Geophysical Prospecting - Volume 71, Issue 8, 2023

Tensors have been proposed to represent pre‐stack seismic data, particularly for seismic data denoising and reconstruction. They naturally permit describing multi‐dimensional seismic signals that depend on time (or frequency) and source and receiver coordinates. A tensor representation aims to preserve the information embedded in the multi‐linear array in a reduced space. Such a representation is part of many algorithms for seismic data reconstruction via tensor completion methodologies. We investigate and apply one particular tensor tree representation to seismic data reconstruction. The Tensor Tree decomposition methodology permits decomposing a high‐order tensor into third‐order tensors. The technique relies on the truncated singular value decomposition, which branches the tensors into low‐dimensional tensors. As a benefit, the tensor tree allows us to reorganize the tensor into a matrix that demands the least singular values to have an optimal low‐rank approximation. We have developed an algorithm that uses the tensor tree for data reconstruction in an iterative optimization scheme and directly compared it to the parallel matrix factorization. At first, we demonstrated the proposed methodology results with five‐dimensional synthetic shot data and then moved forward with five‐dimensional field data, where we analysed it both pre and post‐stack. The tensor tree performs well in reconstructing both synthetic and field data with high fidelity, at the same level as the well‐established parallel matrix factorization.

Microseismic datasets typically have relatively low signal‐to‐noise ratio waveforms. To that end, several noise suppression techniques are often applied to improve the signal‐to‐noise ratio of the recorded waveforms. We apply a linear geometric mode decomposition approach to microseismic datasets for background noise suppression. The geometric mode decomposition method optimizes linear patterns within amplitude–frequency modulated modes and can efficiently distinguish microseismic events (signal) from the background noise. This method can also split linear and non‐linear dispersive seismic events into linear modes. The segmented events in different modes can then be added carefully to reconstruct the denoised signal. The application of geometric mode decomposition is well suited for microseismic acquisitions with smaller receiver spacing, where the signal may exhibit either (nearly) linear or non‐linear recording patterns, depending on the source location relative to the receiver array. Using synthetic and real microseismic data examples from limited‐aperture downhole recordings only, we show that geometric mode decomposition is robust in suppressing the background noise from the recorded waveforms. We also compare the filtering results from geometric mode decomposition with those obtained from FX‐Decon and one‐dimensional variational mode decomposition methods. For the examples used, geometric mode decomposition outperforms both FX‐Decon and one‐dimensional variational mode decomposition in background noise suppression.

Least‐squares reverse time migration, a linearized inversion problem, can provide high‐quality migration image by minimizing the misfit function, which is defined by predicted and observed data. According to the theory of data‐domain least‐squares reverse time migration, a forward source wavefield that is simulated with a fixed background velocity does not change during iterations. However, storing the forward source wavefield directly into computer memory involves substantial memory consumption. Although a source wavefield reconstruction technique can be applied during least‐squares reverse time migration iterations, this approach can increase the computational cost because of the need for additional wavefield simulations. To alleviate this computational issue in storing the forward source wavefield, we propose an efficient least‐squares reverse time migration scheme based on an excitation amplitude method. Unlike conventional excitation amplitude imaging conditions, the proposed least‐squares reverse time migration scheme enables one to reconstruct the forward source wavefield by convolving a source wavelet with the excitation amplitude of Green's function at the excitation time. With this excitation amplitude method, the forward source wavefield can be efficiently stored in the computer memory because the sizes of the excitation amplitude and excitation time maps are equal to the size of one snapshot. To validate the feasibility of our least‐squares reverse time migration scheme, we perform dot‐product tests and compare forward source wavefields, demigrated data and gradient vectors obtained by conventional least‐squares reverse time migration and our proposed least‐squares reverse time migration. Using numerical tests on synthetic data, we confirm that our least‐squares reverse time migration can produce high‐quality migration results with a significant improvement in computational efficiency with respect to performance time and memory consumption.

