Waveform inversion using a back-propagation algorithm and a Huber function norm

Geophysics ◽  
2009 ◽  
Vol 74 (3) ◽  
pp. R15-R24 ◽  
Author(s):  
Taeyoung Ha ◽  
Wookeen Chung ◽  
Changsoo Shin
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Least Squares Method ◽  
Waveform Inversion ◽  
Back Propagation ◽  
Velocity Model ◽  
Back Propagation Algorithm ◽  
Inversion Algorithm ◽  
Coherent Noise ◽  
Complex Valued

Waveform inversion faces difficulties when applied to real seismic data, including the existence of many kinds of noise. The [Formula: see text]-norm is more robust to noise with outliers than the least-squares method. Nevertheless, the least-squares method is preferred as an objective function in many algorithms because the gradient of the [Formula: see text]-norm has a singularity when the residual becomes zero. We propose a complex-valued Huber function for frequency-domain waveform inversion that combines the [Formula: see text]-norm (for small residuals) with the [Formula: see text]-norm (for large residuals). We also derive a discretized formula for the gradient of the Huber function. Through numerical tests on simple synthetic models and Marmousi data, we find the Huber function is more robust to outliers and coherent noise. We apply our waveform-inversion algorithm to field data taken from the continental shelf under the East Sea in Korea. In this setting, we obtain a velocity model whose synthetic shot profiles are similar to the real seismic data.

Traveltime information-based wave-equation inversion

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCC27-WCC36 ◽  
Author(s):  
Yu Zhang ◽  
Daoliu Wang
Keyword(s):  
Wave Equation ◽  
Conventional Method ◽  
Seismic Data ◽  
Waveform Inversion ◽  
Back Propagation ◽  
Velocity Model ◽  
Data Fitting ◽  
Inversion Method ◽  
New Wave ◽  
Seismic Record

We propose a new wave-equation inversion method that mainly depends on the traveltime information of the recorded seismic data. Unlike the conventional method, we first apply a [Formula: see text] transform to the seismic data to form the delayed-shot seismic record, back propagate the transformed data, and then invert the velocity model by maximizing the wavefield energy around the shooting time at the source locations. Data fitting is not enforced during the inversion, so the optimized velocity model is obtained by best focusing the source energy after a back propagation. Therefore, inversion accuracy depends only on the traveltime information embedded in the seismic data. This method may overcome some practical issues of waveform inversion; in particular, it relaxes the dependency of the seismic data amplitudes and the source wavelet.

scholarly journals Full-Waveform Inversion for Imaging Faulted Structures: A Case Study from the Japan Trench Forearc Slope

2021 ◽  
Author(s):  
Ehsan Jamali Hondori ◽  
Chen Guo ◽  
Hitoshi Mikada ◽  
Jin-Oh Park
Keyword(s):  
Seismic Data ◽  
Initial Velocity ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Control Measures ◽  
Japan Trench ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Time Migration ◽  
Shallow Sediments

AbstractFull-waveform inversion (FWI) of limited-offset marine seismic data is a challenging task due to the lack of refracted energy and diving waves from the shallow sediments, which are fundamentally required to update the long-wavelength background velocity model in a tomographic fashion. When these events are absent, a reliable initial velocity model is necessary to ensure that the observed and simulated waveforms kinematically fit within an error of less than half a wavelength to protect the FWI iterative local optimization scheme from cycle skipping. We use a migration-based velocity analysis (MVA) method, including a combination of the layer-stripping approach and iterations of Kirchhoff prestack depth migration (KPSDM), to build an accurate initial velocity model for the FWI application on 2D seismic data with a maximum offset of 5.8 km. The data are acquired in the Japan Trench subduction zone, and we focus on the area where the shallow sediments overlying a highly reflective basement on top of the Cretaceous erosional unconformity are severely faulted and deformed. Despite the limited offsets available in the seismic data, our carefully designed workflow for data preconditioning, initial model building, and waveform inversion provides a velocity model that could improve the depth images down to almost 3.5 km. We present several quality control measures to assess the reliability of the resulting FWI model, including ray path illuminations, sensitivity kernels, reverse time migration (RTM) images, and KPSDM common image gathers. A direct comparison between the FWI and MVA velocity profiles reveals a sharp boundary at the Cretaceous basement interface, a feature that could not be observed in the MVA velocity model. The normal faults caused by the basal erosion of the upper plate in the study area reach the seafloor with evident subsidence of the shallow strata, implying that the faults are active.

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.

Prestack imaging of seismic data using Lp iterative reweighted least-squares wavefield extrapolation filters in the frequency-space domain

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. V243-V252
Author(s):  
Wail A. Mousa
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Least Squares Method ◽  
Filter Design ◽  
Finite Impulse Response ◽  
Weighted Least Squares ◽  
Data Set ◽  
Frequency Space ◽  
Wavefield Extrapolation ◽  
Iterative Reweighted Least Squares

A stable explicit depth wavefield extrapolation is obtained using [Formula: see text] iterative reweighted least-squares (IRLS) frequency-space ([Formula: see text]-[Formula: see text]) finite-impulse response digital filters. The problem of designing such filters to obtain stable images of challenging seismic data is formulated as an [Formula: see text] IRLS minimization. Prestack depth imaging of the challenging Marmousi model data set was then performed using the explicit depth wavefield extrapolation with the proposed [Formula: see text] IRLS-based algorithm. Considering the extrapolation filter design accuracy, the [Formula: see text] IRLS minimization method resulted in an image with higher quality when compared with the weighted least-squares method. The method can, therefore, be used to design high-accuracy extrapolation filters.

scholarly journals Full waveform inversion of short-offset, band-limited seismic data inthe Alboran basin (SE Iberia)

