An application of full-waveform inversion to land data using the pseudo-Hessian matrix

2016 ◽  
Vol 4 (4) ◽  
pp. T627-T635
Author(s):  
Yikang Zheng ◽  
Wei Zhang ◽  
Yibo Wang ◽  
Qingfeng Xue ◽  
Xu Chang
Keyword(s):  
Hessian Matrix ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Velocity Model ◽  
Surface Velocity ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Near Surface ◽  
Full Waveform ◽  
The Time Domain

Full-waveform inversion (FWI) is used to estimate the near-surface velocity field by minimizing the difference between synthetic and observed data iteratively. We apply this method to a data set collected on land. A multiscale strategy is used to overcome the local minima problem and the cycle-skipping phenomenon. Another obstacle in this application is the slow convergence rate. The inverse Hessian can enhance the poorly blurred gradient in FWI, but obtaining the full Hessian matrix needs intensive computation cost; thus, we have developed an efficient method aimed at the pseudo-Hessian in the time domain. The gradient in our FWI workflow is preconditioned with the obtained pseudo-Hessian and a synthetic example verifies its effectiveness in reducing computational cost. We then apply the workflow on the land data set, and the inverted velocity model is better resolved compared with traveltime tomography. The image and angle gathers we get from the inversion result indicate more detailed information of subsurface structures, which will contribute to the subsequent seismic interpretation.

Full waveform inversion: early start of model building process to resolve the complex near surface model in the Exmouth sub-basin, North West Shelf Australia

2018 ◽  
Vol 58 (2) ◽  
pp. 884
Author(s):  
Lianping Zhang ◽  
Haryo Trihutomo ◽  
Yuelian Gong ◽  
Bee Jik Lim ◽  
Alexander Karvelas
Keyword(s):  
Model Building ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Surface Velocity ◽  
Image Point ◽  
Surface Model ◽  
Full Waveform Inversion ◽  
Near Surface ◽  
North West ◽  
Full Waveform

The Schlumberger Multiclient Exmouth 3D survey was acquired over the Exmouth sub-basin, North West Shelf Australia and covers 12 600 km2. One of the primary objectives of this survey was to produce a wide coverage of high quality imaging with advanced processing technology within an agreed turnaround time. The complexity of the overburden was one of the imaging challenges that impacted the structuration and image quality at the reservoir level. Unlike traditional full-waveform inversion (FWI) workflow, here, FWI was introduced early in the workflow in parallel with acquisition and preprocessing to produce a reliable near surface velocity model from a smooth starting model. FWI derived an accurate and detailed near surface model, which subsequently benefitted the common image point (CIP) tomography model updates through to the deeper intervals. The objective was to complete the FWI model update for the overburden concurrently with the demultiple stages hence reflection time CIP tomography could start with a reasonably good velocity model upon completion of the demultiple process.

Waveform tomography of field vibroseis data using an approximate 2D geometry leads to improved velocity models

Geophysics ◽  
2012 ◽  
Vol 77 (1) ◽  
pp. R33-R43 ◽  
Author(s):  
Brendan R. Smithyman ◽  
Ronald M. Clowes
Keyword(s):  
Waveform Inversion ◽  
Velocity Model ◽  
Surface Velocity ◽  
Time Shift ◽  
Full Waveform Inversion ◽  
Near Surface ◽  
Traveltime Tomography ◽  
Full Waveform ◽  
First Arrival ◽  
Waveform Tomography

Waveform tomography, a combination of traveltime tomography (or inversion) and waveform inversion, is applied to vibroseis first-arrival data to generate an interpretable model of P-wave velocity for a site in the Nechako Basin, south-central British Columbia, Canada. We use constrained 3D traveltime inversion followed by 2D full-waveform inversion to process long-offset (14.4 km) first-arrival refraction waveforms, resulting in a velocity model of significantly higher detail than a conventional refraction-statics model generated for a processing workflow. The crooked-line acquisition of the data set makes 2D full-waveform inversion difficult. Thus, a procedure that improves the tractability of waveform tomography processing of vibroseis data recorded on crooked roads is developed to generate a near-surface ([Formula: see text]) velocity model for the study area. The data waveforms are first static corrected using a time shift determined by 3D raytracing, which accounts for the crossline offsets produced by the crooked-line acquisition. The velocity model generated from waveform tomography exhibits substantial improvement when compared with a conventional refraction-statics model. It also shows improved resolution of sharp discontinuities and low-velocity regions when compared to the model from traveltime tomography alone, especially in regions where the geometry errors are moderate. Interpretation of the near-surface velocity model indicates possible subbasins in the Nechako Basin and delineates the Eocene volcanic rocks of the study area. This approach limits the ability of the full-waveform inversion to fit some propagation modes; however, the tractability of the inversion in the near-surface region is improved. This new development is especially useful in studies that do not warrant 3D seismic acquisition and processing.

