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SUMMARY Accurate delineation of salt body shapes is critical for hydrocarbon exploration. Various imaging methods based on seismic data have been developed. Due to the density contrast between salt and sedimentary rocks, gravity data have also been used as a de-risking tool to constrain the salt body shapes. However, quantifying uncertainties of the salt body shapes recovered from gravity data remains underexplored. Our goal is to understand and quantify how different constraints affect uncertainties of the salt body shapes reconstructed from gravity data. We adopt a trans-dimensional Markov chain Monte Carlo (MCMC) approach to explore the uncertainties. To address the computational challenges with MCMC sampling, we resort to two methods: sparse geometry parametrization and randomized parallel tempering. The first uses a set of simple geometries (e.g. ellipses) to approximate the complex shapes of salt bodies, greatly reducing the number of parameters to be sampled and making the MCMC approach computationally feasible. The second serves to further improve the acceptance ratio and computational efficiency. To quantify the uncertainties of the recovered salt body shapes, we design several scenarios to simulate different constraints on the top boundary of salt bodies from seismic imaging. We develop a new method to impose structural constraints on the top boundaries of salt bodies. This new method combines a set of fixed ellipses with randomly sampled ellipses through a concave hull. The results from different scenarios are compared to understand how uncertainties are reduced when stronger constraints are imposed. In addition, to make our uncertainty quantification results more relevant for practitioners, we propose to compute the salt probability models which show the spatial distribution of probabilities of salt materials at each cell. Finally, we investigate the effect of an uncertain salt density on the salt body reconstruction and the case of depth-varying densities in the sedimentary background. We apply our methods to the modified 2-D SEG-EAGE and Sigsbee salt models and quantify the uncertainties of the recovered salt body shapes in different scenarios. Our results highlight the importance of properly interpreting the uncertainty estimates in light of prior information and information content in the data.

For any given rock-physics model, knowledge of correlations among its inputs helps to define geologically and physically meaningful and informed models for a given problem. These informed models can, in turn, reduce the uncertainty in forward and inverse problems. We use a Bayesian framework to identify such correlations among inputs of two rock-physics models. That framework makes use of velocity and porosity measurements on both dry and brine-saturated carbonate samples. Two inclusion-based rock-physics models, the self-consistent approximation and the differential effective medium model, are analyzed along with these data to identify the underlying correlations. To do so, the posterior distribution must be evaluated, which is based on a prior model and the calculated likelihood function. Exhaustive sampling of the posterior is convenient in this case because relatively few input parameters to consider. Results are multi-variate histograms that indicate maximum a posteriori values of the inputs. Correlations among the inputs become evident when the Bayesian analysis is repeated many times with different prior models. These correlated values provide the inputs to optimized maximum a posteriori models. The correlations identified for the two rock-physics models under study should be used in relevant applications. Finally, all rock-physics models, along with an appropriate data set, should be examined in a similar Bayesian framework.

Commercial and low-saturation gas (also called paleoresidual gas [PRG]) show similar strong amplitude signatures on P-wave seismic data. This poses an exploration risk in gas reservoir regions. However, density correlates inversely with gas saturation and can differentiate a zone of full gas saturation from PRG. This can improve the chances of success in terms of predrill prediction of gas saturation. Amplitude-variation-with-offset (AVO) inversion using prestack seismic data is the most commonly used technique that can estimate elastic parameters such as P-wave velocity, S-wave velocity, and density. Out of these three parameters, extracting density from seismic data is the most challenging due to its weak sensitivity to seismic reflection amplitude and the lack of good quality seismic data at far offsets. However, with recent improvements in seismic data acquisition and processing technology, which produces reliable AVO gathers, density estimates have improved. This requires that strong density sensitivity to AVO exists. Note that multiple density models may fit the data equally well. Therefore, quantifying uncertainty is crucial for interpretation and risk assessment. We apply a recently developed stochastic approach based on the Bayesian framework to solve the problem in a transdimensional framework, where the number of model parameters is treated as a variable and estimated along with the elastic properties. We use the reversible jump Hamiltonian Monte Carlo (RJHMC) algorithm to sample models from a variable dimensional model space and obtain a globally optimum model and uncertainty estimates. We use a synthetic and good quality real data set from Columbus Basin in Trinidad, which has a proven gas reservoir, to demonstrate the algorithm. The RJHMC results calibrate well with the logs and show the areal extents of the density anomalies within the 3D volume.

