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- Volume 68, Issue 9, 2020
Geophysical Prospecting - Volume 68, Issue 9, 2020
Volume 68, Issue 9, 2020
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Windowless Q‐factor tomography by the instantaneous frequency
Authors A. Vesnaver, G. Böhm, P. Cance, M. Dal Cin and D. GeiABSTRACTThe estimation of the Q factor of rocks by seismic surveys is a powerful tool for reservoir characterization, as it helps detecting possible fractures and saturating fluids. Seismic tomography allows building 3D macro‐models for the Q factor, using methods as the spectral ratio and the frequency shift. Both these algorithms require windowing the seismic signal accurately in the time domain; however, this process can hardly follow the continuous variations of the wavelet length as a function of offset and propagation effects, and it is biased by the interpreter choice. In this paper, we highlight some drawback of signal windowing in the frequency‐shift method, and introduce a tomographic approach to estimate the Q factor using the complex attributes of the seismic trace. We show that such approach is particularly needed when the dispersion is broadening the waveforms of signals with a long wave‐path. Our method still requires an interpretative event picking, but no other parameters as the time window length and its possible smoothing options. We validate the new method with synthetic and real data examples, involving the joint tomographic inversion of direct and reflected signals. We show that a calibration of the frequency‐shift method is needed to improve the estimation of the absolute Q factor, otherwise only relative contrasts are obtained.
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Review Paper: Methods of measurement for 4D seismic post‐stack time shifts
Authors Colin MacBeth, Hamed Amini and Saeed IzadianABSTRACTThe estimation of time‐lapse time shifts between two, or several, repeated seismic surveys has become increasingly popular over the past eighteen years. These time shifts are a reliable and informative seismic attribute that can relate to reservoir production. Correction for these time shifts or the underlying velocity perturbations and/or subsurface displacement in an imaging sense also permits accurate evaluation of time‐lapse amplitudes by attempting to decouple the kinematic component. To date, there are approximately thirty methods for time‐shift estimation described in the literature. We can group these methods into three main families of mathematical development, together with several miscellaneous techniques. Here we detail the underlying bases for these methods, and the acknowledged benefits and weaknesses of each class of method highlighted. We illustrate this review with a number of time‐lapse seismic examples from producing fields. No method is necessarily superior to the others, as its selection depends on ease of implementation, noise characteristics of the field data, and whether the inherent assumptions suit the case in question. However, cross‐correlation stands out as the algorithm of choice based on the Pareto principle and waveform inversion the algorithm delivering best resolution. This is a companion study to the previous review of time‐shift magnitudes and a discussion of their rock physics basis.
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Adaptive hybrid diffusion model using variational mode decomposition for edge preserving noise attenuation
More LessABSTRACTPreserving the structural and stratigraphic discontinuities or edges is essential in seismic data processing and interpretation. According to several numerical experiments, it is obvious that random noise has a constant spectral density, whereas the structural features vary significantly within different frequency bands, which means that the ratio between the densities of noise and structural features varies significantly in different frequency bands. Therefore, we propose a method called adaptive hybrid diffusion to attenuate random noise, which utilizes a novel adaptive frequency‐based parameter. First, the adaptive hybrid diffusion method decomposes the seismic sections into several band‐limited portions using variational mode decomposition. These portions are called intrinsic mode functions, in which noise and structural energy have distinct differences. Subsequently, utilizing the adaptive frequency‐based parameter, each intrinsic mode function is divided into several monotonous portions that represent the noise or structural area. Afterwards, the total variation and L2 minimization algorithms are utilized separately to suppress the noise in different band‐limited monotonous areas. The algorithms are chosen dynamically, as the portion changes with the change in the adaptive parameter. Finally, these denoised portions are combined to obtain the denoised seismic section. Experimental results on synthetic and field seismic data showed that seismic noise is effectively suppressed by the adaptive hybrid diffusion method, with the edge details of seismic events well preserved.