Tackling cycle skipping in full-waveform inversion with intermediate data

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. R411-R427 ◽  
Author(s):  
Gang Yao ◽  
Nuno V. da Silva ◽  
Michael Warner ◽  
Di Wu ◽  
Chenhao Yang
Keyword(s):  
Objective Function ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Intermediate Data ◽  
Full Waveform ◽  
L2 Norm ◽  
Recorded Data

Full-waveform inversion (FWI) is a promising technique for recovering the earth models for exploration geophysics and global seismology. FWI is generally formulated as the minimization of an objective function, defined as the L2-norm of the data residuals. The nonconvex nature of this objective function is one of the main obstacles for the successful application of FWI. A key manifestation of this nonconvexity is cycle skipping, which happens if the predicted data are more than half a cycle away from the recorded data. We have developed the concept of intermediate data for tackling cycle skipping. This intermediate data set is created to sit between predicted and recorded data, and it is less than half a cycle away from the predicted data. Inverting the intermediate data rather than the cycle-skipped recorded data can then circumvent cycle skipping. We applied this concept to invert cycle-skipped first arrivals. First, we picked up the first breaks of the predicted data and the recorded data. Second, we linearly scaled down the time difference between the two first breaks of each shot into a series of time shifts, the maximum of which was less than half a cycle, for each trace in this shot. Third, we moved the predicted data with the corresponding time shifts to create the intermediate data. Finally, we inverted the intermediate data rather than the recorded data. Because the intermediate data are not cycle-skipped and contain the traveltime information of the recorded data, FWI with intermediate data updates the background velocity model in the correct direction. Thus, it produces a background velocity model accurate enough for carrying out conventional FWI to rebuild the intermediate- and short-wavelength components of the velocity model. Our numerical examples using synthetic data validate the intermediate-data concept for tackling cycle skipping and demonstrate its effectiveness for the application to first arrivals.

Near-surface full-waveform inversion in a transmission surface-consistent scheme

Geophysics ◽  
2020 ◽  
pp. 1-57
Author(s):  
Daniele Colombo ◽  
Ernesto Sandoval ◽  
Diego Rovetta ◽  
Apostolos Kontakis
Keyword(s):  
High Resolution ◽  
Seismic Data ◽  
Waveform Inversion ◽  
Surface Velocity ◽  
Full Waveform Inversion ◽  
Velocity Mapping ◽  
Signal To Noise ◽  
Near Surface ◽  
Velocity Modeling ◽  
Full Waveform

Land seismic velocity modeling is a difficult task largely related to the description of the near surface complexities. Full waveform inversion is the method of choice for achieving high-resolution velocity mapping but its application to land seismic data faces difficulties related to complex physics, unknown and spatially varying source signatures, and low signal-to-noise ratio in the data. Large parameter variations occur in the near surface at various scales causing severe kinematic and dynamic distortions of the recorded wavefield. Some of the parameters can be incorporated in the inversion model while others, due to sub-resolution dimensions or unmodeled physics, need to be corrected through data preconditioning; a topic not well described for land data full waveform inversion applications. We have developed novel algorithms and workflows for surface-consistent data preconditioning utilizing the transmitted portion of the wavefield, signal-to-noise enhancement by generation of CMP-based virtual super shot gathers, and robust 1.5D Laplace-Fourier full waveform inversion. Our surface-consistent scheme solves residual kinematic corrections and amplitude anomalies via scalar compensation or deconvolution of the near surface response. Signal-to-noise enhancement is obtained through the statistical evaluation of volumetric prestack responses at the CMP position, or virtual super (shot) gathers. These are inverted via a novel 1.5D acoustic Laplace-Fourier full waveform inversion scheme using the Helmholtz wave equation and Hankel domain forward modeling. Inversion is performed with nonlinear conjugate gradients. The method is applied to a complex structure-controlled wadi area exhibiting faults, dissolution, collapse, and subsidence where the high resolution FWI velocity modeling helps clarifying the geological interpretation. The developed algorithms and automated workflows provide an effective solution for massive full waveform inversion of land seismic data that can be embedded in typical near surface velocity analysis procedures.

