Papers by Mostafa Naghizadeh
Summary Full-waveform inversion (FWI) is a nonlinear data fitting procedure based on seismic data... more Summary Full-waveform inversion (FWI) is a nonlinear data fitting procedure based on seismic data to derive a accurate velocity model. With the increasing demand for high resolution images in complex geological settings, the importance of improvements in acquisition and inversion become more and more critical. However, these improvements will be obtained at high computational cost, as a typical marine survey contains thousands of shot and receiver positions, and FWI needs several passes through massive seismic data. Computational cost of FWI will grow exponentially as the size of seismic data and desired resolution increase. In this paper we present a modified Gauss-Newton (GN) method that borrows ideas from compressive sensing, where we compute the GN updates from a few randomly selected sequential shots. Each subproblem is solved by using a sparsity promoting algorithm. With this approach, we dramatically reduce the size and hence the computational costs of the problem, whilst we ...
Linear prediction filters in the f-x domain are widely used to interpolate regularly sampled data... more Linear prediction filters in the f-x domain are widely used to interpolate regularly sampled data. In this paper, we study the problem of reconstructing irregularly missing data on a regular grid using linear prediction filters. We propose a two-stage algorithm. First, we reconstruct the unaliased part of the data spectrum using a Fourier method (Minimum Weighted Norm Interpolation). Then, prediction filters for all the frequencies are extracted from the reconstructed low frequencies. The latter is implemented via a Multi-Step Auto-Regressive (MSAR) algorithm. Finally, these prediction filters are used to reconstruct the complete data in the f-x domain. The applicability of the proposed method is examined using synthetic and field data examples.
alias hierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data
Le projet Metal Earth : une initiative de recherche en exploration minérale en 4D
Summary A methodology for the reconstruction of nonuniformly sampled, aliased data is introduced.... more Summary A methodology for the reconstruction of nonuniformly sampled, aliased data is introduced. First, the low frequency (nonaliased) part of the data is reconstructed. Using data inside the reconstructed band, a Multi-Step Auto-Regressive (MSAR) operator extracts the ensemble of prediction filters that are used to reconstruct the high frequency portion of the data. The applicability of the MSAR method to synthetic and real seismic data is discussed.
The time-lapse imaging problem is addressed using least-squares shot-profile migration. The proce... more The time-lapse imaging problem is addressed using least-squares shot-profile migration. The procedure for designing forward (de-migration) and adjoint (migration) operators of shot-profile wave-equation migration algorithm is explained. The least-squares optimization of the problem is achieved using conjugate gradients. Two main approaches for least-squares shot-profile migration of time-lapse data namely, inversion of difference data and joint inversion, are discussed. Some practical considerations for performance of least-squares shot-profile migration are investigated using synthetic data examples. Also, a synthetic data examples is provided for examining the time-lapse shot-profile migration of difference data.
Summary We introduce a strategy for beyond-alias interpolation of seismic data using singular spe... more Summary We introduce a strategy for beyond-alias interpolation of seismic data using singular spectrum analysis. First, in the frequency-space (f-x) domain, a Hankel matrix is built from the spatial samples of the low frequencies. To perform interpolation at each specific frequency, the spatial samples are interlaced with zero samples. Then, another Hankel matrix is built form the zero-interlaced vector of data in a given frequency. Next, the rank-reduced eigenstate of the Hankel matrix at low frequencies is used for beyond-alias conditioning of the Hankel matrix at given frequency. Finally, an anti-diagonal summation of the conditioned Hankel matrix gives the final interpolated data. Synthetic and real data examples are provided to examine the performance of the proposed interpolation method.
Interpolation of Nonstationary Seismic Records using a Fast Generalized Fourier Transform
Summary We introduce a fast and efficient method for the interpolation of nonstationary seismic d... more Summary We introduce a fast and efficient method for the interpolation of nonstationary seismic data. The method uses the fast generalized Fourier transform FGFT to identify the space-wavenumber evolution of nonstationary spatial signals at each temporal frequency. The nonredundant nature of FGFT renders a big computational advantage to this interpolation method. A least-squares fitting scheme is used next to retrieve the optimal FGFT coefficients representative of the ideal interpolated data. For randomly sampled data on a regular grid, we seek a sparse representation of FGFT coefficients to retrieve the missing samples. In addition, to interpolate the regularly sampled seismic data at a given frequency, we use a mask function derived from the FGFT coefficients of the low frequencies. Synthetic and real data examples can be used to examine the performance of the method.
