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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.

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.

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.

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.

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.

SUMMARY The discontinuous Galerkin finite element method (DGM) is a promising algorithm for modelling wave propagation in fractured media. It allows for discontinuities in the displacement field to simulate fractures or faults in a model. Our approach is based on the interior-penalty formulation of DGM, and the fractures are simulated using the linear-slip model, which is incorporated into the weak formulation. On the other hand, the spectral element method (SEM) can be used to simulate elastic wave propagation in non-fractured media. SEM uses continuous basis functions which do not allow for discontinuities in the displacement field. However, the computation cost of DGM is significantly larger than SEM due primarily to increase in the number of degrees of freedom. Here we propose a hybrid Galerkin method (HGM) for elastic wave propagation in fractured media that combines the salient features of each of the algorithm resulting in significant reduction in computational cost compared to DGM. We use DGM in areas containing fractures and SEM in regions without fractures. The coupling between the domains at the interfaces is satisfied in the weak form through interface conditions. The degree of reduction in computation time depends primarily on the density of fractures in the medium. In this paper, we formulate and implement HGM for seismic wave propagation in fractured media. Using realistic 2-D/3-D numerical examples, we show that our proposed HGM outperforms DGM with reduced computation cost and memory requirement while maintaining the same level of accuracy.

A new design of 1-to-2 line all-optical logic decoder has been proposed based on a two-dimensional photonic crystal (PhC) structure. The decoder operates based on the principle of optical interference within the PhC waveguides. An optical bias has been used to generate high-logic states at zero input conditions. Simulations explore a high contrast ratio, in the order of 11.3 dB, for both the output ports of the device. Response times have been calculated from the transient responses of the output ports, and are found as 0.65 and 0.77 ps for the ports 1 and 2, respectively. These results in a bit rate of ≃625 Gbps, considering the worst-case scenario. Phase sensitivity analysis has also been performed which shows that the device output is quite sensitive to the differences in phases of the bias and signals. However, a strategy has been proposed to make the same insensitive to the phase changes. Finally, the small footprint (in the order of 234 μm 2 ); standard operating wavelength; and silicon-based design of the decoder, along with its said merits, make the device highly potential for on-chip photonic-integrated-circuit applications.

Diffraction imaging aims to emphasize small-scale subsurface heterogeneities, such as faults, pinch-outs, fracture swarms, channels, etc. and can help seismic reservoir characterization. The key step in diffraction imaging workflows is based on the separation procedure suppressing higher energy reflections and emphasizing diffractions, after which diffractions can be imaged independently. Separation results often contain crosstalk between reflections and diffractions and are prone to noise. We have developed an inversion scheme to reduce the crosstalk and denoise diffractions. The scheme decomposes an input full wavefield into three components: reflections, diffractions, and noise. We construct the inverted forward modeling operator as the chain of three operators: Kirchhoff modeling, plane-wave destruction, and path-summation integral filter. Reflections and diffractions have the same modeling operator. Separation of the components is done by shaping regularization. We impose sparsity constraints to extract diffractions, enforce smoothing along dominant local event slopes to restore reflections, and suppress the crosstalk between the components by local signal-and-noise orthogonalization. Synthetic- and field-data examples confirm the effectiveness of the proposed method.

An impedance matching theory-based methodology is presented in this study for designing/optimising photonic crystal-based all-optical AND gate. A basic architecture for the AND gate is projected first, and thereafter the same is optimised utilising the proposed methodology. Performance of the AND gate is evaluated based on several metrics that are calculated using a finite-difference-time-domain simulation. The optimised AND gate has exhibited a high extinction ratio in the order of 6.9 dB, within a very small footprint of ≈ 110 μ m 2 . It also supports propagation of a high bit rate (≈1 Tb/S) and has a wide operational bandwidth (≈4 THz), which make the device suitable for different photonic integrated circuit applications.

