Geophysical Prospecting - Volume 72, Issue 2, 2024

Microseismic monitoring is a promising method for the safety monitoring of underground mines. However, it is crucial to isolate microseismic signals related to the collapse of a mine from others for successful monitoring because the monitoring system records various signals. Recently, deep learning‐based classification techniques have achieved high performance in such data classification problems. In this context, we develop an automatic signal classification technique using the modified WaveNet classifier. The main characteristic of the WaveNet structure is its ability to extract features at various frequencies from very long time‐series data, and such an advantage makes the WaveNet suitable for seismic data processing. The data imbalance problem coming from the safe condition of the monitoring target is solved by augmenting the training data with those acquired from another mine and employing class weighting. After training, an optimal classifier is chosen considering the loss function, accuracy and Fβ score. The optimal classifier shows very high accuracy and excellent performance for the test data prediction. Compared to the random forest model and another one‐dimensional convolutional neural network–based network, the suggested classifier has higher reliability in predicting microseismic signals. Even though the proposed WaveNet model has a much more complex structure than the random forest model, the actual application examples demonstrate that the proposed model achieves high efficiency without any preprocessing. The automatic signal classifier developed in this study can be directly applied to various safety monitoring problems, not only mines, to improve the efficiency and reliability of monitoring systems.

In contrast to conventional acquisition practices, simultaneous source acquisition allows for overlapping wavefields to be recorded. Relaxing the shot schedule in this manner has certain advantages, such as allowing for faster acquisition and/or denser shot sampling. This flexibility usually comes at the cost of an extra step in the processing workflow, where the wavefields are deblended, that is, separated. An inversion‐type algorithm for deblending, based on the focal transform, is investigated. The focal transform uses an approximate velocity model to focus seismic data. The combination of focusing with sparsity constraints is used to suppress blending noise in the deblended wavefield.

The focal transform can be defined in different ways to better match the spatial sampling of different types of marine surveys. To avoid solving a large inverse problem, involving a large part of the survey simultaneously, the input data can be split into sub‐sets that are processed independently. We discuss the formation of such sub‐sets for ocean bottom node and streamer‐type acquisitions. Two deblending experiments are then carried out. The first is on numerically blended ocean bottom node field data. The second is on field‐blended towed streamer data with a challenging signal overlap. The latter experiment is repeated using curvelet‐based deblending for comparison purposes, showing the virtues of the focal deblending process. Several challenges of basing deblending around the focal transform are discussed as well as some suggestions for improved implementations.

Thanks to continued performance improvements in software and hardware, wave‐equation‐based imaging technologies, such as full‐waveform inversion and reverse‐time migration, are becoming more commonplace. However, widespread adaptation of these advanced imaging modalities has not yet materialized because current implementations are not able to reap the full benefits from accelerators, in particular those offered by memory‐scarce graphics processing units. Through the use of randomized trace estimation, we overcome the memory bottleneck of this type of hardware. At the cost of limited computational overhead and controllable incoherent errors in the gradient, the memory footprint of adjoint‐state methods is reduced drastically. Thanks to this relatively simple to implement memory reduction via an approximate imaging condition, we are able to benefit from graphics processing units without memory offloading. We demonstrate the performance of the proposed algorithm on acoustic two‐ and three‐dimensional full‐waveform inversion examples and on the formation of image gathers in transverse tilted isotropic media.

Steeply dipping structural imaging is a great challenge due to its poor illumination. Conventional migration methods are unable to produce an accurate image of complex steeply dipping structures. The prismatic wave can improve the illumination of steeply dipping structures and is often used to improve the imaging results of such structures. Traditional elastic wave theory assumes that seismic waves do not attenuate when propagating through subsurface media. However, during seismic wave propagation, the wave energy decays exponentially due to the absorption and attenuation of the ground layer. Subsurface attenuation leads to amplitude loss and phase distortion of seismic waves, resulting in blurring of migration amplitudes when this attenuation is not taken into account during imaging. To address this issue, a frequency‐domain Q‐compensated prismatic reverse time migration method is proposed, which derives Q‐compensated prismatic wavefield propagation operators. In the proposed frequency‐domain Q‐compensated prismatic reverse time migration, Q attenuation is fully compensated along three propagation paths and two propagation types of prismatic waves. The optimized four‐order mixed 25‐point difference format and LU decomposition method are used to solve the Q‐compensated prismatic wavefield propagation equations with high computational efficiency. Numerical and field data examples demonstrate that the proposed frequency‐domain Q‐compensated prismatic reverse time migration method can compensate for deep attenuation energy and improve the imaging resolution of steeply dipping structures.

