Reflectivity Inversion Research Articles

Blind spectral inversion of seismic data

AbstractReflectivity inversion is a key step in reservoir prediction. Conventional sparse‐spike deconvolution assumes that the reflectivity (reflection coefficient series) is sparse and solves for the reflection coefficients by an L1‐norm inversion process. Spectral inversion is an alternative to sparse‐spike deconvolution, which is based on the odd–even decomposition algorithm and can accurately identify thin layers and reduce the wavelet tuning effect without using constraints from logging data, from horizon interpretations or from an initial model of the reflectivity. In seismic processing, an error exists in wavelet extraction because of complex geological structures, resulting in the low accuracy of deconvolution and inversion. Blind deconvolution is an effective method for solving the problem mentioned above, which comprises seismic wavelet and reflectivity sequence, assuming that the wavelets that affect some subsets of the seismic data are approximately the same. Therefore, we combined blind deconvolution with spectral inversion to propose blind spectral inversion. Given an initial wavelet, we can calculate the reflectivity based on spectral inversion and update the wavelet for the next iteration. During the update processing, we add the smoothness of the wavelet amplitude spectrum as a regularization term, thus reducing the wavelet oscillation in the time domain, increasing the similarity between inverted and initial wavelets, and improving the stability of the solution. The blind spectral inversion method inherits the wavelet robustness of blind deconvolution and high resolution of spectral inversion, which is suitable for reflectivity inversion. Applications to synthetic and field seismic datasets demonstrate that the blind spectral inversion method can accurately calculate the reflectivity even when there is an error in wavelet extraction.

A Novel Approach for Autonomous Densely Spaced Acquisition of Buried Objects in Intertidal Environments—Field Examples From Avaldsnes, Norway

ABSTRACTUnderwater archaeology relies on expensive and time‐consuming invasive methods for identifying and excavating objects buried in the seabed or identifying layers in shallow and intertidal environments. Especially shallow and intertidal environments are challenging due to locally high levels of sedimentation that offer good conditions for preserving organic material, that is, archaeological objects, in stabile and low‐oxygen environments. We present a system capable of dense (25 cm × 25 cm) survey coverage that enables nondestructive decimetre‐scale visualization of buried objects and sedimentary layers lying in the subsurface. The system comprises an autonomous surface vehicle (ASV) equipped with a single‐channel 2D Chirp sonar. A description of the vehicle design is presented, and results from five field tests demonstrate the ability of the system to collect high‐resolution acoustic data in a variety of shallow water environments. The system shows an example of the linearized zero offset reflectivity inversion dataset, visualizing a known buried shipwreck from the medieval period in Avaldsnes, Norway. The ASV system holds global implications as it can serve as a noninvasive first‐stage survey in sensitive heritage or archaeological areas. Areas where traditional methods are challenging, or invasive methods are dissuaded.

Seismic wavelet shape-oriented reflectivity inversion method

Abstract Reflectivity inversion plays a pivotal role in reservoir prediction. Conventional sparse-spike deconvolution assumes that the reflectivity (reflection coefficient) is sparse, which is solved based on the l1 norm. However, the restricted isometry property (RIP) of wavelet matrix and seismic effective bandwidth limits the accuracy of the sparse-spike reflectivity inversion. Consequently, we investigate the connection between seismic amplitude shape and reflectivity. When the reflectivity contains more non-zero values, the wavelet bandwidth within the effective seismic data bandwidth approaches a limit corresponding to the Sinc wavelet, where the main-lobe amplitude closely approximates the reflectivity. Conversely, when the reflectivity has fewer non-zero values, a wavelet with a smaller sidelobe provides a more accurate approximation of the reflectivity. In this paper, we propose a high-resolution inversion optimization method based on joint l2 norm and l1 norm constraints. By parameter tuning, we construct the Sinc wavelet or the wavelet with a weak-sidelobe corresponding to the seismic spectrum. Subsequently, we determine the extremum to approximate the reflectivity. To mitigate the RIP condition's constraints, we employ the l2 norm to balance the l1 norm (joint constraint) by introducing l2 norm with low-pass filtering characteristics. This approach yields more accurate reflectivity estimates. By taking the extremum, this approach yields more accurate reflectivity estimates. The synthetic test demonstrates that our method achieves better reflectivity inversion accuracy compared to sparse-spike inversion with l1–l2 norm constraint. Furthermore, field tests indicate that the proposed reflectivity inversion method not only can better match the well curve, but also exhibits excellent resolution.