A recently developed hybrid absorbing boundary condition (ABC) can significantly suppress artificial boundary reflections by inserting a transition area between the boundary and the inner area. The wavefield in the transition area is computed by linearly weighting the wavefield from one-way wave equation (OWWE) and that from two-way wave equation. This leads to a smooth variation from the computational area to the boundary via the transition area and thus greatly reduces boundary reflections. In this paper, we propose two techniques to further enhance the absorbing effect. First, we widen the boundary from one point to several points. Second, we adopt nonlinear weighting coefficients instead of linear ones. Numerical simulations with 2D acoustic finite-difference modeling, combined with Clayton–Engquist OWWE, demonstrate that the proposed techniques can significantly improve the absorption effect without increasing computational cost. Tests using Higdon OWWE-based ABC suggest that the second technique can greatly enhance the absorption effect. Experiments with frequency-domain finite-difference modeling demonstrate similar improvement in absorption effect.

While pseudospectral (PS) methods can feature very high accuracy, they tend to be severely limited in terms of geometric flexibility. Application of global radial basis functions overcomes this, however at the expense of problematic conditioning (1) in their most accurate flat basis function regime, and (2) when problem sizes are scaled up to become of practical interest. The present study considers a strategy to improve on these two issues by means of using hybrid radial basis functions that combine cubic splines with Gaussian kernels. The parameters, controlling Gaussian and cubic kernels in the hybrid RBF, are selected using global particle swarm optimization. The proposed approach has been tested with radial basis-pseudospectral method for numerical approximation of Poisson, Helmholtz, and Transport equation. It was observed that the proposed approach significantly reduces the ill-conditioning problem in the RBF-PS method, at the same time, it preserves the stability and accuracy for very small shape parameters. The eigenvalue spectra of the coefficient matrices in the improved algorithm were found to be stable even at large degrees of freedom, which mimic those obtained in pseudospectral approach. Also, numerical experiments suggest that the hybrid kernel performs significantly better than both pure Gaussian and pure cubic kernels., Accepted in Engineering Analysis With Boundary Elements (2017). For better understanding of this work, see also arXiv:1512.07584

A completely new design for an all-silicon all-optical pass switch has been proposed based on the stimulated Raman scattering (SRS) in silicon nanocrystal embedded slotted photonic crystal waveguide (SPCW). Substantial miniaturisation in the device footprint and operating power has been attained by merging the benefits of the giant SRS gain and the ultra-high optical confinement of the SPCW. The proposed switch offers a tremendously high contrast ratio of ∼ 27 dB between the logic levels and an extraordinary bit rate of 125 Gbps.

On Foundations of Seismology: Bringing Idealizations Down to Earth, by James R. Brown and M. A. Slawinski, ISBN 978-981-4329-49-1, 2017, World Scientific, 184 p., US$88 (print), US$70 (eBook). Coasts in Crisis: A Global Challenge, by Gary Griggs, ISBN 978-052-0293-62-5, 2017, University of California Press, 360 p., US$29.95 (print and eBook).

A global optimization method called very fast simulated annealing (VFSA) inversion has been applied to seismic inversion. Here we address some of the limitations of VFSA by developing a new stochastic inference method, named greedy annealed importance sampling (GAIS). GAIS combines VFSA and greedy importance sampling (GIS), which uses a greedy search in the important regions located by VFSA, in order to attain fast convergence and provide unbiased estimation. We demonstrate the performance of GAIS with application to seismic inversion of field post- and pre-stack datasets. The results indicate that GAIS can improve lateral continuity of the inverted impedance profiles and provide better estimation of uncertainties than using VFSA alone. Thus this new hybrid method combining global and local optimization methods can be applied in seismic reservoir characterization and reservoir monitoring for accurate estimation of reservoir models and their uncertainties.

