Geophysical Prospecting - Volume 71, Issue 2, 2023

Adjoint‐state‐based transmission and reflection traveltime inversion are promising approaches for reconstructing a macro velocity field in both shallow and deep depths. However, the contaminated gradient by the uneven illumination impedes the recovery of an optimal velocity model and results in slow convergence rate in inversion. To mitigate this issue, we propose a novel preconditioned transmission + reflection joint traveltime tomography method with transmission and reflection illumination compensation. The proposed illumination compensation operator is theoretically demonstrated as the diagonal elements of the approximated Hessian, which can be efficiently computed in a way similar to gradient calculation. The proposed method can construct a more accurate velocity model compared to the uncompensated counterpart. Convergence is also accelerated by the relatively uniform velocity updates from the shallow to the deep parts. Furthermore, velocity updating and reflector imaging are simultaneously iterated during the inversion. Synthetic numerical example based on the inclusion model indicates that the proposed preconditioned method can result in uniform gradient values of both transmitted and shot/receiver‐side reflected traveltime. The complex foothill model test shows the improved inversion accuracy of the proposed method with an increased convergence rate and improved reflection traveltime predictions using the inverted velocity model. Experiment on the small foothill model indicates that the reflector and velocity can be updated simultaneously, and the inversion accuracy can be significantly improved by selecting multi reflectors. Finally, the effectiveness and practicality of the proposed method are demonstrated by a field data application in East China Sea.

Traditional full‐waveform inversion is a non‐linear and ill‐posed inversion problem. To reduce the non‐linearity of it, joint migration inversion (joint migration inversion) was proposed as an alternative. Joint migration inversion tries to minimize the mismatch between measured and modelled reflection data. One key feature of joint migration inversion is its parameterization: two separate parameters, reflectivity (for the amplitudes of reflected events) and propagation velocity (for the phase effects). This separation helps to reduce the non‐linearity of the inversion. During joint migration inversion, with the velocity being updated, the reflectors in the updated image are also shifting in depth accordingly, this phenomenon is called depth–velocity ambiguity. This interaction between the two parameters during inversion is desired to keep the image time consistent with the measured data but may lead to non‐robustness of joint migration inversion due to the presence of local minima. Therefore, we propose a more robust joint migration inversion scheme, which parameterizes the models with vertical time, termed pseudo‐time joint migration inversion. In pseudo‐time, the updates of velocity will not result in the associated vertical location changes of reflectors in the estimated image. Instead, the reflectors are mainly getting more focused. One limitation is that the depth‐pseudo‐time conversion process assumes a simple linear relationship between depth and pseudo‐time, which might cause some artefacts in the converted models when there exist strong lateral velocity variations. One subsequent round of depth joint migration inversion is recommended to resolve this issue. We demonstrate the effectiveness of our proposed method with a two‐dimensional synthetic example in an extreme scenario, where the initial velocity model is homogeneous, a realistic offshore two‐dimensional synthetic example, a two‐dimensional field example from the Vøring basin in Norway and a simple three‐dimensional synthetic example. In all examples, pseudo‐time joint migration inversion manages to recover more reasonable updates in the inverted velocity and invert more focused reflectors in the inverted image, compared to depth joint migration inversion.

Hydrocarbon depletion causes fluid saturation and pressure changes, resulting in perturbations in reservoir elasticities and, hence, observable time‐lapse (or 4D) seismic responses. Using controlled physical modelling experiments, we aim to evaluate reservoir heterogeneities‐related scattering effects on seismic signatures and assess pore‐fluid substitution impacts on the 4D seismic attributes. Physical modelling experiments reveal that wave propagations in heterogeneous rocks produce substantially magnified 4D attribute differences related to fluid replacements, contrary to seismic features in homogeneous rocks. In particular, reflected waveforms from the gas‐filled scenario exhibit more apparent discontinuities and amplitude variations than water‐ and oil‐saturated scenarios in the heterogeneous regions. It is interesting to see that fluid substitution‐induced 4D seismic differences are observable within the weakly heterogeneous region but significantly strong within the highly heterogeneous region. Although it is expected that substituting oil with water produces weak perturbations in reservoir elasticities, the 4D difference observations between time‐varying records are apparent. This implies that in addition to reservoir heterogeneities‐induced amplifying effects, 4D seismic anomalies are also caused by pore‐fluid changes. Due to mesoscopic rock heterogeneities, seismic responses are complicated, and 4D difference estimates will be amplified strongly and, thus, unable to quantify variations in fluid saturation appropriately. This implies that obvious difference volumes in the underburden regions do not necessarily correspond to significant variations in pore‐fluid. Subsequently, two end‐member rock physics models were applied to predict the widest range of velocity variations and pore‐fluid behaviours. Although mesoscopic heterogeneities cause varying degrees of difficulties for hydrocarbon detection, the deformed waveform‐induced seismic attribute anomalies, which are often greatly amplified, may be beneficial for more accurately identifying reservoir fluids and monitoring their minor variations in practice.