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Efficient reflection waveform inversion using a locally normalized zero‐lag correlative objective function
More LessABSTRACTFull‐waveform inversion is characterized by cycle‐skipping when the starting background model differs significantly from the true model and low‐frequency data are unavailable. To mitigate this problem, reflection waveform inversion is applied to provide a background velocity model for full‐waveform inversion. This technique attempts to extract background velocity updates along the reflection wavepath by matching the reflection waveforms. However, two issues arise during the implementation of reflection waveform inversion: amplitude and efficiency. The amplitude is always underestimated due to the complex subsurface parameter (i.e. the source signature, density, attenuation etc.). This makes it unreasonable to match the reflection amplitude involved in waveforms, especially in the filed data cases. In addition, generating the background velocity gradient requires the simulation of the reflection wavefield. However, simulating the reflection wavefield is time‐consuming. To address the former, we introduced a locally normalized objective function, while for the latter, we used an efficient strategy by avoiding the explicit generation of the reflection wavefield. Results show that applying the proposed method to both synthetic and field data can provide a good background velocity model for full‐waveform inversion with high efficiency.
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Time‐domain sparsity promoting least‐squares reverse time migration with source estimation
Authors Mengmeng Yang, Zhilong Fang, Philipp Witte and Felix J. HerrmannABSTRACTLeast‐squares reverse‐time migration is well known for its capability to generate artefact‐free true‐amplitude subsurface images through fitting observed data in the least‐squares sense. However, when applied to realistic imaging problems, this approach is faced with issues related to overfitting and excessive computational costs induced by many wave‐equation solves. The fact that the source function is unknown complicates this situation even further. Motivated by recent results in stochastic optimization and transform‐domain sparsity promotion, we demonstrate that the computational costs of inversion can be reduced significantly while avoiding imaging artefacts and restoring amplitudes. While powerful, these new approaches do require accurate information on the source‐time function, which is often lacking. Without this information, the imaging quality deteriorates rapidly. We address this issue by presenting an approach where the source‐time function is estimated on the fly through a technique known as variable projection. Aside from introducing negligible computational overhead, the proposed method is shown to perform well on imaging problems with noisy data and problems that involve complex settings such as salt. In either case, the presented method produces high‐resolution high‐amplitude fidelity images including an estimate for the source‐time function. In addition, due to its use of stochastic optimization, we arrive at these images at roughly one to two times the cost of conventional reverse‐time migration involving all data.
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2D and 3D amplitude‐preserving elastic reverse time migration based on the vector‐decomposed P‐ and S‐wave records
Authors Wei Zhang, Jinghuai Gao, Zhaoqi Gao and Ying ShiABSTRACTThe elastic reverse time migration approach based on the vector‐wavefield decomposition generally uses the scalar product imaging condition to image the multicomponent seismic data. However, the resulting images contain the crosstalk artefacts and the polarity reversal problems, which are caused by the nonphysical wave modes and the angle‐dependent reduction of image amplitudes, respectively. To overcome these two problems, we develop an amplitude‐preserving elastic reverse time migration approach based on the vector‐decomposed P‐ and S‐wave seismic records. This approach includes two key points. The first is that we employ the vector‐decomposed P‐ and S‐wave multicomponent records to independently reconstruct the PP and PS reflection images to mitigate the crosstalk artefacts. The second is that we propose two schemes in addressing the issue of polarity reversal problem in the conventional PP image. One solution is to adopt the angle‐dependent equation. Another one is to reconstruct an amplitude‐preserving PP image with a separated scalar P‐wave particle velocity, which has a clear physical meaning. Numerical examples using two‐dimensional and three‐dimensional models demonstrate that the proposed elastic reverse time migration approach can provide the images with better amplitude‐preserving performance and fewer crosstalk artefacts, compared with the conventional elastic reverse time migration approach based on the scalar product imaging condition.