The existence of fractures in an otherwise isotropic medium induces anisotropy in the medium. Because of existing in situ stress, most fractures are often aligned close to vertical, rendering a reservoir azimuthally anisotropic in character. Joint interpretation of PP and PS seismic data generally provides greater details in resolution of the estimated subsurface rock properties and geological structures than conventional PP seismic data. Here we report on the applicability of PP and PS azimuthal amplitude variation with offset (AVAZ) data in fracture characterization. The theory is based on a linear slip model and the Born formula such that PP- and PS-reflection coefficients are sensitive to fracture weaknesses. First we demonstrate numerical experiments with synthetic PP-AVAZ, PS-AVAZ and joint inversion to estimate fluid indicator. Results show that when the fractures have low saturation of gas, the fluid indicator estimated from PP-AVAZ data is fairly accurate. However, when gas saturation reaches up to 70%, joint inversion can help to improve the resulting poor quality in PP-AVAZ data inversion. For high values of gas-saturation, both PP inversion and joint inversion are sensitive to errors in background Poisson's ratio. Based on the result of our numerical experiment with synthetic data, we analyze a field dataset from the Western Sichuan Basin in China. The inversion result is consistent with well log based interpretation. All known reservoirs are accurately depicted by the estimated fluid indicator while the false gas zones interpreted by other methods are eliminated. When displayed as an inline section, the distribution of reservoirs appears consistent with the interpretation of the stratigraphy and geological structures.

The seismic velocity structure beneath Texas Gulf Coastal Plain (GCP) is imaged by migrating Ps receiver functions with a seismic velocity model found by fitting surface wave dispersion. We use seismic data from a linear array of 22 broadband stations, spaced 16–20 km apart. A Common Conversion Point (CCP) stacking technique is applied to earthquake data to improve the S/N ratios of receiver functions. Using an incorrect velocity model for depth migration of a stacked CCP image may produce an inaccurate image of the subsurface. To find sufficiently accurate P and S-velocity models, we first apply a nonlinear modeling technique to fit Rayleigh wave group velocity dispersion via Very Fast Simulated Annealing. Vs ranges from 1.5 km/s in shallow layers of the GCP to 4.5 km/s beneath the Llano uplift and just outboard of the Balcones Fault Zone (BFZ). The BFZ is characterized by slow velocities that persist to nearly 100 km depth. In the stacked image, the largest amplitude positive-polarity event ranges from the surface, at the Llano uplift, to a maximum depth of ∼16 km beneath Matagorda Island. We attribute this event to the sediment-basement contact, which is expected to produce a large impedance contrast. Another large-amplitude and positive-polarity event at ∼35 km depth, which likely marks the Moho, disappears outboard of the Luling Fault Zone. The disappearance of the Moho beneath the GCP may be due to serpentinization of the upper mantle, which would reduce the impedance contrast between the lower crust and upper mantle dramatically.

Recent developments have made it possible to overcome grid-based limitations of finite difference (FD) methods by adopting the kernel-based meshless framework using radial basis functions (RBFs). Such an approach provides a meshless implementation and is referred to as the radial basis-generated finite difference (RBF-FD) method. In this paper, we propose a stabilized RBF-FD approach with a hybrid kernel, generated through a hybridization of the Gaussian and cubic RBF. This hybrid kernel was found to improve the condition of the system matrix, consequently, the linear system can be solved with direct solvers which leads to a significant reduction in the computational cost as compared to standard RBF-FD methods coupled with present stable algorithms. Unlike other RBF-FD approaches, the eigenvalue spectra of differentiation matrices were found to be stable irrespective of irregularity, and the size of the stencils. As an application, we solve the frequency-domain acoustic wave equation in a 2D half-space. In order to suppress spurious reflections from truncated computational boundaries, absorbing boundary conditions have been effectively implemented., Comment: 22 pages, 14 figures, Accepted for Computer and Mathematics with Applications