Full-waveform inversion (FWI) is a popular technique to obtain high-resolution estimates of earth model parameters using all information present in seismic data. Thus, it can provide important information about the subsurface. The FWI algorithm is formulated as a data-fitting minimization problem that iteratively updates an initial velocity model using the gradient of the misfit until an acceptable match is obtained between the real and synthetic data under a tolerance level based on noise in the data. The inversion is computationally expensive and can converge to a local minimum if the starting model used is not close enough to an optimal model. Here, we propose an alternative approach using a combination of machine learning and the physics of the forward model. Unlike conventional supervised machine learning, known answers are not required to train our network. The shot gathers are input to a convolutional neural network-based autoencoder, the output of which is used as the velocity model that is used to compute synthetic seismograms. The synthetic data are compared against observed input data, and the misfit is estimated. The gradient of the misfit with respect to the velocity model parameters is calculated using the adjoint state method. The adjoint state gradient is then used to update the network weights using the automatic differentiation technique. Once the misfit term converges, the neural network can generate velocity models consistent with the observed data. We observe that the neural network can capture spatial correlations at different scales and thus can introduce regularization in our inverse problem. Experiments with the Marmousi model and SEG Advanced Modeling Corporation Phase 1 salt model suggest that the proposed method can overcome local minima, requires no starting model, and produces robust results in the presence of noise and complex salt body structures.

SUMMARY The converted wave data (P-to-s or S-to-p), traditionally termed as receiver functions, are often contaminated with noise of different origin that may lead to the erroneous identification of phases and thus influence the interpretations. Here, we utilize an unsupervised deep learning approach called Patchunet to de-noise the converted wave data. We divide the input data into several patches, which are input to the encoder and decoder network to extract some meaningful features. The method de-noises an image patch by patch and utilizes the redundant information on similar patches to obtain the final de-noised results. The method is first tested on a suite of synthetic data contaminated with various amounts of Gaussian and realistic noise and then on the observed data from three permanent seismic stations: HYB (Hyderabad, India), LBTB (Lobatse, Botswana, South Africa) and COR (Corvallis, Oregon, USA). The method works very well even when the signal-to-noise ratio is poor or with the presence of spike noise and deconvolution artifacts. The field data demonstrate the effectiveness of the method for attenuating the random noise especially for the mantle phases, which show significant improvements over conventional receiver function based images.

Elastic full waveform inversion can construct highresolution P-wave and S-wave velocity models in complex geological settings. However, several factors make the application of elastic FWI challenging. Elastic FWI is prone to the problem of cycle skipping phenomenon when low-frequency in the data are unavailable and the starting model is inaccurate. Multiparameter FWI also suffers from crosstalk issue due to coupling between different model parameters. We extend our physics guided deep convolutional autoencoder network to the problem of multiparameter elastic full waveform inversion. Our training is completely unsupervised. Our autoencoder which is composed of convolutional neural networks (CNNs) maps the multicomponent shot gathers to the target velocity models. The output from the network is given as input to partial differential equations which generate synthetic data. We compare the observed data against the synthetic data and then compute the misfit. We calculate the gradient of the misfit with respect to the model parameters and then use it to update the neural network weights. We note that the neural network generates velocity models that explains the observed data. We demonstrate that the network can introduces regularization in the inversion and overcome issues related to cycle skipping and parameter crosstalks. A toy model, the marmousi model and left part of the BP salt model are used to demonstrate the effectiveness of the proposed approach. Finally, we provide an explanation of the efficacy of the proposed approach by examining the nature of the loss landscape of neural networks based full waveform inversion.

SUMMARY Subsurface velocity model building is a crucial step for seismic imaging. It is a challenging problem for conventional methods such as full-waveform inversion (FWI) and wave equation migration velocity analysis (WEMVA), due to the highly nonlinear relationship between subsurface velocity values and seismic responses. In addition, traditional FWI and WEMVA methods are often computationally expensive. In this paper, we propose to apply a deep learning technique to construct subsurface velocity models automatically from common-image gather (CIG) volumes. In our method, pairs of synthetic velocity models and CIG volumes are generated to train a convolutional neural network. Our proposed network achieves promising results on different synthetic data sets. The training performance of several commonly used loss functions is also studied.