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Combining discrete cosine transform and convolutional neural networks to speed up the Hamiltonian Monte Carlo inversion of pre‐stack seismic data
More LessABSTRACTMarkov chain Monte Carlo algorithms are commonly employed for accurate uncertainty appraisals in non‐linear inverse problems. The downside of these algorithms is the considerable number of samples needed to achieve reliable posterior estimations, especially in high‐dimensional model spaces. To overcome this issue, the Hamiltonian Monte Carlo algorithm has recently been introduced to solve geophysical inversions. Different from classical Markov chain Monte Carlo algorithms, this approach exploits the derivative information of the target posterior probability density to guide the sampling of the model space. However, its main downside is the computational cost for the derivative computation (i.e. the computation of the Jacobian matrix around each sampled model). Possible strategies to mitigate this issue are the reduction of the dimensionality of the model space and/or the use of efficient methods to compute the gradient of the target density. Here we focus the attention to the estimation of elastic properties (P‐, S‐wave velocities and density) from pre‐stack data through a non‐linear amplitude versus angle inversion in which the Hamiltonian Monte Carlo algorithm is used to sample the posterior probability. To decrease the computational cost of the inversion procedure, we employ the discrete cosine transform to reparametrize the model space, and we train a convolutional neural network to predict the Jacobian matrix around each sampled model. The training data set for the network is also parametrized in the discrete cosine transform space, thus allowing for a reduction of the number of parameters to be optimized during the learning phase. Once trained the network can be used to compute the Jacobian matrix associated with each sampled model in real time. The outcomes of the proposed approach are compared and validated with the predictions of Hamiltonian Monte Carlo inversions in which a quite computationally expensive, but accurate finite‐difference scheme is used to compute the Jacobian matrix and with those obtained by replacing the Jacobian with a matrix operator derived from a linear approximation of the Zoeppritz equations. Synthetic and field inversion experiments demonstrate that the proposed approach dramatically reduces the cost of the Hamiltonian Monte Carlo inversion while preserving an accurate and efficient sampling of the posterior probability.
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Pure P‐ and S‐wave equations in transversely isotropic media
Authors Alexey Stovas, Tariq Alkhalifah and Umair bin WaheedABSTRACTPure‐mode wave propagation is important for applications ranging from imaging to avoiding parameter tradeoff in waveform inversion. Although seismic anisotropy is an elastic phenomenon, pseudo‐acoustic approximations are routinely used to avoid the high computational cost and difficulty in decoupling wave modes to obtain interpretable seismic images. However, such approximations may result in inaccuracies in characterizing anisotropic wave propagation. We propose new pure‐mode equations for P‐ and S‐waves resulting in an artefact‐free solution in transversely isotropic medium with a vertical symmetry axis. Our approximations are more accurate than other known approximations as they are not based on weak anisotropy assumptions. Therefore, the S‐wave approximation can reproduce the group velocity triplications in strongly anisotropic media. The proposed approximations can be used for accurate modelling and imaging of pure P‐ and S‐waves in transversely isotropic media.
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Convolutional neural networks for automated microseismic detection in downhole distributed acoustic sensing data and comparison to a surface geophone array
Authors Gary Binder and Ali TuraABSTRACTDistributed acoustic sensing is a growing technology that enables affordable downhole recording of strain wavefields from microseismic events with spatial sampling down to ∼1 m. Exploiting this high spatial information density motivates different detection approaches than typically used for downhole geophones. A new machine learning method using convolutional neural networks is described that operates on the full strain wavefield. The method is tested using data recorded in a horizontal observation well during hydraulic fracturing in the Eagle Ford Shale, Texas, and the results are compared to a surface geophone array that simultaneously recorded microseismic activity. The neural network was trained using synthetic microseismic events injected into real ambient noise, and it was applied to detect events in the remaining data. There were 535 detections found and no false positives. In general, the signal‐to‐noise ratio of events recorded by distributed acoustic sensing was lower than the surface array and 368 of 933 surface array events were found. Despite this, 167 new events were found in distributed acoustic sensing data that had no detected counterpart in the surface array. These differences can be attributed to the different detection threshold that depends on both magnitude and distance to the optical fibre. As distributed acoustic sensing data quality continues to improve, neural networks offer many advantages for automated, real‐time microseismic event detection, including low computational cost, minimal data pre‐processing, low false trigger rates and continuous performance improvement as more training data are acquired.