Sleipner gas field in the North Sea is the world's first industrial scale CO2 injection project designed specifically to reduce the emission of greenhouse gas. Here CO2 separated from natural gas produced at Sleipner gas field is injected into the Utsira sand, which is a major saline aquifer in the North Sea basin. From time-lapse (4D) seismic data, CO2 plume is observed as a number of bright sub-horizontal reflections within the reservoir. Correlation of log data with the seismic data indicates that CO2 accumulates within a series of interbedded sandstones and mudstones beneath a thick cap rock of mudstone. Nine reflective horizons have been mapped within the reservoir on the six seismic surveys from 1999 to 2008. Comparison with the baseline seismic survey of 1994 (pre-injection) provides clear impression of the migration of CO2 plume. In this paper, we attempt to model CO2 distribution quantitatively within the reservoir by applying a pressure-dependent differential effective medium (PDEM) theory using 4D seismic data. Pre- and post-injection acoustic impedances are calculated by inverting post-stack seismic data of 1994 and 2001 using a model-based inversion technique. A 3D CO2 saturation volume is estimated using PDEM theory from inverted acoustic impedance of the year 2001 taking the reference of that from the results of pre-injection data of the year 1994. Since the gas distribution type is seldom known, we estimate the saturation distribution using both a homogeneous and a patchy distribution pattern in our rock physics model. We estimate saturation for homogeneous distribution of CO2 to be 0–20% and for CO2 as patches of gas as 0–80% of the total porosity within ∼200 m thick reservoir unit. 5–7% uncertainty in the predicted CO2 saturation is estimated using a Monte-Carlo simulation technique. Our results indicate that a large amount of CO2 is accumulated as patches of gas within sand layers capped by mud layers, though some amount of gas may have mixed uniformly with water.

Seismic inverse problem of estimating P- and S-wave reflectivity from seismic traces has recently been revisited using a basis pursuit denoising inversion (BPI) approach. The BPI uses a wedge dictionary to define model constraints, which has been successful in resolving thin beds. Here we address two fundamental problems associated with BPI, namely, the uniqueness of the estimate and the choice of regularization weight λ to be used in the model norm. We investigated these using very fast simulated re-annealing (VFSR) and gradient projection sparse reconstruction (GPSR) approaches. For a synthetic model with two reflectors separated by one time sample, we are able to demonstrate convergence of VFSR to the true model with different random starting models. Two numerical approaches to estimating the regularization weight were investigated. One uses λ as a hyper-parameter and the other uses this as a temperature-like annealing parameter. In both cases, we were able to obtain λ fairly rapidly. Finally, an analytic formula for λ that is iteration adaptive was also implemented. Successful applications of our approach to synthetic and field data demonstrate validity and robustness.

The numerical simulation of wave propagation in media with solid and fluid layers is essential for marine seismic exploration data analysis. The numerical methods for wave propagation that are applicable to this physical settings can be broadly classified as partitioned or monolithic: The partitioned methods use separate simulations in the fluid and solid regions and explicitly satisfy the interface conditions, whereas the monolithic methods use the same method in all the domain without any special treatment of the fluid-solid interface. Despite the accuracy of the partitioned methods, the monolithic methods are more common in practice because of their convenience. In this paper, we analyse the accuracy of several monolithic methods for wave propagation in the presence of a fluid-solid interface. The analysis is based on grid-dispersion criteria and numerical examples. The methods studied here include: the classical finite-difference method (FDM) based on the second-order displacement formulation of the elastic wave equation (DFDM), the staggered-grid finite difference method (SGFDM), the velocity-stress FDM with a standard grid (VSFDM) and the spectral-element method (SEM). We observe that among these, DFDM and the first-order SEM have a large amount of grid dispersion in the fluid region which renders them impractical for this application. On the other hand, SGFDM, VSFDM and SEM of order greater or equal to 2 yield accurate results for the body waves in the fluid and solid regions if a sufficient number of nodes per wavelength is used. All of the considered methods yield limited accuracy for the surface waves because the proper boundary conditions are not incorporated into the numerical scheme. Overall, we demonstrate both by analytic treatment and numerical experiments, that a first-order velocity-stress formulation can, in general, be used in dealing with fluid-solid interfaces without using staggered grids necessarily.