First International Meeting for Applied Geoscience & Energy Expanded Abstracts
Three seismic profiles, acquired as part of the Metal Earth project, were used to image the easte... more Three seismic profiles, acquired as part of the Metal Earth project, were used to image the eastern Sudbury structure and its surrounding terranes. The seismic data processing flow was tailored for an optimal binning of crooked lines, correcting refraction statics, attenuating random and coherent noises, and pre-stack time migration of the seismic records. The final migrated seismic sections exhibit relatively undisturbed and shallowly south-dipping units at the North Range and thrust faulting and overturning at the South Range of the Sudbury structure. The Grenville front was distinguished by a steeply south-dipping package of reflections. The depths of the Huronian metasedimentary units were estimated to be approximately 1.5 and 3 km at the north and south of the Sudbury structure, respectively. The interpretations of this study on the eastern Sudbury structure were consistent with the Lithoprobe seismic reflection results on the central and southwestern part of the Sudbury structure.
Generalized cross-dip moveout correction of crooked 2D seismic reflection surveys
GEOPHYSICS
In hard rock settings, reflection seismic surveys are often acquired on crooked roadways. Acquisi... more In hard rock settings, reflection seismic surveys are often acquired on crooked roadways. Acquisition geometry-related noise resulting from these crooked profiles obscures the final image in places where there are crossline dipping reflectors. This noise can be prevented with cross-dip moveout (CDMO) corrections. The conventional practice is to apply corrections on straight processing lines; however, this aggravates reflection duplication and stretching artifacts. We have adopted an efficient method for CDMO correction that operates on any common midpoint (CMP) binning geometry. Our method suppresses reflection duplication in high-fold CMP bins. The strike and dip of the reflectors are decomposed into two horizontal orthogonal components and input into a 3D traveltime equation. Using a synthetic model, a processing workflow was developed to locally apply these generalized CDMO corrections. This workflow was then applied to a seismic profile acquired over the Larder-Lake Cadillac Def...
Geophysical Prospecting
In 2017, the Metal Earth multidisciplinary exploration project acquired a total of 921 km of regi... more In 2017, the Metal Earth multidisciplinary exploration project acquired a total of 921 km of regional deep seismic reflection profiles and 184 km of high-resolution seismic reflection profiles in the Abitibi and Wabigoon greenstone belts of the Superior province of Canada. The Abitibi belt hosts several world-class mineral deposits, whereas the Wabigoon has sparse economic mineral deposits. Two high-resolution surveys in the Swayze area, a poorly endowed part of the western Abitibi greenstone belt, served as pioneer surveys with which to better understand subsurface geology and design a strategy to process other surveys in the near future. Swayze seismic data were acquired with crooked survey geometries along roads. Designing an effective seismic processing flow to address these geometries and complex geology required straight common midpoint lines along which both two-dimensional prestack dipmoveout correction and poststack migration processing were applied. The resulting seismic sections revealed steeply dipping and subhorizontal reflections; some correlate with folded surface rocks. An interpreted fault/deformation zone imaged in Swayze north would be a target for metal endowment if it extends the Porcupine-Destor structure. Because of the crooked line geometry of the surveys, two-dimensional /three-dimensional prestack time migration and swath three-dimensional processing were tested. The prestack time migration algorithm confirmed reflections at the interpreted base of the Abitibi greenstone belt. The swath three-dimensional images provided additional spatial details about the geometries of some reflections, but also had less resolution and did not detect many reflectors observed in two dimensions. Geological contacts between felsic, mafic and ultramafic greenstone rock layers are thought the main cause of reflectivity in the Swayze area.
Minerals
The Metal Earth project acquired 927 km of deep seismic reflection profiles from August to Novemb... more The Metal Earth project acquired 927 km of deep seismic reflection profiles from August to November of 2017. Seismic data acquired in this early stage of the Metal Earth project benefited greatly from recent advances in the petroleum sector as well as those in mineral exploration. Vibroseis acquisition with receivers having a 5 Hz response (10 dB down) generated records from a sweep signal starting at 2 Hz, sweeping up to 150 Hz or 200 Hz. Not only does this broadband signal enhance reflections from the deepest to the shallowest crust, but it also helps the use of full waveform inversion (e.g., to mitigate cycle-skipping) and related techniques. Metal Earth regional-scale transects using over 5000 active sensors target mineralizing fluid pathways throughout the crust, whereas higher spatial-resolution reflection and full-waveform surveys target structures at mine camp scales. Because Metal Earth was proposed to map and compare entire Archean ore and geologically similar non-ore syst...
SEG Technical Program Expanded Abstracts 2011
Scattering theory is a framework from within which a range of inversion methods suited to the tim... more Scattering theory is a framework from within which a range of inversion methods suited to the time-lapse/4D seismic reflection problem may be derived. A consistently posed linear inverse scattering treatment of time-lapse difference data, for instance, provides a framework both for deriving algorithms for imaging of regions of 4D structural change, and for explaining their behavior. Amongst the many implementations of linearized inverse scattering that could in principle be applied to difference data, a recent least-squares, shot-profile methodology provides the additional wherewithal to regularize the imaging problem, which may be a useful property when coping with the various repeatability issues particular to 4D. Synthetic testing demonstrates the use of difference data, under a small 4D change/small contrast assumption, to determine regions of time-lapse variation.