We consider the problem of image-domain least-squares migration (LSM) based on efficiently constructing the Hessian matrix with sparse beam data. Specifically, we use the ultra-wide-band phase space beam summation method, in which beams are used as local basis functions to represent scattered data collected at the surface. The beam domain data are sparse. One can identify seismic events with significant contributions so that only beams with nonnegligible amplitudes need to be used to image the subsurface. In addition, due to the beams’ spectral localization, only beams that pass near an imaging point need to be taken into account. These two properties reduce the computational complexity of computing the Hessian matrix — an essential ingredient for LSM. As a result, we can efficiently construct the Hessian matrix based on analyzing the sparse beam domain data.

Geophysical phenomena like volcanic eruptions, tectonic plate movements, and earthquakes directly influence the gravitational pull in the region of occurrence. Measurement of anomalies in the gravitational pull has been a useful technique in analyzing such activities quantitatively. Gravitational variations also carry indications of the presence of the earth’s minerals and other such useful resources. In this paper, a novel on-chip micro-cantilever-based optical gravimeter has been proposed for the precise measurement of gravitational changes. Simulations comprising both three-dimensional full-vector finite element and finite difference time domain methods have been carried out for analyses, demonstrating an extensive reading range of 6000 mGal with a resolution of $1.17~\mu $ Gal and sensitivity of $1~\mu $ Gal/ $\sqrt {Hz}$ at 1 Hz.

Identifying thinly bedded reservoirs is important in exploration, appraisal, and development. The thin beds that we are referring to are of meter scale or less. Conventional seismic attributes are not able to resolve thin-bed effects. A new frequency-dependent amplitude variation with offset (FAVO) seismic attribute is developed for the prediction of thin beds. It is based on seismic wave scattering theory for vertically inhomogeneous media, in which the seismic response from a laterally homogeneous interval is represented by the Born series. The Born series characterizes the P-P and P-SV wave reflections, transmissions, and interbed multiples within the target interval with different order terms. The newly derived attribute corresponds to the second-order term of the Born series, in which P-S wave reflection and transmission energy is taken into consideration, and it is called the second-order FAVO gradient attribute. In a thinly bedded interval where sand/shale interfaces are abundant, the P-SV wave mode conversions are numerous. This leads to a strong second-order FAVO gradient attribute response compared to that of a blocky sand, silt, or shale interval under the assumption that there is no significant rock- and fluid-property differences between the intervals. Therefore, the new seismic attribute has the potential to be a thin-bed interval indicator. We have adopted a strategy to estimate the new attribute using conventional P-wave seismic data. The attribute is extracted from seismic data at the frequency range at which the second-order scattering effect is the most prominent. Synthetic and field data examples from offshore Trinidad are studied to demonstrate the second-order scattering effect and the potential usage of the second-order FAVO attribute for thin-bed reservoir characterization.

Migration techniques are an integral part of seismic imaging workflows. Least-squares reverse time migration (LSRTM) overcomes some of the shortcomings of conventional migration algorithms by compensating for illumination and removing sampling artifacts to increase spatial resolution. However, the computational cost associated with iterative LSRTM is high and convergence can be slow in complex media. We implement prestack LSRTM in a deep-learning framework and adopt strategies from the data science domain to accelerate convergence. Our hybrid framework leverages the existing physics-based models and machine-learning optimizers to achieve better and cheaper solutions. Using a time-domain formulation, we find that minibatch gradients can reduce the computation cost by using a subset of total shots for each iteration. The minibatch approach not only reduces source crosstalk, but it is also less memory-intensive. Combining minibatch gradients with deep-learning optimizers and loss functions can improve the efficiency of LSRTM. Deep-learning optimizers such as adaptive moment estimation are generally well-suited for noisy and sparse data. We compare different optimizers and determine their efficacy in mitigating migration artifacts. To accelerate the inversion, we adopt the regularized Huber loss function in conjunction. We apply these techniques to 2D Marmousi and 3D SEG/EAGE salt models and find improvements over conventional LSRTM baselines. Our approach achieves higher spatial resolution in less computation time measured by various qualitative and quantitative evaluation metrics.