Seismic Blind Deconvolution Based on Self-Supervised Machine Learning

Seismic deconvolution is a useful tool in seismic data processing. Classical non-machine learning deconvolution methods usually apply quite a few constraints to both wavelet inversion and reflectivity inversion. Supervised machine learning deconvolution methods often require appropriate training labels. The existing self-supervised machine learning deconvolution methods need a given wavelet, which is a non-blind process. To overcome these issues, we propose a blind deconvolution method based on self-supervised machine learning. This method first estimates an initial zero-phase wavelet by smoothing the amplitude spectrum of averaged seismic data. Then, the loss function of self-supervised machine learning is taken as the error between the observed seismic data and the reconstructed seismic data that come from the convolution of phase-rotated wavelet and reflectivity generated by the network. We utilize a residual neural network with long skip connections as the reflectivity inversion network and a fully connected convolutional neural network as the wavelet phase inversion network. Numerical experiments on synthetic data and field data show that the proposed method can obtain reflectivity inversion results with higher resolution than the existing self-supervised machine learning method without given wavelet.

UReslham: Radar reflectivity inversion for smart agriculture with spatial federated learning over geostationary satellite observations

AbstractThe frequent occurrence of severe convective weather has certain adverse effects on the smart agriculture industry. To enhance the prediction of severe convective weather, the inversion model effectively fills radar reflectivity data gaps by leveraging geostationary satellite data, offering more comprehensive and accurate support for meteorological information in smart agriculture systems. Nevertheless, collaborative cross‐regional inversion driven by dispersed radar data faces challenges in efficiency, privacy, and model accuracy. To this end, we employ an U‐shaped residual network with an embedded light hybrid attention mechanism and utilize a federated averaging algorithm for efficient distributed training across multiple devices which could preserve the privacy of data from different locations, thereby improving inversion performance. In addition, to address the unbalanced nature of radar data, a weighted loss function is designed to enhance the model's sensitivity to high radar reflectivity. Experimental results demonstrate that the proposed model exhibits a certain level of improvement in evaluating radar reflectivity inversion performance across different thresholds compared to other models, thus substantiating the superiority of the proposed approach.

Coupled Inversion of Amplitudes and Traveltimes of Primaries and Multiples for Monochannel Seismic Surveys

Engineers need to know properties of shallow marine sediments to build piers, pipelines and even offshore windfarms. We present a method for estimating the density, P velocity and thickness of these sediments. The traveltime inversion of primary and multiple reflections enables their semiquantitative estimation in marine surveys when using a minimal acquisition system such as a monochannel Boomer. Picking errors, ambient noise and interfering events lead to significant errors in the estimates. Similar, albeit milder, instabilities occur when inverting the signal amplitudes to determine the reflectivity of the layer interfaces. In this paper, we introduce a coupling between the separate inversion of amplitudes and traveltimes to obtain a better Earth model. The P velocity shows up in two stable terms provided by the separate inversions: the acoustic impedance of shallow sediments (through the amplitudes) and the transit time across the sediment layer (through the traveltimes). We couple the two inversion engines by imposing a smoothness condition on velocity and density and thickness of the layer while keeping the impedance and traveltime constant. We thus exploit the ambiguity of the solution to introduce geological criteria and reduce the noise contribution. We validated the proposed method with synthetic and real data.