Full-waveform inversion of multicomponent data for horizontally layered VTI media

Geophysics ◽  
2013 ◽  
Vol 78 (5) ◽  
pp. WC113-WC121 ◽  
Author(s):  
Nishant Kamath ◽  
Ilya Tsvankin
Keyword(s):  
Joint Inversion ◽  
Hessian Matrix ◽  
Waveform Inversion ◽  
Transversely Isotropic ◽  
Media Analysis ◽  
Full Waveform Inversion ◽  
S Wave ◽  
Full Waveform ◽  
The Time Domain ◽  
Vti Media

Although full-waveform inversion (FWI) has shown significant promise in reconstructing heterogeneous velocity fields, most existing methodologies are limited to acoustic models. We extend FWI to multicomponent (PP and PS) data from anisotropic media, with the current implementation limited to a stack of horizontal, homogeneous VTI (transversely isotropic with a vertical symmetry axis) layers. The algorithm is designed to estimate the interval vertical P- and S-wave velocities ([Formula: see text] and [Formula: see text]) and Thomsen parameters [Formula: see text] and [Formula: see text] from long-spread PP and PSV reflections. The forward-modeling operator is based on the anisotropic reflectivity technique, and the inversion is performed in the time domain using the gradient (Gauss-Newton) method. We employ nonhyperbolic semblance analysis and Dix-type equations to build the initial model. To identify the medium parameters constrained by the data, we perform eigenvalue/eigenvector decomposition of the approximate Hessian matrix for a VTI layer embedded between isotropic media. Analysis of the eigenvectors shows that the parameters [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] (density is assumed to be known) can be resolved not only by joint inversion of PP and PS data, but also with PP reflections alone. Although the inversion becomes more stable with increasing spreadlength-to-depth ([Formula: see text]) ratio, the parameters of the three-layer model are constrained even by PP data acquired on conventional spreads ([Formula: see text]). For multilayered VTI media, the sensitivity of the objective function to the interval parameters decreases with depth. Still, it is possible to resolve [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] for the deeper layers using PP-waves, if the ratio [Formula: see text] for the bottom of the layer reaches two. Mode-converted waves provide useful additional constraints for FWI, which become essential for smaller spreads. The insights gained here by examining horizontally layered models should help guide the inversion for heterogeneous TI media.

Application of multiparameter full-waveform inversion in Central Luconia Basin, Sarawak

2016 ◽  
Vol 4 (4) ◽  
pp. SU17-SU24 ◽  
Author(s):  
Vanessa Goh ◽  
Kjetil Halleland ◽  
René-Édouard Plessix ◽  
Alexandre Stopin
Keyword(s):  
Model Building ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Thin Layers ◽  
Earth Model ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Full Waveform ◽  
Velocity Variations ◽  
Central Luconia

Reducing velocity inaccuracy in complex settings is of paramount importance for limiting structural uncertainties, therefore helping the geologic interpretation and reservoir characterization. Shallow velocity variations due, for instance, to gas accumulations or carbonate reefs, are a common issue offshore Malaysia. These velocity variations are difficult to image through standard reflection-based velocity model building. We have applied full-waveform inversion (FWI) to better characterize the upper part of the earth model for a shallow-water field, located in the Central Luconia Basin offshore Sarawak. We have inverted a narrow-azimuth data set with a maximum inline offset of 4.4 km. Thanks to dedicated broadband preprocessing of the data set, we could enhance the signal-to-noise ratio in the 2.5–10 Hz frequency band. We then applied a multiparameter FWI to estimate the background normal moveout velocity and the [Formula: see text]-parameter. Full-waveform inversion together with broadband data processing has helped to better define the faults and resolve the thin layers in the shallow clastic section. The improvements in the velocity model brought by FWI lead to an improved image of the structural closure and flanks. Moreover, the increased velocity resolution helps in distinguishing between two different geologic interpretations.

scholarly journals A GPU implementation of the second order adjoint state theory to quantify the uncertainty on FWI results