Traditional full-waveform inversion (FWI) methods only render a “best-fit” model that cannot account for uncertainties of the ill-posed inverse problem. Additionally, local optimization-based FWI methods cannot always converge to a geologically meaningful solution unless the inversion starts with an accurate background model. We seek the solution for FWI in the Bayesian inference framework to address those two issues. In Bayesian inference, the model space is directly probed by sampling methods such that we obtain a reliable uncertainty appraisal, determine optimal models, and avoid entrapment in a small local region of the model space. The solution of such a statistical inverse method is completely described by the posterior distribution, which quantifies the distributions for parameters and inversion uncertainties. To efficiently sample the posterior distribution, we introduce a sampling algorithm in which the proposal distribution is constructed by the local gradient and the diagonal approximate Hessian of the local log posterior. Our algorithm is called the gradient-based Markov chain Monte Carlo (GMCMC) method. The GMCMC FWI method can quantify inversion uncertainties with estimated posterior distribution given sufficiently long Markov chains. By directly sampling the posterior distribution, we obtain a global view of the model space. Theoretically speaking, statistical assessments do not depend on starting models. Our method is applied to the 2D Marmousi model with the frequency-domain FWI setting. Numerical results suggest that our method can be readily applied to 2D cases with affordable computational efforts.

A novel design of multiple-slotted 1-D photonic crystal nanobeam cavity has been proposed in this article. The design utilizes the benefits of high optical density offered by the narrow slots as well as improved light–matter interaction and, thereby, sensitivity due to the multiple slots. Different design parameters, such as width, separation, and number of slots, and number and sizes of holes, are optimized for achieving better quality factor (QF) and sensitivity simultaneously. A QF and sensitivity using two or three number of slots have been found in the order of $3.2\times 10^{7}$ and 1016 nm/refractive index unit (RIU) or $1.26\times 10^{7}$ and 1049 nm/RIU, respectively. Tolerance of the design for possible random fabrication imperfections has also been evaluated. It depicts that the structure is tolerant up to 20-nm random deviations, with low impact to sensitivity, albeit at a moderate cost to the QF for deviations above 10 nm. Finally, the optimized design has been used in a theoretical study for analyzing the applicability of the sensor in assessing glucose levels in human urine samples. The theoretical results suggest that the proposed design can be utilized for realizing efficient industrial and bimolecular sensors.

In the paper, a two dimensional slotted photonic crystal cavity (2D-SPCC) has been designed and optimized for the application of sensing. The optimized 2D-SPCC has been incorporated in a silicon cantilever to form a nano-opto-electro-mechanical system (NOEMS) for sensing the physical parameters like - force, displacement and strain. An applied force at the cantilever-tip generates strain which results in deformation of the SPCC parameters like slot-width. This structural change in the 2D-SPCC changes the optical behavior of the device, which can be sensed, and thus operate as a physical sensor. Resonant wavelengths of the SPCC are determined for different length and breadth of the cantilever. The results show a linear dependence of the resonant wavelength with the change in the physical parameters. The 2D-SPCC has a high quality factor and sensitivity of $\sim\!9 \, \times\, 10^6$ and 4.2 nm $\mu$ N respectively, due to which the minimum detectable force, displacement and strain for the proposed design are found as 0.0202 $\mu$ N, 0.090 707 $\mu$ m and 0.019 979 respectively for a cantilever of length 40 $\mu$ m and breadth 20 $\mu$ m. Hence, the proposed NOEMS sensor is expected to be highly relevant for different industrial applications.

An optical notch filter has been designed based on a silicon-slab Photonic Crystal (PhC) W1 waveguide. Birefringence originated usual performance degradation of notch filters has been eliminated by optimizing the slab-thickness and radius of the holes to embed a TE pass filter in the same structure. This resulted in TE and TM transmittances as $\approx$ $\mathrm{-1.5}$ dB and $\approx$ $\mathrm{-28}$ dB respectively at the wavelength $\mathrm{1550}$ nm. Structural parameters of the device are represented by normalizing them with respect to the lattice constant such that the structure can be scaled based on the application wavelength. Thereafter, generation of the mini stop band (MSB), i.e. notch-band, has been studied for various relative longitudinal-shifts of the lateral cladding for different filling fractions. Two different longitudinal-shifts are combined in a footprint of $\mathrm{9.8 \times 7.35}$ ${\mu \rm {m}^{2}}$ to realize a $\mathrm{10}$ nm notch-band having a notch suppression of $\approx$ $\mathrm{27}$ dB. Application of the notch-filter as a refractive index sensor has been investigated that exhibits its sensitivity as $\mathrm{500}$ nm/RIU. The potentiality of the device in applications like - bio-sensing (e.g., detection of morphological forms of certain bacteria, and some typical viral particles) and industrial measurements (typically, sensing of Ethyl Alcohol percentage in aqueous solution) has also been explored.