In this paper, a new geometric inversion method is proposed for obtaining the elastic parameters of an anisotropic focal regions More precisely, the eigenvalues of a vertical transversely isotropic elasticity tensor of a focal region are inverted up to a constant for a given only one moment tensor with the accuracy depending on the strength of anisotropy. The reason for using only one moment tensor is that although there might occur several earthquakes in the same focal region, the orientation of the sources is similar to each other. Hence, one cannot obtain independent equations from each earthquake in order to use them in the inversion of elastic parameters of the focal region. Moreover, this method can be applied for real‐time inversion once the moment tensor of an earthquake is evaluated. The inversion method relies on the geometric fact that a moment tensor can be written as a linear combination of the eigenvectors of the anisotropic focal region's elasticity tensor. Then, in the inversion, we use the fact that each coefficient of this unique decomposition is proportional to the eigenvalues of the focal region's elasticity tensor. Two approximations are used in this inversion method, in particular for the potency and the source orientations. The strength of anisotropy of the focal region determines how accurate these approximations are, and, hence, it also determines the resolutions of the inverted eigenvalues. Because of the anisotropy of the focal region, the errors in the inversion do depend on orientations of the dip and rake angles but not on the strike angle since the focal region is vertically transversely isotropic. The accuracy of the inversion for the five parameters of vertical transversely isotropic is shown for every 10°‐gridded orientation of the dip and rake angles on the stereographic projection. The results are very promising along some orientations as shown in the figures. The last section of the paper deals with the inversion of eigenvalues, up to a constant, for a given set of moment tensors; not by using only one moment tensor. It turns out that the best fit corresponds to the average of inversions obtained for different orientations of the sources.

In the seismic wave exploration field, first break picking is an important underlying task. With the emergence of massive seismic data, it is urgent to develop automatic and accurate picking algorithms to relieve the huge workload of manual picking. Although many traditional and machine learning based techniques have been developed, it is still a challenging task to obtain satisfactory picking results in practice because of complex subsurface structures and low signal‐to‐noise ratio. Ensemble learning has been demonstrated to be a powerful tool to produce good prediction results in many fields. Its core idea is to create multiple models with some special techniques and then to combine the prediction results of each model with a fusion strategy. Structured random forests , a type of ensemble learning method, have been proven to be quite effective in implementing structured learning tasks. Based on the observation that adjacent traces can provide useful information to pick the first arrival time for a specific trace, we propose in this paper a novel structured random forest based first break picking framework. In particular, a multi‐scale normalization technique is presented to make full use of the amplitude information at different scales. To capture local features of first breaks, an enhanced feature map based on the short‐term/long‐term average ratio method is also computed. By extracting patches from two channel feature maps, we construct a structured random forest to predict the locations of the first breaks. On the basis of the probability score map produced by the structured random forest, an effective post‐processing strategy is proposed to further deal with the detected results. By conducting experiments with synthetic and field data, the proposed method is shown to be effective in identifying first breaks. It is significantly superior to the short‐term/long‐term average ratio method and support vector machine in terms of picking accuracy. With the advantage of parallel computing, the computational cost of structured random forest is acceptable, that is, it is much lower than the support vector machine while being higher than the short‐term/long‐term average ratio method. In addition, the experiments also confirm that the multi‐scale normalization plays an important role in improving the picking performance of the structured random forest.

The salt interpretation can be quite time‐intensive and challenging. Full‐waveform inversion, as a data‐driven optimization algorithm with full wavefield modelling, has become one of the essential tools for earth model building. However, full‐waveform inversion application in the complex salt geology, especially with streamer data collection, is limited, whereas the ocean‐bottom node with ultra‐long offsets and low frequencies unleashes the power of full‐waveform inversion. Sparse ocean‐bottom node acquisition has become a standard approach to improve the earth model building by the addition of ultra‐long offsets and possibly low frequencies. The new survey designs with ocean‐bottom node coupled with simultaneous shooting can be deployed on a regional basis covering thousands of square kilometres in a cost‐effective manner. In complex geological settings, including irregular salt geometry, salt interpretation has a direct impact on subsalt imaging. The recent development of robust objective functions allows full‐waveform inversion work with sparse ocean‐bottom node surveys in the deep‐water environment as the Gulf of Mexico to build and refine the salt geometries and correct the background velocity error in subsalt, uncovering the structural configuration of the basin that has not been seen before. Although full‐waveform inversion mostly employs the acoustic wave equation, we know that the high velocity boundaries in the earth model may require elastic wavefield propagation. Increased physics in full‐waveform inversion allows us to interrogate the power of elastic full‐waveform inversion versus acoustic full‐waveform inversion, and here, we demonstrate that elastic full‐waveform inversion has an advantage over acoustic full‐waveform inversion despite the extra cost associated with implementing the more complete physics.