Interpolation techniques provide an effective method for recovery of missing traces. In recent years, many researchers have applied deep learning methods to seismic data interpolation. Generally, one can choose synthetic data as a training set; however, the features of synthetic data are always inconsistent with those of field data, which may lead to inaccurate interpolation. Meanwhile, U‐Net is a common network structure used in seismic data interpolation; however, the four downsampling and upsampling structures of U‐Net have limited adaptability for different data. In this study, the deep learning method based on U‐Net++ was proposed for seismic data interpolation, which contains U‐Net with different depths. The different depths were connected by skip pathways, and the best depth of the network was chosen for different seismic data by deep supervision. Furthermore, a new strategy for training sets was designed: frequency‐wavenumber (f‐k) bandpass filters were used to convert natural images into a natural seismic training set, which has a stronger generalization capability than synthetic data as the training set. The characteristics of the new training set can effectively improve the accuracy of missing data reconstruction. Compared with the conventional U‐Net and traditional interpolation techniques, for example, the Fourier Bregman method, the proposed method produces more accurate and reasonable interpolation results. Further, it can reconstruct both irregular and regular missing seismic data, even in the presence of strong random noise and aliasing. Synthetic and field data tests showed the effectiveness, robustness and generalization of the proposed method.

Seismic diffracted wavefield has substantial potential for high‐resolution subsurface imaging of discontinuous geological structures; however, they are often masked by higher amplitude reflection, thus requiring separation. According to the low‐rank nature of a seismic wavefield, the diffracted wavefield can be extracted using the rank‐reduction method. The traditional low‐rank diffraction separation suffers from a threshold selection problem, especially for field data. To improve threshold accuracy, we propose a method in the common‐offset or poststack domains based on the f–x ensemble empirical mode decomposition and multichannel singular spectrum analysis. We demonstrate that such decomposition allows the determination of the diffraction threshold according to the difference between the singular values of the data before and after it. Synthetic and field data examples prove that the decomposition can effectively predict and suppress the horizontal reflected signal, while attenuating the energy of the dipping reflected signal. The following multichannel singular spectrum analysis suppresses the dipping reflection and separates the diffraction according to the precise threshold obtained earlier. The proposed method effectively improves the accuracy of the diffraction threshold selection, enhances diffraction and attenuates reflection, resulting in an enhanced image of small‐scale geological structures.

Rock physics modelling in deeply buried tight carbonate reservoirs is more challenging than the clastic reservoir because of its complex pore systems. Therefore, modelling complex pore geometries in carbonates reservoir plays an important role in the geophysical measurements to infer pore‐type distribution and their volume fraction, which control the fluid flow properties governed by their complex geological history. This paper presents the use of a robust and practical integrated and iterative seismic petrophysics, and rock physics modelling workflow for the characterization of a deep tight mixed (carbonate and clastic) sedimentary reservoir of a recently discovered oil field located in the Potwar Basin onshore Pakistan. The case study incorporates a careful assessment of well‐log data quality, workflow used for well data conditioning and consequent improvement in data quality, seismic petrophysics and rock physics modelling results. Rock physics diagnostics identified data quality issues and rectified them using appropriate measures to ensure that the rock physics modelling scheme reliably predicts elastic logs honouring different pore types (reference, soft, stiff and cracks) distribution validating from the well observations. Two inclusion‐based rock physics models (Xu and Payne for carbonate and Keys and Xu for clastic) are used to predict rock elastic (P‐sonic, S‐sonic and density) properties responses. Utmost care is exercised to integrate all available data/information, such as Formation Micro‐Imager, mud‐log, testing data and calibrated pore‐type inversion results from well‐log data with the pore geometry revealed by Formation Micro‐Imager and core information. The rock physics modelling provided consistency between elastic and petrophysical properties by calibrating the estimated properties with the measure logs and improved understanding in terms of lithology and fluid separation in the tight carbonate interval. Finally, rock physics‐modelled elastic logs (P‐sonic, S‐sonic and density) are used along with seismic data (partial stacks) and horizons interpretation model to compute pre‐stack synthetic seismograms to calibrate with the preconditioned seismic data. A significant improvement in the well‐to‐seismic calibration is achieved from rock physics modelled logs compared with the original (measured) elastic logs at well location using pre‐stack seismic data, which, further, can help produce reliable reservoir rock properties of interest from the inversion of seismic data.