A new device architecture of an all-optical logic inverter (AOLI) has been proposed in this study. The AOLI functions based on stimulated Raman scattering (SRS) in silicon nanocrystal embedded slotted photonic crystal waveguide (SPCW). The operating power and footprint size of the proposed device have significantly been scaled down to ∼1.5 mW and ∼ 8.5 × 42 μ m 2 , respectively, by combining the benefits of giant SRS gain of silicon nanocrystal and ultra-high spatio-temporal confinement of the SPCW. Cascadability of the proposed AOLI has been investigated using the maximum product criterion of the noise margin. The successful operation of the AOLI has been demonstrated for the repetition rate of the pulses as high as 100 Gbps. Finally, tolerance of performance of the design under different types of fabrication imperfections has also been calculated to establish its sustainability in a practical scenario.

SUMMARY We consider the problem of inhomogeneous subsurface imaging using beam waves. The formulation is based on the ultra-wide-band phase-space beam summation (UWB-PS-BS) method, which is structured upon windowed Fourier transform (WFT) expansions of surface fields and sources. In this approach, the radiated field is given as a superposition of beam propagators. Here, we use the beams first for expanding the surface sources and the scattered data, and then for imaging where we use the backpropagation and cross-correlation of beams. This formulation enables a target oriented imaging approach, where we take into account only pairs of source and receiver beams that pass near a region of interest, and thus extract only the relevant data arriving from this region. It also leads to a priori sparse representation of both the beam domain data and the beam propagators. A physical cogent for the beam domain data is obtained under the Born approximation. The beam domain data can be approximated as the local interaction between the beam propagators and the medium reflectivity. Thus, one may interpret the beam domain data as a local Snell’s law reflection in the direction defined by the vector summation of the incident beam and backpropagated beam ray parameters. We demonstrate a physical model for the beam domain data and the salient features of the proposed imaging algorithm using numerical examples.

Sensitivity of reservoir properties to broadband seismic amplitudes can be weak, which makes interpretation ambiguous. Examples of challenging interpretation scenarios include distinguishing blocky reservoirs from fining sequences, low gas saturation from high gas saturation, and variable reservoir quality. Some of these rock and fluid changes might indicate stronger sensitivity to amplitudes over narrow frequency bands, which is a characteristic of frequency-dependent amplitude variation with offset (FAVO). We have developed a FAVO model for reservoir characterization, following a seismic scattering phenomenon through a set of isotropic elastic layers. The frequency dependency in our model comes from the time delays due to wave propagation within layers. The FAVO modeled response is a complex-valued amplitude varying with angle and frequency, and it is a function of the seismic velocities and thicknesses of individual layers, along with the conventional AVO response at all interfaces. Our FAVO seismic analysis consists of two main steps: (1) forward modeling using well logs to understand rock and fluid sensitivity to amplitudes to identify tuning frequencies with maximum amplitude excursions and (2) seismic analysis at tuning frequencies. With well-log models, we observed that the frequency-dependent tuning response is primarily dependent on the lithology stacking pattern of a reservoir; in the cases studied, the fluid and reservoir quality have secondary effects on the frequency dependence of the amplitudes. We evaluate synthetic models and field data from the Columbus Basin, Trinidad, to illustrate our frequency-dependent seismic analysis methods. For one of the sandstone reservoirs, a frequency-dependent attribute indicates better spatial resolution of the anomaly than a conventional amplitude extraction. FAVO attributes are complementary to conventional AVO attributes.

Seismic interferometry has been shown to extract body wave arrivals from ambient noise seismic data. However, surface waves dominate ambient noise data, so cross-correlating and stacking all available data may not succeed in extracting body wave arrivals. A better strategy is to find portions of the data in which body wave energy dominates and to process only those portions. One challenge is that passive seismic recordings comprise huge volumes of data, so identifying portions with strong body-wave energy could be difficult or time-consuming. We use spatio-temporal features, calculated with data recorded by all receivers together, to perform unsupervised clustering. Using data recorded by a dense seismic array in Sweetwater, TX we were able to identify five clusters, representing a subsets of the complete dataset that contain similar features, and extract a 7 km/s body wave arrival from one cluster. This arrival did not emerge when we performed the same cross-correlation and stacking regimen on the entire dataset.