The primary focus of this study is to explore the potential mineral areas. Advanced Spaceborne Thermal Emission and Reflection Radiometer images and radiometric data were combined in the Tikirt region to map hydrothermal alteration zones associated with mineralized deposits. Advanced Spaceborne Thermal Emission and Reflection Radiometer images were analysed using band ratios, principal component analysis and a fuzzy logic model to discover argillic, phyllic, propylitic and iron oxide alterations and to generate a mineral prospectivity map. In addition, mono‐element maps of radiometric elements (K in %, eU in ppm, eTh in ppm) and their behaviour in the ternary image have been elaborated to determine the concentrations of radiometric elements and the variation of radiometric character along the exposed terrains. The F parameter was calculated to target high potassium concentration areas associated with hydrothermal alteration zones. Combining the two methods highlighted four hydrothermal alteration zones considered very promising from a mining point of view. These zones are generally linked to the magma bodies affected by normal faults and exhibit a clear spatial correlation with mineral occurrences.

Well mineralogy can be estimated from probabilistic, direct and machine learning models; however, all these models have limitations. The maximum number of components in probabilistic models is restricted to the number of logs plus one. Direct models require the precise composition of minerals. Machine learning models demand unbiased databases, a challenge as the samples are collected in reservoir intervals. These limitations impact the evaluation for the Santos Basin pre‐salt rocks due to the complexity of facies and magnesian clays. This work proposes creating a hybrid model through the combination of probabilistic and machine learning models. First, mineral fractions of calcite, dolomite, quartz, k‐feldspar, detrital clay, plagioclase and pyroxene are estimated by the algorithm XGBoost trained using rock samples. Then, a probabilistic model reconstructs the well logs and machine learning estimations through the seven minerals mentioned plus magnesian clays, pyrite, barite and fluids. The difference between the real and reconstructed responses is minimized, weighted by the curves’ uncertainties. The hybrid model is used to estimate the mineralogy of three wells drilled in the Santos Basin, honouring the mineralogy of the rock samples collected in these wells and improving the quantification of dolomite, pyroxene and magnesian clay. Among the advances introduced, the following stand out: The use of machine learning estimates and well logs improved the quantification of magnesian clay; the machine learning estimates regularized the probabilistic model, generating more coherent results; the uncertainties of the machine learning algorithms dealt with database bias. The hybrid model mitigated limitations related to database bias without the costs associated with collecting more samples.

The elastic moduli of subsurface rocks saturated with geofluid often depend on the wave frequency and confining pressure due to the wave‐induced fluid flow and their significant intrinsic compressibility. Therefore, the knowledge of the pressure‐dependent dispersion of elastic moduli is usually used in broad practical scenarios such as geofluid discrimination and in situ abnormal pressure detection. We propose a simple dual‐porosity model to describe the pressure and frequency dependence of elastic moduli of fluid‐saturated rocks. First, we follow the idea of the Shapiro dual‐porosity model to yield more accurate formulas for pressure‐dependent stiff porosity and crack porosity. Then the new formulas for stiff and crack porosities are utilized to express the bulk and shear moduli of dry rocks as a function of pressure. Further, the bulk and shear moduli of a modified frame (i.e. a rock skeleton with the dry stiff pores and fluid‐saturated cracks) are formulated with the pressure‐dependent elastic moduli of dry rock. In order to consider the wave energy attenuation induced by fluid in cracks, the frequency‐independent fluid modulus imbedded in the formulas for bulk and shear moduli of a modified frame is replaced with a frequency‐dependent one incorporating the effect of viscoelastic relaxation. The effective bulk and shear moduli of entire fluid‐saturated body can be computed by inserting the pressure‐dependent stiff porosity and elastic moduli of a modified frame into the Gassmann equation. Moreover, appropriate simplification is performed on the central equations in the case of low porosity and weak deformation of stiff pores to yield an approximate model. Modelling results show that the proposed model can reasonably account for the nonlinear variation of bulk and shear moduli with the elevating effective pressure and cautiously predict the wave dispersion and attenuation. We validate our model by comparing the predicted elastic moduli with the corresponding results given by Shapiro model–based equations and with the laboratory measurements of five different fluid‐saturated rock samples.

Outcrop analogues play a key role in the characterization of subsurface carbonate platforms. The lack of well data and relevant outcrop analogues can result in the misinterpretation of seismic data. To address this issue, we apply an integrated workflow based on sedimentology, geophysics and petrophysics on outcrop analogues present onshore Lebanon, to constrain the carbonate platform's properties on onshore seismic data. A thorough sedimentary description is completed for a 400‐m‐thick Cenomanian–Turonian carbonate platform located in Kfarhelda, northern Lebanon. P‐wave velocity is acquired directly on the outcrop, and the petrophysical properties are measured on 44 samples. A 1D synthetic seismogram is computed with Ricker wavelet 25 Hz resembling seismic resolution. The resulting reflectors are mainly (1) high amplitude reflectors at the limit between two facies with contrasting physical properties enhanced by diagenesis, (2) moderate amplitude reflectors corresponding to stratigraphic limits at the transition between facies and (3) very low amplitude reflectors in karstified units. The integration of outcrop and seismic data is based on the generation of the synthetic seismogram to identify the geological origin of reflectors. The best fit between the synthetic seismic and seismic profile is used to interpret a seismic facies representing bedded limestones of Sannine and Maameltain formations (Cenomanian–Turonian). Two other distinctive reflectors are identified at the boundary of the Marly Limestone Zone, and the Channel facies unit characterized by bioclastic packstone to floatstone. This study highlights the importance of using outcrop analogues to identify the seismic signal of stratigraphic sequences and improve the interpretation of onshore seismic data.