Receiver functions (RFs) are derived by deconvolution of the horizontal (radial or transverse) component of ground motion from the vertical component, which segregates the PS phases. Many methods have been proposed to employ deconvolution in frequency as well as in time domain. These methods vary in their approaches to impose regularization that addresses the stability problem. Here, we present application of a new time‐domain deconvolution technique called basis pursuit deconvolution (BPD) that has recently been applied to seismic exploration data. Unlike conventional deconvolution methods, the BPD uses an L1 norm constraint on model reflectivity to impose sparsity. In addition, it uses an overcomplete wedge dictionary based on a dipole reflectivity series to define model constraints, which can achieve higher resolution than that obtained by the traditional methods. We demonstrate successful application of BPD based RF estimation from synthetic data for a crustal model with a near‐surface thin layer of thickness 5, 7, 10, and 15 km. The BPD can resolve these thin layers better with much improved signal‐to‐noise ratio than the conventional methods. Finally, we demonstrate application of the BPD receiver function (BPRF) method to a field dataset from Kutch, India, where near‐surface sedimentary layers are known to be present. The BPRFs are able to resolve reflections from these layers very well.

Impact fragmentation is an energetic process that has affected all planetary bodies. To understand its effects in basalt, we studied Lonar Crater, which is a rare terrestrial simple impact crater in basalt and analogues to kilometer-scale simple craters on Mars. The Lonar ejecta consists of basaltic fragments with sizes ranging from silt to boulder. The cumulative size and mass frequency distributions of these fragments show variation of power index for different size ranges, suggesting simple and complex fragmentation. The general shape of the fragments is compact, platy, bladed, and elongated with an average edge angle of 100°. The size distribution of cobble- to boulder-sized fragments is similar to the fracture spacing distribution in the upper crater wall, indicating the provenance of those large fragments. Its consistency with a theoretical spallation model suggests that the large fragments were ejected from near surface of the target, whereas the small fragments from deeper level. The petrophysical properties of the ejecta fragments reflect the geophysical heterogeneity in the target basalt that significantly reduced the original size of spall fragments. The presence of Fe/Mg phyllosilicates (smectites) both in the ejecta and wall indicates the role of impact in excavating the phyllosilicates from the interior of basaltic target affected by aqueous alteration. The seismic images reveal a thickness variation in the ejecta blanket, segregation of boulders, fractures, and faults in the bedrock beneath the crater rim. The fracturing, fragmentation, and fluvial degradation of Lonar Crater have important implications for Mars.

Summary A shallow 2D tomographic P-wave velocity image is obtained in the Deccan Volcanic Province (DVP) of India using first-arrival seismic data along a 90 km long N-S trending profile in the Deccan Syneclise region. The tomographic image depicts smooth velocity variations of Quaternary (2.0-2.5 km/s) sediments, basalt (5.0-5.5 km/s) and sub-basalt Mesozoic sediments (4.0-4.5 km/s) as well as basement (5.8-6.0 km/s) configuration down to a maximum depth of 5.0 km. Due to late Cretaceous volcanism with outpouring of basaltic lava flows, this region is affected by numerous dyke intrusions and thick basaltic trap forming sills with the presence of horst and graben structures due to deep basinal faults. Although imaging below the basalt is a major challenge for the oil industry, with the help of tomographic imaging technique of long-offset seismic refraction data, we are able to image sporadic sub- and intra-trappean Mesozoic sediments (

Although seismicity near Koyna Reservoir (India) has persisted for ~50 years and includes the largest induced earthquake (M 6.3) reported worldwide, the seismotectonic framework of the area is not well understood. We recorded ~1800 earthquakes from 6 January 2010 to 28 May 2010 and located a subset of 343 of the highest-quality earthquakes using the tomoDD code of Zhang and Thurber (2003) to better understand the framework. We also inverted first arrivals for 3-D Vp, Vs, and Vp/Vs and Poisson's ratio tomography models of the upper 12 km of the crust. Epicenters for the recorded earthquakes are located south of the Koyna River, including a high-density cluster that coincides with a shallow depth (

Numerical Simulation in Applied Geophysics, by Juan Enrique Santos and Patricia Mercedes Gauzellino, ISBN 978-3-319-48456-3, 2016, Birkhauser, 309 p.