2018 ◽  
Vol 8 (2) ◽  
Author(s):  
Sergio Alberto Abreo ◽  
Ana Beatríz Ramírez- Silva ◽  
Oscar Mauricio Reyes- Torres
Keyword(s):  
Wave Equation ◽  
Probability Distribution ◽  
Hessian Matrix ◽  
Waveform Inversion ◽  
Computational Cost ◽  
State Theory ◽  
Second Order ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Adjoint State

The second order scattering information provided by the Hessian matrix and its inverse plays an important role in both, parametric inversion and uncertainty quantification. On the one hand, for parameter inversion, the Hessian guides the descent direction such that the cost function minimum is reached with less iterations. On the other hand, it provides a posteriori information of the probability distribution of the parameters obtained after full waveform inversion, as a function of the a priori probability distribution information. Nevertheless, the computational cost of the Hessian matrix represents the main obstacle in the state-of-the-art for practical use of this matrix from synthetic or real data. The second order adjoint state theory provides a strategy to compute the exact Hessian matrix, reducing its computational cost, because every column of the matrix can be obtained by performing two forward and two backward propagations. In this paper, we first describe an approach to compute the exact Hessian matrix for the acoustic wave equation with constant density. We then provide an analysis of the use of the Hessian matrix for uncertainty quantification of the full waveform inversion of the velocity model for a synthetic example, using the 2D acoustic and isotropic wave equation operator in time.

High-resolution depth imaging of long-offset 2D data using full-waveform inversion: The Malvinas Basin, Argentina

2019 ◽  
Vol 38 (3) ◽  
pp. 220-225
Author(s):  
Laurence Letki ◽  
Mike Saunders ◽  
Monica Hoppe ◽  
Milos Cvetkovic ◽  
Lewis Goss ◽  
...  
Keyword(s):  
High Resolution ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Depth Imaging ◽  
Additional Information ◽  
Full Waveform ◽  
Seismic Image ◽  
2D Data

The Argentina Austral Malvinas survey comprises 13,784 km of 2D data extending from the shelf to the border with the Falkland Islands. The survey was acquired using a 12,000 m streamer and continuous recording technology and was processed through a comprehensive broadband prestack depth migration workflow focused on producing a high-resolution, high-fidelity data set. Source- and receiver-side deghosting to maximize the bandwidth of the data was an essential ingredient in the preprocessing. Following the broadband processing sequence, a depth-imaging workflow was implemented, with the initial model built using a time tomography approach. Several passes of anisotropic reflection tomography provided a significant improvement in the velocity model prior to full-waveform inversion (FWI). Using long offsets, FWI made use of additional information contained in the recorded wavefield, including the refracted and diving wave energy. FWI resolved more detailed velocity variations both in the shallow and deeper section and culminated in an improved seismic image.

Efficient Laplace-domain full waveform inversion using a cyclic shot subsampling method

Geophysics ◽  
2013 ◽  
Vol 78 (2) ◽  
pp. R37-R46 ◽  
Author(s):  
Wansoo Ha ◽  
Changsoo Shin
Keyword(s):  
Waveform Inversion ◽  
Computation Time ◽  
Velocity Model ◽  
Divide And Conquer ◽  
Iteration Step ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Laplace Domain ◽  
Full Waveform ◽  
Subsampling Method

Full waveform inversion is a method used to recover subsurface parameters, and it requires heavy computational resources. We present a cyclic shot subsampling method to make the full waveform inversion efficient while maintaining the quality of the inversion results. The cyclic method subsamples the shots at a regular interval and changes the shot subset at each iteration step. Using this method, we can suppress the aliasing noise present in regular-interval subsampling. We compared the cyclic method with divide-and-conquer, random, and random-in-each-subgroup subsampling methods using the Laplace-domain full waveform inversion. We found examples of a 2D marine field data set from the Gulf of Mexico and a 3D synthetic salt velocity model. In the inversion examples using the subsampling methods, we could reduce the computation time and obtain results comparable to that without a subsampling technique. The cyclic method and two random subsampling methods yielded similar results; however, the cyclic method generated the best results, especially when the number of shot subsamples was small, as expected. We also examined the effect of subsample updating frequency. The updating frequency does not have a significant effect on the results when the number of subsamples is large. In contrast, frequent subsample updating becomes important when the number of subsamples is small. The random-in-each-subgroup scheme showed the best results if we did not update the subsamples frequently, while the cyclic method suffers from aliasing. The results suggested that the cyclic subsampling scheme can be an alternative to the random schemes and the distributed subsampling schemes with a frequently changing subset are better than lumped subsampling schemes.

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