelope inversion method, especially when low frequency is missing in multicomponent data and when initial model is far from the true model. The elastic envelope can reduce the nonlinearity of inversion and can provide an excellent starting model.

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Long-Wavelength Earth Model via Accelerated Full-Waveform Inversion

10.5194/egusphere-egu21-12687 ◽

2021 ◽

Author(s):

Solvi Thrastarson ◽

Dirk-Philip van Herwaarden ◽

Lion Krischer ◽

Martin van Driel ◽

Christian Boehm ◽

...

Keyword(s):

Waveform Inversion ◽

Large Data ◽

Earth Model ◽

Full Waveform Inversion ◽

Waveform Data ◽

Long Wavelength ◽

Computational Overhead ◽

Full Dataset ◽

Full Waveform ◽

Seismic Waveform

As the volume of available seismic waveform data increases, the responsibility to use the data in an effective way emerges. This requires computational efficiency as well as maximizing the exploitation of the information associated with the data.In this contribution, we present a long-wavelength Earth model, created by using the data recorded from over a thousand earthquakes, starting from a simple one-dimensional background (PREM). The model is constructed with an accelerated full-waveform inversion (FWI) method which can seamlessly include large data volumes with a significantly reduced computational overhead. Although we present a long-wavelength model, the approach has the potential to go to much higher frequencies, while maintaining a reasonable cost.Our approach combines two novel FWI variants. (1) The dynamic mini-batch approach which uses adaptively defined subsets of the full dataset in each iteration, detaching the direct scaling of inversion cost from the number of earthquakes included. (2) Wavefield-adapted meshes which utilize the azimuthal smoothness of the wavefield to design meshes optimized for each individual source location. Using wavefield adapted meshes can drastically reduce the cost of both forward and adjoint simulations as well as it makes the scaling of the computing cost to modelled frequencies more favourable.

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Waveform inversion using a logarithmic wavefield

Geophysics ◽

10.1190/1.2194523 ◽

2006 ◽

Vol 71 (3) ◽

pp. R31-R42 ◽

Cited By ~ 215

Author(s):

Changsoo Shin ◽

Dong-Joo Min

Keyword(s):

Objective Function ◽

Field Data ◽

Velocity Structure ◽

Waveform Inversion ◽

Synthetic Data ◽

Velocity Model ◽

Matrix Formalism ◽

Inversion Algorithm ◽

Data Set ◽

Short Period

Although waveform inversion has been studied extensively since its beginning [Formula: see text] ago, applications to seismic field data have been limited, and most of those applications have been for global-seismology- or engineering-seismology-scale problems, not for exploration-scale data. As an alternative to classical waveform inversion, we propose the use of a new, objective function constructed by taking the logarithm of wavefields, allowing consideration of three types of objective function, namely, amplitude only, phase only, or both. In our wave form inversion, we estimate the source signature as well as the velocity structure by including functions of amplitudes and phases of the source signature in the objective function. We compute the steepest-descent directions by using a matrix formalism derived from a frequency-domain, finite-element/finite-difference modeling technique. Our numerical algorithms are similar to those of reverse-time migration and waveform inversion based on the adjoint state of the wave equation. In order to demonstrate the practical applicability of our algorithm, we use a synthetic data set from the Marmousi model and seismic data collected from the Korean continental shelf. For noise-free synthetic data, the velocity structure produced by our inversion algorithm is closer to the true velocity structure than that obtained with conventional waveform inversion. When random noise is added, the inverted velocity model is also close to the true Marmousi model, but when frequencies below [Formula: see text] are removed from the data, the velocity structure is not as good as those for the noise-free and noisy data. For field data, we compare the time-domain synthetic seismograms generated for the velocity model inverted by our algorithm with real seismograms and find that the results show that our inversion algorithm reveals short-period features of the subsurface. Although we use wrapped phases in our examples, we still obtain reasonable results. We expect that if we were to use correctly unwrapped phases in the inversion algorithm, we would obtain better results.

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Prestack waveform inversion based on analytical solution of the viscoelastic wave equation

Geophysics ◽

10.1190/geo2019-0493.1 ◽

2021 ◽

Vol 86 (1) ◽

pp. R45-R61

Author(s):

Yuanqiang Li ◽

Jingye Li ◽

Xiaohong Chen ◽

Jian Zhang ◽

Xin Bo

Keyword(s):

Analytical Solution ◽

Seismic Reflection ◽

Waveform Inversion ◽

Synthetic Data ◽

Low Frequency ◽

S Wave ◽

Single Interface ◽

Wave Velocities ◽

Avo Inversion ◽

Viscoelastic Wave

Amplitude-variation-with-offset (AVO) inversion is based on single interface reflectivity equations. It involves some restrictions, such as the small-angle approximation, including only primary reflections, and ignoring attenuation. To address these shortcomings, the analytical solution of the 1D viscoelastic wave equation is used as the forward modeling engine for prestack inversion. This method can conveniently handle the attenuation and generate the full wavefield response of a layered medium. To avoid numerical difficulties in the analytical solution, the compound matrix method is applied to rapidly obtain the analytical solution by loop vectorization. Unlike full-waveform inversion, the proposed prestack waveform inversion (PWI) can be performed in a target-oriented way and can be applied in reservoir study. Assuming that a Q value is known, PWI is applied to synthetic data to estimate elastic parameters including compressional wave (P-wave) and shear wave (S-wave) velocities and density. After validating our method on synthetic data, this method is applied to a reservoir characterization case study. The results indicate that the reflectivity calculated by our approach is more realistic than that computed by using single interface reflectivity equations. Attenuation is an integral effect on seismic reflection; therefore, the sensitivity of seismic reflection to P-and S-wave velocities and density is significantly greater than that to Q, and the seismic records are sensitive to the low-frequency trend of Q. Thus, we can invert for the three elastic parameters by applying the fixed low-frequency trend of Q. In terms of resolution and accuracy of synthetic and real inversion results, our approach performs superiorly compared to AVO inversion.