The oscillatory bubble pulses generated by airguns in seawater are known to produce artefacts in seismic images. Although such artefacts are suppressible by employing larger airgun arrays in acquisition, small airgun arrays are used more often now to minimize the environmental impacts, thus raising the need for further suppressing bubble pulses at data processing stage. For a deep marine reflection dataset recently acquired by a small airgun array, we compare the effectiveness of three popular debubbling methods that estimate the far‐field source signature based on theoretical simulation and wavelets extracted from seafloor reflections and direct arrivals, respectively. In this case, due to the lack of near‐field measurements for calibration, the debubbling via simulation underperforms the two wavelet extraction methods. Overlapping events in the noisy response of seafloor sediments lead to the failure of the wavelet extraction from primary seafloor reflections. The estimated source signature based on direct arrivals achieves the best bubble suppression result, indicating the importance of signal‐to‐noise ratio and a low level of directionality of the small airgun array source.

The possibilities offered by the use of variational mode decomposition–based Hilbert marginal spectrum and the differential cepstrum for gas‐bearing detection are studied in this paper. We propose a novel variational mode decomposition–based Hilbert marginal differential cepstrum for hydrocarbon detection. Variational mode decomposition–based Hilbert marginal spectrum is first computed. Then discrete cosine transform is carried out to the differential logarithmic variational mode decomposition–based Hilbert marginal spectrum to obtain the variational mode decomposition–based Hilbert marginal differential cepstrum. For hydrocarbon detection, the seismic amplitude anomaly section is generated by extracting the first and second common quefrency sections. Compared with the traditional Fourier‐based cepstrum, the wavelet‐based cepstrum and the Berthil cepstrum, it has the ability to effectively reveal more detailed frequency‐dependent amplitude anomalies with high accuracy and resolution. Model tests and field data applications from a carbonate reservoir in China show that the variational mode decomposition‐based Hilbert marginal differential cepstrum can provide a better gas‐prone interpretation. The proposed method can be a complementary approach to current cepstrum‐based hydrocarbon detection methods and the spectrum decomposition methods.

In this paper, we present a frequency‐domain volume integral method to model the microseismic wavefield in heterogeneous anisotropic‐elastic media. The elastic wave equation is written as an integral equation of the Lippmann–Schwinger type, and the seismic source is represented as a general moment tensor. The actual medium is split into a background medium and a scattered medium. The background part of the displacement field is computed analytically, but the scattered part requires a numerical solution. The existing matrix‐based implementation of the integral equation is computationally inefficient to model the wavefield in three‐dimensional earth. An integral equation for the particle displacement is, hence, formulated in a matrix‐free manner through the application of the Fourier transform. The biconjugate gradient stabilized method is used to iteratively obtain the solution of this equation. The integral equation method is naturally target oriented, and it is not necessary to fully discretize the model. This is very helpful in the microseismic wavefield computation at receivers in the borehole in many cases; say, for example, we want to focus only on the fluid injection zone in the reservoir–overburden system and not on the whole subsurface region. Additionally, the integral equation system matrix has a low condition number. This provides us flexibility in the selection of the grid size, especially at low frequencies for given wave velocities. Considering all these factors, we apply the numerical scheme to three different models in order of increasing geological complexity. We obtain the elastic displacement fields corresponding to the different types of moment tensor sources, which prove the utility of this method in microseismic. The generated synthetic data are intended to be used in inversion for the microseismic source and model parameters.