Shales are rocks with a complex structure. Shales contain high clay content, which constitutes a load‐bearing skeleton. In this study, we present a novel rock physics model to obtain elastic stiffness coefficients of both clays and shales. The robustness of the model is then verified by a field dataset from Eagle Ford shale. We utilize the extended Maxwell homogenization scheme as a rock physics model for transversely isotropic media, which honours the aspect ratio of each inhomogeneity embedded in an effective inclusion domain. Estimated anisotropy parameters ε, γ and δ, on average, are 0.19, 0.29 and 0.04, respectively, based on our modelling results in Eagle Ford shale. Anisotropic modelling results exhibit a good correlation with dipole sonic logs. Both dipole sonic log analysis and rock physics results demonstrate that clay content is the main driver of anisotropy in the field, and there is a direct relationship between clay volume and anisotropy parameters of ε and γ. The method shown here can be readily applied to other unconventional reservoirs.

Ground‐penetrating radar full‐waveform inversion is a high‐resolution method for inverting permittivity and conductivity; however, the issue of multi‐parameter crosstalk during the inversion process, in which perturbations of permittivity and conductivity can produce nearly identical observed data, poses a challenge. Additionally, full‐waveform inversion is highly nonlinear and computationally expensive. In this study, we conducted a sensitivity analysis based on permittivity and conductivity perturbations, which demonstrates that their sensitivities vary with frequency. Specifically, conductivity perturbation has a larger impact on low‐frequency data, whereas permittivity perturbation increasingly affects high‐frequency data. Based on the sensitivity analysis, we propose a modified stepped inversion strategy to mitigate multi‐parameter crosstalk. We also employed wavefield reconstruction inversion, which relaxes the wave‐equation constraint as a penalty term and, thus, can help us avoid local minima of the objective function. In contrast, full‐waveform inversion is more prone to get stuck owing to mismatches between modelled and measured data during the inversion process. Finally, we tested the proposed approach on crosshole synthetic data, which achieved significant computational savings and higher inversion efficiency for fewer forward simulations. Our results demonstrate that the proposed approach is a promising method for inverting subsurface structures and has the potential for practical applications in the future.

This study reports results of gravity and magnetic surveys conducted for the first time in the western segment of the Zagros Fold‐and‐Thrust Belt in the Kurdistan Region. This study attempts to delineate deep structures in an area, which has not been surveyed before. CG‐5 Autograv gravimeter and G‐857 portable proton‐precession magnetometer were used to acquire gravity and magnetic data from 750 stations along over eleven traverses across and parallel to the Zagros trend (NW–SE). Six of these traverses are parallel to the Zagros trend, whereas the others are perpendicular to the trend of the other traverses and can be tied where they intersect. The total length of the traverses is about 1000 km. Tilt Angle of horizontal gradient method is used to detect regional gravity and magnetic lineaments. The mapped lineaments from regional gravity and magnetic surveys are divided into two categories: the NE–SW lineaments, which represent transversal faults in the study area, and the NW–SE lineaments, which represent the Zagros Thrust Faults, some of which may be linked to the inverted basement normal faults of Arabian passive margin (the NW–SE Najd Fault system). The results show that there is a relationship between the regional gravity and magnetic lineaments outlining the same deep geological features. The data presented here confirm the presence of regional longitudinal and transversal lineaments documented in other studies (e.g. Anah‐Qalat Dizeh Fault, Surdash‐Tikrit Fault, Sirwan Fault, Khanaqin Fault, Zagros Mountain Front Fault, Baranan Back Thrust Fault and High Zagros Reverse Fault) and outlines new lineaments not mapped before. Most of the detected regional lineaments in the current study coincide with the previously confirmed lineaments, which have played a significant role in the tectonic evolution of the Zagros Fold‐and‐Thrust Belt. As such, this study contributes to a better understanding of the subsurface structure of the Kurdistan segment of the Zagros Fold‐and‐Thrust Belt and probably the rest of the belt.