We present a new unified model for the permeability, electrical conductivity and streaming potential coupling coefficient in variably saturated fractured media. For those, we conceptualize the fractured medium as a partially saturated bundle of parallel capillary slits with varying sizes. We assume that the fracture size distribution of the corresponding medium follows a fractal scaling law, which allows us to establish a pressure head‐saturation relationship based on the Laplace equation. We first describe the flow rate, the conduction current and the electrokinetic streaming current within a single fracture. Then, we upscale these properties at the scale of an equivalent fractured media partially saturated in order to obtain the relative permeability, the electrical conductivity and the streaming potential coupling coefficient. The newly proposed model explicitly depends on pore water chemistry, interface properties, microstructural parameters of fractured media and water saturation. Model predictions are in good agreement with both experimental and simulated data and with another model from the literature. The results of this work constitute a useful framework to estimate hydraulic properties and monitor water flow in fractured media.

A Bayesian inversion methodology is proposed that inverts angle‐stacked 4D seismic maps to changes in pressure, water saturation and gas saturation. The inversion method is applied to data from a siliciclastic reservoir in the west of Shetlands, UK continental shelf. We present inversion results for three seismic monitor surveys and demonstrate the added value of pressure‐saturation inversion by providing insights into reservoir connectivity and fluid dynamics across 14 years of reservoir production. In these surveys, 4D seismic signals related to waterflood, pressure increase and depletion, and gas exsolution are evident and overlap each other in many regions. To regularize this ill‐posed inversion problem, we propose a Bayesian formulation that incorporates spatially variant prior information derived from a history‐matched reservoir simulation model and well pressure measurements. The benefit of incorporating these multi‐disciplinary data as prior information is demonstrated by comparing to inversion results using a spatially invariant prior. We show that the method takes advantage of the multi‐disciplinary prior information to make more precise inferences where the seismic data are most uncertain. This leads to more realistic spatial distributions for the pressure and water‐saturation inversion results. The non‐uniqueness in this non‐linear inversion is studied by analysing uncertainty estimates produced by stochastic sampling of the Bayesian posterior distribution. Posterior standard deviations are observed to be related to the sensitivity of the seismic amplitudes to the changes in each dynamic property as well as the degree of overlap between changes in different dynamic properties. Estimated pressure increases have a posterior standard deviation of approximately 1 MPa, whereas posterior standard deviations for pressure decrease are on average 4 MPa, with higher values applicable to regions of gas exsolution. The posterior standard deviation for estimates of gas saturation change is 0.07 for moderate, visible saturation signals, but 0.005 for low‐to‐zero gas saturation change. The posterior standard deviation for estimated water saturation change is mainly influenced by overlapping changes in pressure and gas saturation. When water changes dominate the 4D seismic signal, posterior standard deviations are on average 0.05. These values rise to 0.25 in areas where the water change is obscured by pressure or gas‐saturation changes.

Particle swarm optimization is widely applied in self‐potential inversion, but most of these applications are limited to simple polarized bodies like inclined sheets and spheres. In this paper, two variants of particle swarm optimization are formed by introducing the resistivity constraint matrix and the damping factor and are then applied to two‐dimensional self‐potential source inversion. The two variants are combined to balance the exploration and exploitation capabilities in different situations, and the rationality of the parameter selection is validated through the stability analysis. To ensure both compactness and smoothness of the inversion results, we adopt an objective function based on L1–L2 norm regularization. Finally, we verify the effectiveness of the proposed algorithm through synthetic examples, the Cu–Fe model sandbox experiment and a field example. By imposing certain constraints, particle swarm optimization also shows great potential in high‐dimensional self‐potential source inversion, instead of being limited to the inversion of a few parameters.