Imaging shallow crustal structure is essential to extend the geological information from surface mapping to a depth and to develop tectonic models. We applied seismic tomography modelling to refraction data acquired along a 200-km-long line in the Dharwar craton of the Indian shield, and we derived a crustal velocity model that was evaluated with checkerboard tests to demonstrate the reliability of the model. We also tested the model for artefacts. Upper-crustal velocities vary between 5.7 and 6.4 km s–1 and are determined to 10 km depth, probably due to very low-velocity gradients in the upper crust. Undulating high and low velocities in the top layers of the crust are terminated at a depth of 7–8 km, consistent with a probable detachment. We interpret the undulating upper-crustal velocity layers to represent a fold-thrust belt structure that developed during a collision in a transpressional tectonic regime, consistent with the model of Chadwick et al., which suggests oblique convergence and accretion of two crustal blocks in the region. The velocity structure also correlates reasonably well with the distinct geological units. We interpret relatively low velocities between the undulating layers as representative of faults that bound various tectonic domains.

SUMMARY Imaging of deep crustal features from narrow-angle deep seismic reflection data, especially from fold belt region, has been a challenging task. The common reflection surface (CRS) stack is an alternative seismic imaging technique for multicoverage reflection data. It is an automatic stacking process, which does not require explicit knowledge of stacking velocity. This CRS stack is especially useful when the data quality is poor and foldage is low. In this paper, we demonstrate an application of the CRS stack to a deep seismic reflection data set acquired across the Aravalli‐Delhi fold belt of the northwestern India, which provides a seismic stack section with much improved signal-to-noise ratio. Comparing the conventional common midpoint (CMP) Stack with the CRS stack, we find that the Moho and other crustal reflections have been resolved clearly and the continuity of the reflectors has also been enhanced with the CRS stack method. The major findings from our CRS processing include clear image of the Moho discontinuity below the Marwar Basin and Sandmata Complex, and prominent upper and mid-crustal reflections. Our study for the first time images an extension of crustal-scale Jahazpur thrust below the Sandmata Complex, which becomes listric at the Moho. Some of the crustal features derived in this study were not identified in the earlier investigations using the CMP stack. Our study clearly demonstrates that the CRS stacking method is more appropriate for imaging the crustal and subcrustal structures of the thrust fold belt region than the conventional CMP method, where limited velocity information is available. Crustal thickness across the Proterozoic orogenic Aravalli‐Delhi fold belt varies between 38 and 50km. Global correlation of the seismic results suggests no relation between crustal thickness and age of the crustal block, but it depends on the thermorheological and tectonic history of the region. Palaeosignatures of the Proterozoic subduction and collision processes are still preserved in major portion of the crust in this study area as well as in several parts of the world.

Results from a typical post-stack or pre-stack seismic inversion are band-limited primarily due to missing low and high frequencies in the wavelet. Thin beds that are of primary interest in reservoir characterization are generally poorly resolved. Inversion methods are designed to incorporate a priori information in several different ways. In this paper, we examine and compare performances of two such methods: a stochastic method that draws a starting broad-band model based on some statistics, derived from well logs, and a deterministic method that incorporates constraints using a model norm, based on the basis pursuit decomposition. We apply a stochastic method employing very fast simulated annealing for optimization, using fractal-based starting models, and a basis pursuit inversion (deterministic method) to a single post-stack dataset to assess the performance of the two algorithms. We find that both methods are able to derive a broad-band acoustic impedance from the band-limited post-stack seismic data. The results show a similar structure and therefore result in possible increasing confidence in the interpretation. The essence of our study is that the calibration of results from two different methods can provide an interpreter with more information in interpreting broad-band inversion results hitherto not derived from standard deterministic algorithms.

Studying fault properties from reflection seismic data is essential for seismic interpretations. A three-dimensional (3D) industry standard reflection seismic volume acquired over the Nankai Trough offshore the Kii Peninsula in Japan has been used to map the splay fault system since many parts of these faults appear as strong reflectors in the stacked seismic data. However, some parts of the splay faults are too steep to be well imaged by reflection seismic data. This may cause misinterpretation of the splay fault properties and seismogenesis. To better interpret the data, we applied a model-based inversion which combines seismic data with well log data to obtain elastic properties and rock properties. Our inversion uses both a low-frequency initial model and a hybrid which considers the fractal statistics of the well log data. The latter shows better estimation of model parameters and thus can provide us with more confidence in interpreting the impedance. The inverted results show that seismic inversion is able to provide clear images of the elastic and rock properties of the regions around and at the well locations. Impedance anomalies along the shallow splay faults suggest the change of fluids, weakness and other physical parameters. Interpretation of one strong reflector cutting through the drilling site C0001 based on the seismic images alone is ambiguous since it can be interpreted either as a sedimentary bed or a splay fault. Our inverted results demonstrate that this reflector is more likely splay fault breached.