Wide‐spectrum reconstruction of a velocity model based on the wave equation reflection inversion method and its application

AbstractMost seismic data used for conventional exploration lack far‐offset signals and effective low‐frequency components. This makes it difficult for conventional full waveform inversion methods to recover the low‐wavenumber components of mid‐ and deep‐layer models. To resolve the bottleneck of ray‐theoretical reflection traveltime tomography, wave equations, such as reflection inversion methods, are receiving increasing attention. We reconstructed a wide‐spectrum velocity model based on the multiscale wave‐equation reflection inversion method for model decomposition. First, using the dynamic image warping method to obtain reflection traveltime residuals, the wave‐equation reflection traveltime inversion was used to recover the low‐wavenumber components of the background model, which also solved the cycle‐skipping problem. Second, the medium‐wavenumber component of the model is then supplemented by the reflection waveform inversion, while the reflectivity model is obtained relying on the least‐squares reverse time migration method. Based on this method, the background and perturbation models are updated alternately and iteratively. At the same time, the stratum structural tensor information was extracted using the perturbed model image to construct a preconditioned operator for the stratum structural constraint, suppress unreasonably high‐wavenumber components in the generalized gradient and improve the geological consistency of the inversion results. Testing of the model using the Sigsbee2b model and seismic field data from the East China Sea showed that, compared with the conventional reflection traveltime tomography method based on prestack depth migration, the wave‐equation reflection inversion strategy with well‐matched information from traveltimes to waveforms significantly improved the accuracy of the middle and deep velocity modelling and enhanced the imaging quality of the whole body.

Applications of high-resolution seismic frequency and phase attribute analysis techniques

Seismic prospecting for oil and gas exploration and development is limited by seismic data resolution. Improving the accuracy of quantitative interpretation of seismic data in thin layers, thereby identifying effective reservoirs and delineating favorable areas, can be a key factor for successful exploration and development. Historically, the limit of seismic resolution is usually assumed to be about 1/4 wavelength of the dominant frequency of the data in the formation of interest. Constrained seismic reflectivity inversion can resolve thinner layers than this assumed limit. This leads to a series of highresolution quantitative interpretation methods and techniques have been developed. Case studies in carbonates, clastic, and unconventional reservoirs indicate that the application of quantitative interpretation techniques such as high-resolution seismic frequency and phase attribute analysis can resolve and allow/or allow quantitative estimation of rock and fluid properties in such seismically thin layers. Band recovery using high resolution seismic processing technology can greatly improve the ability to recognize geological details such as thin layers, faults, and karst caves. Multiscale fault detection technology can effectively detect small-scale faults in addition to more readily recognized large-scale faults. Based on traditional seismic amplitude information, high-resolution spectral decomposition and phase decomposition technology expands seismic attribute analysis to the frequency and phase dimensions, boosting the interpretable geological information content of the seismic data including subsurface geological characteristics and hydrocarbon potential and thereby improving the reliability of seismic interpretation. These technologies, based on high-resolution quantitative interpretation techniques, make the identification of effective reservoirs more efficient and accurate.

Introducing Nonuniform Sparse Proximal Averaging Network for Seismic Reflectivity Inversion

We consider the problem of seismic reflectivity inversion, which pertains to the high-resolution recovery of interface locations and reflection coefficients from seismic measurements, which are vital for estimating the subsurface structure. We develop two model-based neural networks within the framework of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">deep-unfolding</i> . First, we propose a nonuniform minimax concave penalty regularized formulation for reflectivity inversion and unfold the resulting iterative algorithm into a network. Second, we propose a nonuniform sparse model that relies on a combination of regularizers (composite regularization) and develop the nonuniform sparse proximal averaging network (NuSPAN). We demonstrate the efficacy of the proposed approaches over the benchmark techniques through numerical experiments on synthetic 1-D seismic traces and 2-D wedge models. We also report validations on the 2-D Marmousi2 simulated model and 3-D real field measurements from the Penobscot 3D survey off the coast of Nova Scotia, Canada. The accuracy of the proposed approaches is higher than the state-of-the-art techniques in terms of amplitude and support recovery. Further, for Marmousi2, the proposed deep-unfolding networks result in 600× faster inference than the fast iterative shrinkage-thresholding algorithm (FISTA). In terms of combined training and inference times, the learned iterative shrinkage-thresholding algorithm (LISTA) is the fastest. The inference speed-up is significant given that the volume of data is typically large in seismic signal processing.