Four-dimensional f-k Interpolation of Wide Azimuth Towed Streamer Data
72nd EAGE Conference and Exhibition incorporating SPE EUROPEC 2010, 2010
SUMMARY We extend the frequency-wavenumber (f-k) interpolation method introduced by Gulunay (2003... more SUMMARY We extend the frequency-wavenumber (f-k) interpolation method introduced by Gulunay (2003) into a Four-Dimensional (4D) application. The 4D f-k interpolation is used to interpolate between streamers and shots in Wide Azimuth Towed Streamer (WATS) data. The f-k interpolation method utilizes the low frequency non-aliased portion of data to interpolate aliased high frequencies. Therefore, it can handle highly aliased spatial domains. In addition, the multidimensional nature of the 4D f-k interpolator extracts information from non-aliased spatial axes to interpolate highly aliased axes correctly. Synthetic and real data examples are provided to examine the performance of the proposed interpolation scheme.
fx Gabor Seismic Data Reconstruction
71st EAGE Conference and Exhibition incorporating SPE EUROPEC 2009, 2009
We introduce an fx Gabor reconstruction algorithm that can regularize seismic data in the presenc... more We introduce an fx Gabor reconstruction algorithm that can regularize seismic data in the presence of strong variations of dip. The available data in the fx domain are modeled via a Gabor discrete expansion. The coefficients of the Gabor expansion are
71st EAGE Conference and Exhibition incorporating SPE EUROPEC 2009, 2009
The multidimensional discrete sampling theory is investigated from the interpolation point of vie... more The multidimensional discrete sampling theory is investigated from the interpolation point of view. We define a sampling operator and its associated wavenumber signature, the scaling function, and investigate sampling conditions for optimal band-limited Fourier reconstruction. We present a case where a 2D signal (band-limited in one spatial dimension) can be recovered by designing an acquisition grid that minimizes the mixing between the unknown spectrum of the well-sampled signal and aliasing artifacts. The analysis can be easily extended to higher dimensions and used to define potential strategies for acquisition-guided Fourier reconstruction.
72nd EAGE Conference and Exhibition incorporating SPE EUROPEC 2010, 2010
We propose a robust interpolation scheme for aliased regularly sampled seismic data that uses the... more We propose a robust interpolation scheme for aliased regularly sampled seismic data that uses the curvelet transform. In a first pass, the curvelet transform is used to compute the curvelet coefficients of the aliased seismic data. The aforementioned coefficients are divided into two groups of scales: alias-free and alias-contaminated scales. The alias-free curvelet coefficients are upscaled to estimate a mask function that is used to constrain the inversion of the aliascontaminated scale coefficients. The mask function is incorporated into the inversion via a minimum norm least squares algorithm that determines the curvelet coefficients of the desired alias free data. Once the alias-free coefficients are determined, the curvelet synthesis operator is used to reconstruct seismograms at new spatial positions. The proposed method can be used to reconstruct both regularly and irregularly sampled seismic data. A synthetic data example is used to illustrate the performance of the proposed curvelet interpolation method.
73rd EAGE Conference and Exhibition incorporating SPE EUROPEC 2011, 2011
We propose a curvelet domain strategy to subtract ground-roll from seismic records. We built curv... more We propose a curvelet domain strategy to subtract ground-roll from seismic records. We built curvelet domain mask functions from higher scales which are groud-roll-free and project them to the lower scales that are contaminated with ground-roll energy. The mask function helps to preserve the reflected energy and eliminate the ground-roll energy. A synthetic seismic data example is provided to analyze the performance of the proposed method.
73rd EAGE Conference and Exhibition incorporating SPE EUROPEC 2011, 2011
We propose a fast and efficient method for the interpolation of nonstationary seismic data. The m... more We propose a fast and efficient method for the interpolation of nonstationary seismic data. The method uses the fast generalized Fourier transform FGFT to identify the space-wavenumber evolution of nonstationary spatial signals at each temporal frequency. The nonredundant nature of FGFT renders a big computational advantage to this interpolation method. A least-squares fitting scheme is used next to retrieve the optimal FGFT coefficients representative of the ideal interpolated data. For randomly sampled data on a regular grid, we seek a sparse representation of FGFT coefficients to retrieve the missing samples. A synthetic seismic data example was used to examine the performance of the method.
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Papers by Mostafa Naghizadeh