The Serra das Éguas Complex, in Brumado, state of Bahia, located in the northeastern region of Brazil, is a geological structure comprising volcanochemical, siliciclastic and carbonate units that contain layers and lenses of magnesite, important as a refractory in steel, cement, glass and copper and other applications. Considering the importance of such sort of deposit, this work aims to (i) study the physical properties of magnesite deposits via direct measurements of radiometric spectrometry and magnetic susceptibility associated with chemical analysis of the available borehole core samples; (ii) analyse the magnetic and radiometric data acquired by the combined airborne survey over the area with known magnesite deposits; (iii) estimate the magnetic response of the magnesite deposits and surrounding rock formations via 2D forward and 3D inverse magnetic modelling; (iv) evaluate and, if necessary, reconsider the stratigraphic sequences of the identified geological units of the Complex using the results of the 2D and 3D magnetic modelling. Through forward/inverse models, we noted an expressive magnetic signature likely related to the iron formations and metamafic and meta‐ultramafic rocks. The radiometric data analysis on the drill cores showed that the reddish magnesite has a well‐defined U/Th signature. Furthermore, the results show that the carbonate unit, which contains the magnesite deposits, has the lowest amplitude of magnetization values, and both signatures might be helpful for their identification. Additionally, the magnetic models show that the carbonate unit lies in the upper part of the stratigraphic sequence of the Serra das Éguas Complex. This conclusion drives us to propose a new stratigraphy sequence, where the volcanochemical unit that includes the iron formations lies at the bottom of this stratigraphic sequence.

The use of potential field methods for geophysical exploration purposes is nowadays quite common: these techniques consent to retrieve geological knowledge over extended regions and can give complementary information where other invasive or expensive techniques, such as seismic acquisitions, fail (e.g., in the recovery of geometries of geological horizons beneath a thick salt layer). Recent dedicated satellite gravity and magnetic missions, such as GRACE, GOCE and SWARM together with the exploitation of offshore satellite altimetry and airborne/shipborne surveys, have paved the way to the realization of a variety of global models, characterized by spatial resolutions of about 4 km (both for gravity anomaly and lithosphere magnetic anomalies) and high accuracy (about mGal and 20 nT). These models are a valuable source of information to study the geological evolution and characterization of the lithosphere structure, especially at a regional scale. In the present work, some preliminary technical aspects related to the use of these models to perform three‐dimensional inversion are discussed, thus defining an empirical but rigorous procedure to set up gravity and magnetic inversion. In particular, we address the questions whether the classical planar approximation is acceptable for regional inversions or if a spherical one is required. We also provide guidance for choosing the best gravity functional (e.g., gravity anomalies or second radial derivative of the anomalous potential) and the optimal sizing of the three‐dimensional volume area to be modelled depending on the specific target investigated. The application of the proposed methods to the Mediterranean case study is also presented.

The mapping of the vertical and lateral variations in the physical properties of the few‐meter cover layer over near‐surface aquifers is important for hydrogeological modelling, particularly for the quantification of the recharge of groundwater systems. The first ground‐based time‐domain electromagnetic survey over a small catchment (Avesnelles, France) of the watershed of Orgeval (Seine basin) was carried out to determine discontinuities in the first silt layer as well as in the Brie multilevel aquifer limestone horizon. The results highlighted the following: (1) a good sensitivity of the time‐domain electromagnetic survey to the presence of multi‐decametric resistive sand lenses, particularly in a location where they were previously identified and (2) the interest in conducting a survey at a fine sampling step but extending to the meso‐scale. To overcome the sampling issue over a watershed of several hundred square kilometres, we proposed numerically assessing the use of a prototype of low‐cost airborne transient electromagnetic systems towed by light fixed‐wing airplanes (with transmitting and receiving loops in the same plane). The present numerical analysis, in 1D for the vertical (i.e. thickness) variation and in 3D for the lateral extensions of localized sandy and resistive units, showed that a conductive few‐meter cover can be mapped even with a system flying at 50 m with, however, the need of a priori constraint on the resistivity of the first layer to estimate its thickness variation as accurately as possible. Even if it did not bring more sensitivity to the layer thickness and despite the severe difficulty of practical implementation with a decametric emission loop, the vertical co‐planar configuration potentially offered better near‐surface lateral resolution (down to ∼40 m) to delineate the sandy units (discontinuities) within the silt layer (if units are at least 50 m in size) and provided better spatial constraints compared to the classical horizontal co‐planar geometry used in the time‐domain electromagnetic. Even if not aerodynamically in the plane of the emission loop, the measurement of the Hx component with a vertical dipole emission loop (PERPxz geometry for perpendicular) improved the lateral resolution (down to ∼20 m; still with at least 50 m size sand units) and confirmed that a geometry different from the classical horizontal co‐planar configuration could be valuable.