Many geological features of scientific and/or economic interest have structural orientations that are neither horizontal nor vertical. Being able to recover such dipping structures from geophysical inversions is, therefore, important. Different regularization strategies have been proposed to help recover dipping structures. One notable example is total variation. However, there seems to be a lack of understanding within the geophysical community regarding why total variation regularization allows dipping structures to be recovered, whereas L1 norm regularization does not. In this paper, we compare these two regularization strategies from an optimization point of view using two simple block models. We also perform three‐dimensional inversions using a synthetic example and a field data example involving gravity gradient data to demonstrate the resolving power of total variation in potential field data inversion.

Data acquisition using equal spacing has been a standard practice in geophysics. The dense uniform sampling derived from Nyquist–Shannon sampling includes redundant samples, and it is sufficient but not necessary to adequately record target signals. We propose an ergodic sampling, which avoids the redundant samples in the dense uniform sampling and possesses the ability to capture the sufficiently similar information content as does Nyquist sampling. Ergodicity means that a key part of the system can represent the average performance of the entire system. Our ergodic samples are a critical subset of dense uniform samples and can represent the full uniform Nyquist samples. To find such a critical subset, we first examine the properties of different sampling patterns, including the sampling interval distribution, sampling angle distribution, areal sample density, and resolution in the spectral domain. We define the information sampling ability of sampling patterns based on these properties. The concept of information sampling ability that we have proposed serves as the criterion to compare different sampling patterns and assess their sampling performances. The sampling patterns with the same information sampling ability have the same capability to gather information, even though the appearance of sampling patterns may be different. We formulate an optimization problem to find this critical subset of sample locations, which has the fewest number of samples but has a similar information sampling ability as that of the desired dense uniform samples. This critical subset is irregularly located, has the optimized properties and forms the ergodic sampling pattern. We define this process of sampling design and associated understanding as the ergodic sampling. Ergodic sampling can be applied to gain two major benefits in practice. First, this approach can save a significant number of samples. We demonstrate ergodic sampling using one‐dimensional synthetic data and a two‐dimensional field geophysical dataset. The simulations confirm that, compared with other sampling strategies, ergodic sampling can use fewer samples to acquire the same amount of information, so that we can save cost. Alternatively, with the same budget, we can use the same number of samples through ergodic sampling to acquire more information. The new ergodic sampling can lead to a new generation of economic and efficient geophysical data acquisition, which could assist in increasing the discovery rate in resource exploration, tackling more earth science problems with a limited budget and can also benefit the environment in the process by reducing the invasiveness in potentially sensitive regions.

Multi‐parameter elastic full‐waveform inversion is a technique that utilizes both P‐ and S‐waves of observed seismic data to produce high‐resolution velocity and density models with accurate amplitude information by minimizing the discrepancy between the predicted and observed multi‐component data. However, due to the nonlinear nature of the multi‐parameter inverse problem, elastic full‐waveform inversion is prone to local minima and ‘cycle‐skipping’. To overcome these challenges, this paper proposes an elastic full‐waveform inversion method that incorporates a double‐cross‐shaped discrete flux‐corrected transport. This method additionally introduces diffusion fluxes in two diagonal directions, which helps to capture low‐frequency information in the observed seismic data and maintain forward modelling stability. Multi‐scale inversion is achieved by gradually decreasing the diffusion flux correction parameter. Numerical experiments on both two typical models and a field data example demonstrate the effectiveness of the proposed elastic full‐waveform inversion method based on the double‐cross‐shaped discrete flux‐corrected transport in generating high‐precision velocity and density models.

Considerably different from sandstones, sands have point‐like contact of grains. In contrast, sandstones have cementation between grains, which has diminished the very narrow gap at contact of grains. In this paper, ultrasonic S‐wave in brine‐saturated glass beads and Ottawa sands is used to detect the very narrow space at contact of grains. The data of the dry beads/sands and brine are inputted into Biot theory to yield phase velocity of the saturated beads/sands. By fitting the theoretical velocity with the ultrasonic measurement, phase velocity, the quality factor and S‐wave permeability are determined as functions of frequency. The predicted ultrasonic quality factors appear to be very close to that of water‐saturated Berea sandstone. Our previous study showed that for Berea sandstone, the low‐frequency S‐wave permeability is approximately half of Darcy permeability. However, for glass beads and Ottawa sands, the S‐wave permeabilities at low frequencies are one‐order magnitude lower than Darcy permeabilities. This well shows that S‐wave permeability of the beads/sands is associated with the very narrow gap at contact of grains which is successfully detected by ultrasonic S‐wave in the indirect way.