2019 ◽  
Author(s):  
Clàudia Gras ◽  
Valentí Sallarès ◽  
Daniel Dagnino ◽  
C. Estela Jiménez ◽  
Adrià Meléndez ◽  
...  
Keyword(s):  
Travel Time ◽  
Seismic Data ◽  
Waveform Inversion ◽  
Velocity Model ◽  
P Wave ◽  
Full Waveform Inversion ◽  
Time Inversion ◽  
Full Waveform ◽  
Travel Time Tomography ◽  
Band Limited

Abstract. We present a high-resolution P-wave velocity model of the sedimentary cover and the uppermost basement until ~ 3 km depth obtained by full-waveform inversion of multichannel seismic data acquired with a 6 km-long streamer in the Alboran Sea (SE Iberia). The inherent non-linearity of the method, especially for short-offset, band-limited seismic data as this one, is circumvented by applying a data processing/modeling sequence consisting of three steps: (1) data re-datuming by back-propagation of the recorded seismograms to the seafloor; (2) joint refraction and reflection travel-time tomography combining the original and the re-datumed shot gathers; and (3) FWI of the original shot gathers using the model obtained by travel-time tomography as initial reference. The final velocity model shows a number of geological structures that cannot be identified in the travel-time tomography models or easily interpreted from seismic reflection images alone. A sharp strong velocity contrast accurately defines the geometry of the top of the basement. Several low-velocity zones that may correspond to the abrupt velocity change across steeply dipping normal faults are observed at the flanks of the basin. A 200–300 m thick, high-velocity layer embedded within lower velocity sediment may correspond to evaporites deposited during the Messinian crisis. The results confirm that the combination of data re-datuming and joint refraction and reflection travel-time inversion provides reference models that are accurate enough to apply full-waveform inversion to relatively short offset streamer data in deep water settings starting at field-data standard low frequency content of 6 Hz.

Target-oriented wave-equation inversion

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. A35-A38 ◽  
Author(s):  
Alejandro A. Valenciano ◽  
Biondo Biondi ◽  
Antoine Guitton
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Seismic Data ◽  
Hessian Matrix ◽  
Velocity Model ◽  
Complex Model ◽  
Inverse Filtering ◽  
Band Limited ◽  
Filtering Problem ◽  
Number Of Iterations

A target-oriented strategy can be applied to estimate a wave-equation least-squares inverse (LSI) image. By explicitly computing the wave-equation Hessian, the LSI image is obtained as the solution of a nonstationary least-squares inverse filtering problem. The rows of the Hessian are the nonstationary filters containing information about the acquisition geometry, the velocity model, and the band-limited characteristics of the seismic data. By exploiting the sparsity and the structure of the Hessian matrix, a large number of iterations, necessary to achieve convergence, can be computed cheaply. The results on a structurally complex model show the improvements of the LSI image versus the migrated image.

Adaptive subtraction using complex-valued curvelet transforms

Geophysics ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. V51-V60 ◽  
Author(s):  
Ramesh (Neelsh) Neelamani ◽  
Anatoly Baumstein ◽  
Warren S. Ross
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Seismic Reflection ◽  
Characteristic Frequency ◽  
Large Scale ◽  
Curvelet Transform ◽  
Real Data ◽  
Text Data ◽  
Data Set ◽  
Complex Valued

We propose a complex-valued curvelet transform-based (CCT-based) algorithm that adaptively subtracts from seismic data those noises for which an approximate template is available. The CCT decomposes a geophysical data set in terms of small reflection pieces, with each piece having a different characteristic frequency, location, and dip. One can precisely change the amplitude and shift the location of each seismic reflection piece in a template by controlling the amplitude and phase of the template's CCT coefficients. Based on these insights, our approach uses the phase and amplitude of the data's and template's CCT coefficients to correct misalignment and amplitude errors in the noise template, thereby matching the adapted template with the actual noise in the seismic data, reflection event-by-event. We also extend our approach to subtract noises that require several templates to be approximated. By itself, the method can only correct small misalignment errors ([Formula: see text] in [Formula: see text] data) in the template; it relies on conventional least-squares (LS) adaptation to correct large-scale misalignment errors, such as wavelet mismatches and bulk shifts. Synthetic and real-data results illustrate that the CCT-based approach improves upon the LS approach and a curvelet-based approach described by Herrmann and Verschuur.

scholarly journals Source‐independent full‐waveform inversion of seismic data

Geophysics ◽  
2003 ◽  
Vol 68 (6) ◽  
pp. 2010-2015 ◽  
Author(s):  
Ki Ha Lee ◽  
Hee Joon Kim
Keyword(s):  
Frequency Domain ◽  
Seismic Data ◽  
Waveform Inversion ◽  
Source Spectrum ◽  
Full Waveform Inversion ◽  
Source Inversion ◽  
Inversion Algorithm ◽  
Source Information ◽  
Full Waveform ◽  
Precise Knowledge

A rigorous full‐waveform inversion of seismic data has been a challenging subject, partly because of the lack of precise knowledge of the source. Since currently available approaches involve some form of approximations to the source, inversion results are subject to the quality and choice of the source information used. We propose a new full‐waveform inversion methodology that does not involve source spectrum information. Thus, potential inversion errors from source estimation can be eliminated. A gather of seismic traces is first Fourier transformed into the frequency domain, and a normalized wavefield is obtained for each trace in the frequency domain. Normalization is done with respect to the frequency response of a reference trace selected from the gather, so the complex‐valued normalized wavefield is dimensionless. The source spectrum is eliminated during the normalization procedure. With its source spectrum eliminated, the normalized wavefield lets us construct an inversion algorithm without the source information. The inversion algorithm minimizes misfits between a measured normalized wavefield and a numerically computed normalized wavefield. The proposed approach has been demonstrated successfully using a simple 2D scalar problem.

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