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

Geophysics ◽

10.1190/geo2013-0332.1 ◽

2015 ◽

Vol 80 (1) ◽

pp. R1-R13 ◽

Cited By ~ 11

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.

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Adding Prior Information in FWI through Relative Entropy

Entropy ◽

10.3390/e23050599 ◽

2021 ◽

Vol 23 (5) ◽

pp. 599

Author(s):

Danilo Cruz ◽

João de Araújo ◽

Carlos da Costa ◽

Carlos da Silva

Keyword(s):

Inverse Problem ◽

Relative Entropy ◽

Global Minimum ◽

Prior Information ◽

Waveform Inversion ◽

Petroleum Industry ◽

Synthetic Data ◽

Full Waveform Inversion ◽

Full Waveform

Full waveform inversion is an advantageous technique for obtaining high-resolution subsurface information. In the petroleum industry, mainly in reservoir characterisation, it is common to use information from wells as previous information to decrease the ambiguity of the obtained results. For this, we propose adding a relative entropy term to the formalism of the full waveform inversion. In this context, entropy will be just a nomenclature for regularisation and will have the role of helping the converge to the global minimum. The application of entropy in inverse problems usually involves formulating the problem, so that it is possible to use statistical concepts. To avoid this step, we propose a deterministic application to the full waveform inversion. We will discuss some aspects of relative entropy and show three different ways of using them to add prior information through entropy in the inverse problem. We use a dynamic weighting scheme to add prior information through entropy. The idea is that the prior information can help to find the path of the global minimum at the beginning of the inversion process. In all cases, the prior information can be incorporated very quickly into the full waveform inversion and lead the inversion to the desired solution. When we include the logarithmic weighting that constitutes entropy to the inverse problem, we will suppress the low-intensity ripples and sharpen the point events. Thus, the addition of entropy relative to full waveform inversion can provide a result with better resolution. In regions where salt is present in the BP 2004 model, we obtained a significant improvement by adding prior information through the relative entropy for synthetic data. We will show that the prior information added through entropy in full-waveform inversion formalism will prove to be a way to avoid local minimums.

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A waveform inversion technique for measuring elastic wave attenuation in cylindrical bars

Geophysics ◽

10.1190/1.1443299 ◽

1992 ◽

Vol 57 (6) ◽

pp. 854-859 ◽

Cited By ~ 6

Author(s):

Xiao Ming Tang

Keyword(s):

Elastic Wave ◽

Wave Attenuation ◽

Waveform Inversion ◽

Finite Size ◽

Low Frequency ◽

Frequency Range ◽

Multiple Reflections ◽

Low Frequencies ◽

The Time Domain ◽

Attenuation Values

A new technique for measuring elastic wave attenuation in the frequency range of 10–150 kHz consists of measuring low‐frequency waveforms using two cylindrical bars of the same material but of different lengths. The attenuation is obtained through two steps. In the first, the waveform measured within the shorter bar is propagated to the length of the longer bar, and the distortion of the waveform due to the dispersion effect of the cylindrical waveguide is compensated. The second step is the inversion for the attenuation or Q of the bar material by minimizing the difference between the waveform propagated from the shorter bar and the waveform measured within the longer bar. The waveform inversion is performed in the time domain, and the waveforms can be appropriately truncated to avoid multiple reflections due to the finite size of the (shorter) sample, allowing attenuation to be measured at long wavelengths or low frequencies. The frequency range in which this technique operates fills the gap between the resonant bar measurement (∼10 kHz) and ultrasonic measurement (∼100–1000 kHz). By using the technique, attenuation values in a PVC (a highly attenuative) material and in Sierra White granite were measured in the frequency range of 40–140 kHz. The obtained attenuation values for the two materials are found to be reliable and consistent.

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The Low-Frequency Array (LOFAR): Opening a New Window on the Universe

Symposium - International Astronomical Union ◽

10.1017/s0074180900169591 ◽

2002 ◽

Vol 199 ◽

pp. 474-483

Author(s):

Namir E. Kassim ◽

T. Joseph W. Lazio ◽

William C. Erickson ◽

Patrick C. Crane ◽

R. A. Perley ◽

...

Keyword(s):

Angular Resolution ◽

Broad Band ◽

Low Frequency ◽

Electromagnetic Spectrum ◽

Interferometric Imaging ◽

Very Large Array ◽

Long Wavelength ◽

Calibration Techniques ◽

Long Baselines ◽

The Universe

Decametric wavelength imaging has been largely neglected in the quest for higher angular resolution because ionospheric structure limited interferometric imaging to short (< 5 km) baselines. The long wavelength (LW, 2—20 m or 15—150 MHz) portion of the electromagnetic spectrum thus remains poorly explored. The NRL-NRAO 74 MHz Very Large Array has demonstrated that self-calibration techniques can remove ionospheric distortions over arbitrarily long baselines. This has inspired the Low Frequency Array (LOFAR)—-a fully electronic, broad-band (15—150 MHz)antenna array which will provide an improvement of 2—3 orders of magnitude in resolution and sensitivity over the state of the art.

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

Journal of Geophysics and Engineering ◽

10.1093/jge/gxz062 ◽

2019 ◽

Vol 16 (6) ◽

pp. 1017-1031 ◽

Cited By ~ 5

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.

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