Multitask Deep Learning for Least-Squares Imaging: Seismic Reflectivity Inversion and Quantitative Error Analysis

Multitask Deep Learning for Least-Squares Imaging: Seismic Reflectivity Inversion and Quantitative Error Analysis

Nonstationary seismic reflectivity inversion based on prior-engaged semisupervised deep learning method

Reflectivity inversion methods based on a stationary convolution model are essential for seismic data processing. They compress the seismic wavelet, and by broadening the bandwidth of seismic data, they assist the interpretation of seismic sections. Unfortunately, they do not apply to realistic nonstationary deconvolution cases in which the seismic wavelet varies as it propagates in the subsurface. Deep learning techniques have been proposed to solve inverse problems in which networks can behave as the regularizer of the inverse problem. Our goal is to adopt a semisupervised deep learning approach to invert reflectivity when the propagating wavelet is considered unknown and time-variant. To this end, we have designed a prior-engaged neural network by unrolling an alternating iterative optimization algorithm, in which convolutional neural networks are used to solve two subproblems. One is to invert the reflectivity, and the other is to estimate the time-varying wavelets. In general, it is well known that, when working with geophysical inverse problems such as ours, one has limited access to labeled data for training the network. We circumvent the problem by training the network via a data-consistency cost function in which seismic traces are honored. Reflectivity estimates also are honored at spatial coordinates in which true reflectivity series derived from borehole data are available. The cost function also penalizes time-varying wavelets from varying abruptly along the spatial direction. Experiments are conducted to find the effectiveness of our method. We also compare our approach to a nonstationary blind deconvolution algorithm based on regularized inversion. Our findings reveal that the developed method improves the vertical resolution of seismic sections with noticeable correlation coefficient improvements over the nonstationary blind deconvolution. In addition, our method is less sensitive to initial estimates of nonstationary wavelets. Moreover, it needs less human intervention when setting parameters than regularized inversion.

Structure and Evolution of Northern Juan de Fuca Crust and Uppermost Mantle Over the Last 8 Ma From an Active‐Source Seismic Tomography Study

AbstractWe present results from a two‐dimensional wide‐angle controlled source seismic transect designed to characterize the velocity structure of the oceanic crust and uppermost mantle spanning the northern Juan de Fuca (JdF) plate from near Endeavor ridge to the Cascadia margin. Reflection and refraction travel time inversion is used to derive a tomographic Vp model of sediments, crust, and upper mantle. Velocity model results are compared to baseline reference Vp values for unaltered crustal and upper mantle rocks at temperatures assuming plate cooling. Effective medium theory is used to infer the degree of hydration of the crust and mantle. Results indicate a somewhat fractured and hydrated upper crust (≤2.5 wt% water), a near dry lower crust (≤0.7 wt%) and upper mantle (≤0.5 wt%) west of the deformation front, and an ∼75 km wide region of modestly lower velocity in the mid‐plate. Comparison with prior results from a complementary transect offshore Oregon indicates significant differences in Vp of the upper crust, with lower Vp‐inferred porosity along most of the Washington transects that may reflect different extents of fault‐related alteration and sediment burial histories. Approaching the deformation front, Washington transect Vp structure indicates dryer conditions than offshore Oregon, consistent with differences in extent of subduction bend faulting found in reflection imaging studies. On both transects, quasi‐abrupt changes in plate properties at ages of 8, 6, and 3.4/4 Ma are found. Distinct crustal accretion modes are recognized, aligning with changes in JdF plate motion and recent history of Cobb‐Eickelberg hotspot influence on crustal accretion at the JdF ridge.

An Improved Vicarious Calibration Method Based on Multi-Grayscale Targets

Vicarious calibration is a well-developed method for electro-optical (EO) sensor calibration that has been used since the early 1980s. The radiometric calibration of reflectance solar band is mainly applied to reflection inversion. In this paper, a radiometric calibration-reflectance inversion (RCRII) model is proposed as an improved vicarious calibration method. Taking the reflectance of grayscale targets with constant spectrum, suitable uniformity, and near-Lambertian characteristics as the known information, the grayscale target calibration is realized, and the initial value of calibration coefficient and offset are calculated. Then, the adjacency effect is evaluated and corrected by reflectance inversion, and the results are fed back to the calibration process to realize the iterative process of calibration inversion rescaling. The results indicate that the absolute difference between the reflectance calculated with the RCRII model and measured reflectance is less than 0.01. By comparing with Sentinel-2A images, it is cross-verified that the difference of radiance between them is within 4%, and the absolute reflectance difference is less than 0.01, in the range of 0.1~0.3 reflectance.