SUMMARY Purely numerical methods for modelling seismic wave propagation are now fairly popular. In this paper, we report on the development of a hybrid finite element-finite difference method. Our method first employs semi-discretization of the finite element method in a part of the spatial domain (in the z-direction for 2-D situation) to obtain a wave equation in weak form, and then uses the finite difference method to solve it. This offers significant advantages in applying non-uniform grids with improved accuracy. To improve the computational efficiency, we introduce the spectral element method to replace the traditional finite element method, which leads to a diagonal mass matrix with sufficient accuracy. After that, we carry out detailed analyses of the dispersion behaviours for both uniform and non-uniform cases; the dispersioncurvesdemonstratehighprecisionofourmethodinnumericalmodelling,especially in dealing with non-uniform grids. Some examples are presented to demonstrate performance of this method and confirm the analytic results.

To improve quantitative interpretation of seismic data, we analyze the effect of fluid substitution in a porous and fractured medium on elastic properties and reflection coefficients. This analysis uses closed-form expressions suitable for fluid substitution in transversely isotropic media with a horizontal symmetry axis (HTI). For the HTI medium, the effect of changing porosity and water saturation on (1) P-wave moduli, (2) horizontal and vertical velocities, (3) anisotropic parameters, and (4) reflection coefficients are examined. The effects of fracture density on these four parameters are also studied. For the model used in this study, a 35% increase in porosity lowers the value of P-wave moduli by maximum of 45%. Consistent with the reduction in P-wave moduli, P-wave velocities also decrease by maximum of 17% with a similar increment in porosity. The reduction is always larger for the horizontal P-wave modulus than for the vertical one and is nearly independent of fracture density. The magnitude of the anisotropic parameters of the fractured medium also changes with increased porosity depending on the changes in the value of P-wave moduli. The reflection coefficients at an interface of the fractured medium with an isotropic medium change in accordance with the above observations and lead to an increase in anisotropic amplitude variation with offset (AVO) gradient with porosity. Additionally, we observe a maximum increase in P-wave modulus and velocity by 30% and 8%, respectively, with a 100% increase in water saturation. Water saturation also changes the anisotropic parameters and reflection coefficients. Increase in water saturation considerably increases the magnitude of the anisotropic AVO gradient irrespective of fracture density. From this study, we conclude that porosity and water saturation have a significant impact on the four studied parameters and the impacts are seismically detectable.

The staggered-grid finite-difference (SFD) method is widely used in numerical modeling of wave equations. Conventional SFD stencils for spatial derivatives are usually designed in the space domain. However, when they are used to solve wave equations, it becomes difficult to satisfy the dispersion relations exactly. Liu and Sen (2009c) proposed a new SFD scheme for one-dimensional (1D) scalar wave equation based on the time–space domain dispersion relation and plane wave theory, which is made to satisfy the exact dispersion relation. This new SFD scheme has greater accuracy and better stability than a conventional scheme under the same discretizations. In this paper, we develop this new SFD scheme further for numerical solution of 2D and 3D scalar wave equations. We demonstrate that the modeling accuracy is second order when the conventional 2 M -th-order space-domain SFD and the second order time-domain finite-difference stencils are directly used to solve the scalar wave equation. However, under the same discretization, our 1D scheme can reach 2 M -th-order accuracy and is always stable; 2D and 3D schemes can reach 2 M -th-order accuracy along 8 and 48 directions, respectively, and have better stability. The advantages of the new schemes are also demonstrated with dispersion analysis, stability analysis, and numerical modeling.