Geological structures have been shown by studies to have influence on the occurrence, storage and transportation of groundwater. Understanding the structural network of an area unearths a deep insight into the groundwater dynamics of the area. A geological structural analysis was carried out to reveal the geological structural network of Ghana's Voltaian basin. Using aeromagnetic data, structural density models were generated using the Center for Exploration Targeting grid analysis technique for two depth ranges (that is up to 100 m and 300 m) over the Voltaian basin. The total length of geological structures (lineaments) delineated at depths up to 100 m and 300 m were more than 5000 km and more than 8000 km, respectively. Given this, the study area was observed to be structurally dense at each of the aforementioned depths. The structural density models were discretized into five classes (very low, low, moderate, moderately high and very high regions), each of which was evaluated to determine their spatial association with known locations of groundwater occurrences within the study area using the frequency ratio technique. Frequency ratio results for both structural density models derived at 100 m and 300 m depths show the existence of a strong correlation between high structural density model classes and the known groundwater occurrences. The structural density models were further evaluated using the receiver operating characteristics curve. The area under the receiver operating characteristics curve scores indicates that, although both structural density models showed very good performance (with receiver operating characteristics scores greater than 0.7), the 300‐m depth structural density model performed better than the structural density model generated at a depth of 100 m (with their receiver operating characteristics scores being 0.721 and 0.715, respectively). The obtained results corroborate with literature assertion that groundwater occurrence within the Voltaian basin is mainly associated with structural features. It is expected that the outputs of this study would guide future groundwater exploration programmes within the study area.

We introduce a blended‐acquisition method: temporally signatured and/or modulated and spatially dispersed source array. The former, signatured and dispersed source array has much less constraints in the encoding with operational flexibility, allowing non‐uniform sampling and non‐patterned shooting both in the space and time dimension. The latter, modulated and dispersed source array allows straightforward deblending by filtering and physically separating frequency channels in the frequency domain. We demonstrate our method by synthesizing the blended acquisition followed by deblended‐data‐reconstruction processing in order to discuss the virtues. The examples show that this method could make the blended‐acquisition encoding and operations indeed simple and robust; the same is true for the deblending processing.

Processing land seismic data, especially vibroseis data, is often challenging due to complicated near‐surface situations and source‐generated noise. The case study deals with noisy vibroseis data acquired in the Jaisalmer Basin. The near‐surface estimation in this area is difficult due to a possible velocity reversal manifested in the shingled patterns of the first breaks. The near‐surface workflow incorporates a model‐adaptive first break‐picking approach, essentially integrating two problems of first‐break‐picking and model estimation into a single problem. The signal‐conditioning workflow is based on cascaded scaling and single‐channel‐based noise reduction to prevent the removal of weak signals. Horizon‐based migration velocity analysis was used to focus reflectors on the constant velocity‐migrated stacks. This was particularly useful in areas with dubious velocity trends based on semblance panels. The velocity volume has structural consistency, which provides a better time‐migrated image. The workflow also incorporates a targeted post‐stack processing sequence to enhance continuity, sharpen discontinuities and improve the resolution, as notable by comparing the legacy‐processing results of the same dataset.

In this study, we propose a frequency‐domain autocorrelation as an imaging condition for time‐reversal imaging. The previous imaging conditions in time‐reversal imaging require time‐domain calculations such as inverse Fourier transform. The computational burden of these calculations is critical; therefore, time‐reversal imaging is not the proper method for real‐time event localization. We exclude these time‐domain calculations for efficiency. Instead, the maximum amplitude position of the frequency‐domain autocorrelation of the time‐reversal wavefield is determined as a source location. We conducted numerical tests to validate our imaging condition. The synthetic data test shows that our proposed algorithm provides a more credible source localization result than the conventional grid‐search method does in a noisy environment even using only one frequency component with many receivers. We also applied our algorithm to two real datasets acquired from the small monitoring network in Pohang. The real‐data test shows a comparable result with the result of the grid‐search method.