Sparse seismic reflectivity inversion using an adaptive fast iterative shrinkage‐thresholding algorithm

ABSTRACTSeismic reflectivity inversion using l1‐norm regularization produces sparse solutions by applying an l1‐norm constraint. The fast iterative shrinkage‐thresholding algorithm is one of the most effective methods to solve l1‐norm regularized inversion problems. A large number of iterations are commonly required in the fast iterative shrinkage‐thresholding algorithm because its solution converges slowly towards the sparse solution. To improve its convergence rate, we introduce a modifying strategy for the traditional fast iterative shrinkage‐thresholding algorithm. When implementing the soft‐thresholding operator, the thresholding value is adaptively adjusted by assigning the reciprocal of the solution in the previous iteration as a weight to the thresholding value of the current iteration. In this way, small variables in the solution produce large coefficients applied to the thresholding value, which causes small variables to quickly converge to zero. The adaptive fast iterative shrinkage‐thresholding algorithm shows significantly improved computational efficiency and accuracy compared to the traditional fast iterative shrinkage‐thresholding algorithm. It produces good results for both numerical and field examples of l1‐norm regularized seismic reflectivity inversion.

Compact Smoothness and Relative Sparsity Algorithm for High-Resolution Wavelet and Reflectivity Inversion of Seismic Data

Wavelet and reflectivity inversion (WRI) is an important issue in seismic data processing. To overcome the ill-posedness of WRI inversion with more efficient parameter selection and better lateral continuity of reflectivities, we propose a new WRI algorithm named compact smoothness and relative sparsity (CSRS) algorithm, where a normalized compact constraint and a normalized smooth regularization is proposed for the wavelet inversion, and a relative sparsity constraint is proposed for the reflectivity inversion. The proposed constraints and regularization make the parameters of WRI easy to be selected. The proposed relative sparsity constraint can lead to a reflectivity profile with good lateral continuity as it can be suitable for various seismic data with a fixed sparsity parameter. We also propose an efficient algorithm for solving corresponding WRI optimization problem. The whole WRI problem is divided into reflectivity inversion subproblem and wavelet inversion subproblem by using alternating iterative method, where the initial wavelet is estimated by smoothing the absolute amplitude spectrum of averaged seismic data. The proximal algorithm is applied to solve both reflectivity inversion subproblem and wavelet inversion subproblem. By replacing Toeplitz matrix multiplication with fast Fourier transform (FFT) and using compact wavelet, our algorithm can be efficient for 3D seismic data. The numerical examples on 2D synthetic data, 2D offshore field data and 3D onshore field data demonstrate that, compared to Toeplitz-sparse matrix factorization (TSMF) algorithm, the CSRS algorithm with fixed default parameters can get high-resolution reflectivities with better lateral continuity, and requires much less computational time.

Geoacoustic Estimation of the Seafloor Sound Speed Profile in Deep Passive Margin Setting Using Standard Multichannel Seismic Data

Seafloor geoacoustic properties are important in determining sound propagation in the marine environment, which broadly affects sub-sea activities. However, geoacoustic investigation of the deep seafloor, which is required by the recent expansion of deep-water operations, is challenging. This paper presents a methodology for estimating the seafloor sound speed, c0, and a sub-bottom velocity gradient, K, in a relatively deep-water-compacting (~1000 m) passive-margin setting, based on standard commercial 2D seismic data. Here we study the seafloor of the southeastern Mediterranean margin based on data from three commercial seismic profiles, which were acquired using a 7.2 km-long horizontal receiver array. The estimation applies a geoacoustic inversion of the wide-angle reflections and the travel times of the head waves of bending rays. Under the assumption of a constant positive K, the geoacoustic inversion converges to a unique set of parameters that best satisfy the data. The analysis of 24 measurement locations revealed an increase in the average estimates of c0 from 1537 ± 13 m s−1 to 1613 ± 12 m s−1 for seafloor depths between ~1150 m and ~1350 m. K ranged between 0.75 and 0.85 m s−1 with an average of 0.80 ± 0.035 s−1. The parameters were consistent across the different locations and seismic lines and they match the values that were obtained through depth-migration-velocity analysis and empiric relations, thereby validating our estimation methodology.