SUMMARY We investigate the stability of some high-order finite element methods, namely the spectral element method and the interior-penalty discontinuous Galerkin method (IP-DGM), for acoustic or elastic wave propagation that have become increasingly popular in the recent past. We consider the Lax-Wendroff method (LWM) for time stepping and show that it allows for a larger time step than the classical leap-frog finite difference method, with higher-order accuracy. In particular the fourth-order LWM allows for a time step 73 per cent larger than that of the leap-frog method; the computational cost is approximately double per time step, but the larger time step partially compensates for this additional cost. Necessary, but not sufficient, stability conditions are given for the mentioned methods for orders up to 10 in space and time. The stability conditions for IP-DGM are approximately 20 and 60 per cent more restrictive than those for SEM in the acoustic and elastic cases, respectively.

SUMMARY The purpose of this study is to investigate the possibility of inverting for the fracture parameters using the ray-Born approximation. The fracture parameters normal and tangential weaknesses ΔN and ΔT, derived using a low-frequency effective medium theory, are indicators of the crack density and fracture infill (liquid-filled or dry). In our implementation of ray-Born inversion, ΔN and ΔT are unknown model parameters. We treat the background medium as isotropic, and its elastic properties are assumed to be already determined using other conventional methods prior to inversion. In our current implementation, we assume that the fractures are vertical and the orientation of the symmetry axis of the effective anisotropic medium or the fracture normal is known. We formulate the inverse problem in a least-squares sense and apply the conjugate-gradient method to minimize the error function. To overcome the problem of non-uniqueness in the inversion and to ensure that the inverted model parameters are physically meaningful and unique, we added an analytical function of model parameters to the error function. We show, using a numerical example, that the fracture parameters cannot be reliably obtained from single-component seismic data (vertical or horizontal). Simultaneous inversion of both components is needed for more robust estimates of ΔN and ΔT. The inversion scheme was implemented in the frequency domain, which allowed us to experiment with the number of frequencies used in the inversion. We found that a very small number of frequency samples covering the spectrum of the source wavelet could produce reasonable estimates of ΔN and ΔT. We tested our method on a synthetic data set generated using ray-Born forward modelling. For the experiment shown in the paper, the least-squares inversion scheme produced encouraging results. We also applied our method to a synthetic data set generated using a 3-D anisotropic finite-difference code. The results indicated that our method could predict the parameter trends, but with some inaccuracies in the values of ΔN and ΔT.

Seismic data do not contain some low- and high-frequency information because of the band-limited nature of the source wavelet. A deterministic inversion of such band-limited seismic data produces smooth models which are devoid of high-frequency variations observed in well logs. Stochastic inversion methods often based on random Gaussian priors can have a limitation of producing high frequencies in the desired model particularly the frequency band not constrained by the input seismic data. In this paper, we propose a new stochastic poststack inversion algorithm where fractal models constructed from statistical properties of well logs are used to generate a priori models. This provides a high-resolution model without injecting spurious high-frequency estimates in model space. Stacked seismic data are used in the inversion in which a suitable objective function is minimized using a nonlinear optimization method called 'very fast simulated annealing'. We demonstrate the effectiveness of our method for the estimation of acoustic impedance with the application to a field dataset.

SUMMARY We derive explicit and new implicit staggered-grid finite-difference (FD) formulas for derivatives of first order with any order of accuracy by a plane wave theory and Taylor’s series expansion. Furthermore, we arrive at a practical algorithm such that the tridiagonal matrix equations are formed by the implicit FD formulas derived from the fractional expansion of derivatives. Our results demonstrate that the accuracy of a (2N + 2)th-order implicit formula is nearly equivalent to or greater than that of a (4N)th-order explicit formula. The new implicit method only involves solving tridiagonal matrix equations. We also demonstrate that a( 2N + 2)th-order implicit formulation requires nearly the same amount of memory and computation as those of a (2N + 4)th-order explicit formulation but attains the accuracy achieved by a (4N)th-order explicit formulation when additional cost of visiting arrays is not considered. Our analysis of efficiency and numerical modelling results for elastic wave propagation demonstrates that a high-order explicit staggered-grid method can be replaced by an implicit staggered-grid method of some order, which will increase the accuracy but not the computational cost.