In viscoacoustic least‐squares reverse time migration methods, the reflectivity image associated with the Q factor is negligible, inverting only the velocity (v) parameter or v‐related variables such as squared slowness or bulk modulus. However, the Q factor influences the amplitude and phase of the seismic data, especially in basins containing gas reservoirs or storing . Therefore, the Q factor and its associated parameters must be considered in the context of viscoacoustic least‐squares reverse time migration. Thus, we propose a multiparameter viscoacoustic least‐squares reverse time migration procedure, which obtains the inverse of bulk modulus (κ) and the Q magnitude (τ) simultaneously. We derive and implement the multiparameter forward and adjoint pair Born operators and the gradient formulas concerning κ and τ parameters. Then, we apply these derivations in our proposed multiparameter approach, which can produce images with better balanced amplitudes and more resolution than conventional reverse time migration images.

Conventional methods solve the full‐waveform inversion making use of gradient‐based algorithms to minimize an error function, which commonly measure the Euclidean distance between observed and predicted waveforms. This deterministic approach only provides a ‘best‐fitting’ model and cannot account for the uncertainties affecting the predicted solution. Local methods are also usually prone to get trapped into local minima of the error function. On the other hand, casting this inverse problem into a probabilistic framework has to deal with the formidable computational effort of the Bayesian approach when applied to non‐linear problems with expensive forward evaluations and large model spaces. We present a gradient‐based Markov Chain Monte Carlo full‐waveform inversion in which the posterior sampling is accelerated by compressing the data and model spaces through the discrete cosine transform, and by also defining a proposal that is a local, Gaussian approximation of the target posterior probability density. This proposal is constructed using the local Hessian and gradient informations of the log posterior, which are made computationally manageable thanks to the compression of the data and model spaces. We demonstrate the applicability of the approach by performing two synthetic inversion tests on portions of the Marmousi and BP acoustic model. In these examples, the forward modelling is performed using Devito, a finite difference domain‐specific language that solves the discretized wave equation on a Cartesian grid. For both examples, the results obtained by the implemented method are also validated against those obtained using a classic deterministic approach. Our tests illustrate the efficiency of the proposed probabilistic method, which seems quite robust against cycle‐skipping issues and also characterized by a computational cost comparable to that of the local inversion. The outcomes of the proposed probabilistic inversion can also play the role of starting models for a subsequent local inversion step aimed at improving the spatial resolution of the probabilistic result, which was limited by the model compression.

Full‐waveform inversion of multicomponent data can provide an improved estimation of medium parameters using both compressional‐ and shear‐wave information. However, most earlier studies that involved a full‐waveform inversion of ocean‐bottom data are based on acoustic anisotropic or elastic isotropic approximations. Here, we consider realistic elastic anisotropic media and develop an efficient full‐waveform inversion framework for estimating model parameters. We simulate seismic wavefields using a previously developed coupled acoustic/elastic wave propagator that implements a mimetic finite‐difference method with fully staggered grids to accurately handle the fluid/solid boundary conditions. The algorithm employs a multiscale approach starting from low frequencies and incorporating higher frequency bands in the later inversion stages. We analyse the influence of different types of input data on the accuracy of the inverted anisotropy parameters for hard and soft water bottoms. The employed misfit function incorporates information from both hydrophones and ocean‐bottom geophones. Numerical examples indicate that injecting multiple data components simultaneously increases the complexity of the objective function and often degrades the quality of the estimated medium parameters. Thus, we propose a sequential strategy using a single data component at a time. Pressure (hydrophone) data alone can provide satisfactory results if long offsets (i.e., with the offset/depth ratio ≥ 3) are available. Adding the horizontal particle‐displacement or ‐velocity components increases the accuracy of the estimated shear‐wave vertical velocity () and P‐wave normal‐moveout () velocity, especially for strongly heterogeneous sub‐water‐bottom models.