Switchable electric polarization of phosphorene in mixed dimensional van der Waals heterostructure

Switchable electric polarization in semiconductors has promising applications in nanoelectronic and optoelectronic devices. Here, we propose a type of two-dimensional (2D) polarization switchable by angstrom-scale position shifts of phosphorene on PbTe. As a homo-atomic analogue to the 2D ferroelectric monolayer GeS, non-ferroelectric phosphorene acquires in-plane electric polarization by breaking the in-plane and out-of-plane symmetry via proximity of phosphorene to PbTe compound in the mixed dimensional vertical P/PbTe heterostructure. We demonstrate via first-principles calculations the asymmetric charge distribution on the two P sublattices in phosphorene, rendered by the alternative cation and anion chains in PbTe substrate that breaks the glide reflection symmetry and inversion symmetry of phosphorene, leading to the in-plane polarization. It is found that the in-plane polarization in phosphorene can be significantly modulated by interlayer strain and external electric field. More interestingly, the in-plane electric polarization switches sign when phosphorene shifts on PbTe substrate by an interval between the cation and anion chains with a low transition barrier of a few meV/P-atom. Our study demonstrates that the switching of 2D in-plane polarization via spatial shifting in phosphorene-based van der Waals heterostructures, with promising applications in 2D polarization functionalized nanoelectronic and optoelectronic devices.

TESTING OF AN OPTIMIZATION ALGORITHM FOR AVAZ INVERSION ON SYNTHETIC DATASET

In the paper, we study an optimization algorithm for a nonlinear AVAZ inversion of PP reflections from an anisotropic media. The algorithm is based on the exact formulas for PP wave reflection coefficient for an anisotropic HTI medium and could be applied in the case of strong-contrast boundary and various anisotropy degree. Algorithm testing on synthetic dataset for radial survey system shows that estimation of anisotropy parameters γ , δ and HTI medium symmetry axis is robust in the case of signal to noise ratio ≥ 5. For estimation of parameter ε far offset data is needed.

Reflectivity decomposition: Theory and application

Sparse reflectivity inversion of processed reflection seismic data is intended to produce reflection coefficients that represent boundaries between geologic layers. However, the objective function for sparse inversion is usually dominated by large reflection coefficients, which may result in unstable inversion for weak events, especially those interfering with strong reflections. We have determined that any seismogram can be decomposed according to the characteristics of the inverted reflection coefficients that can be sorted and subset by magnitude, sign, and sequence, and new seismic traces can be created from only reflection coefficients that pass the sorting criteria. We call this process reflectivity decomposition. For example, original inverted reflection coefficients can be decomposed by magnitude, large ones removed, the remaining reflection coefficients reconvolved with the wavelet, and this residual reinverted, thereby stabilizing inversions for the remaining weak events. As compared with inverting an original seismic trace, subtle impedance variations occurring in the vicinity of nearby strong reflections can be better revealed and characterized when only the events caused by small reflection coefficients are passed and reinverted. When we apply reflectivity decomposition to a 3D seismic data set in the Midland Basin, seismic inversion for weak events is stabilized such that previously obscured porous intervals in the original inversion can be detected and mapped, with a good correlation to the actual well logs.

A history of tunnels and using active seismic methods to find them

The modern use of clandestine tunnels has antagonized military and law enforcement agencies alike over the past 50 years, not only in their simplicity and effectiveness, but also in the challenges of defending against them. Likewise, geophysicists have been confounded, finding what should be a straightforward target on paper — detecting an anomaly with often vastly different physical properties than its surroundings — a much more difficult task than models would suggest. We have evaluated half a century of applied seismic investigation, gaining a history of the use of active seismic methods to detect subterranean tunnels in war zones, along borders, and around facility perimeters. Previously published studies using a variety of seismic methods such as reflection, refraction, surface waves, diffraction, resonance, and full-waveform inversion were aggregated to serve as a reference for void and tunnel detection-related research and to show the progression of the methods used over time.