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Seismic signal enhancement based on the low‐rank methods
Authors Min Bai, Guangtan Huang, Hang Wang and Yangkang ChenABSTRACTBased on the fact that the Hankel matrix constructed by noise‐free seismic data is low‐rank, low‐rank approximation (or rank‐reduction) methods have been widely used for removing noise from seismic data. Due to the linear‐event assumption of the traditional low‐rank approximation method, it is difficult to define a rank that optimally separates the data subspace into signal and noise subspaces. For preserving the most useful signal energy, a relatively large rank threshold is often chosen, which inevitably leaves residual noise. To reduce the energy of residual noise, we propose an optimally damped rank‐reduction method. The optimal damping is applied via two steps. In the first step, a set of optimal damping weights is derived. In the second step, we derive an optimal singular value damping operator. We review several traditional low‐rank methods and compare their performance with the new one. We also compare these low‐rank methods with two sparsity‐promoting transform methods. Examples demonstrate that the proposed optimally damped rank‐reduction method could get significantly cleaner denoised images compared with the state‐of‐the‐art methods.
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Experimental study on frequency‐dependent elastic properties of weakly consolidated marine sandstone: effects of partial saturation
Authors Hui Li, Luanxiao Zhao, De‐hua Han, Jinghuai Gao, Hemin Yuan and Yirong WangABSTRACTInvestigating seismic dispersion and attenuation characteristics of loosely compacted marine sandstone is essential in reconciling different geophysical measurements (surface seismic, well logging and ultrasonic) for better characterization of a shallow marine sandstone reservoir. We have experimented with a typical high‐porosity and high‐permeability sandstone sample, extracted from the Paleogene marine depositional setting in the Gulf of Mexico, at the low‐frequency band (2–500 Hz) as well as ultrasonic point (106 Hz), to investigate the effects of varying saturation levels on a rock's elasticity. The results suggest that the Young's modulus of the measured sample with adsorbed moisture at laboratory conditions (room temperature, 60%–90% humidity) exhibits dispersive behaviours. The extensional attenuation can be as high as 0.038, and the peak frequency occurs around 60 Hz. The extensional attenuation due to moisture adsorption can be dramatically mitigated with the increase of confining pressure. For partial saturation status, extensional attenuation increases as increasing water saturation by 79% with respect to the measured frequencies. Additionally, the results show that extensional attenuation at the fully water‐saturated situation is even smaller than that at adsorbed moisture conditions. The Gassmann–Wood model can overall capture the P‐wave velocity‐saturation trend of measured data at seismic frequencies, demonstrating that the partially saturated unconsolidated sandstone at the measured seismic frequency range is prone to be in the relaxed status. Nevertheless, the ultrasonic velocities are significantly higher than the Gassmann–Wood predictions, suggesting that the rocks are in the unrelaxed status at the ultrasonic frequency range. The poroelastic modelling results based on the patchy saturation model also indicate that the characteristic frequency of the partially saturated sample is likely beyond the measured seismic frequency range.
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Step‐on versus step‐off signals in time‐domain controlled source electromagnetic methods using a grounded electric dipole
Authors Amir Haroon, Andrei Swidinsky, Sebastian Hölz, Marion Jegen and Bülent TezkanABSTRACTThe time‐domain controlled source electromagnetic method is a geophysical prospecting tool applied to image the subsurface resistivity distribution on land and in the marine environment. In its most general set‐up, a square‐wave current is fed into a grounded horizontal electric dipole, and several electric and magnetic field receivers at defined offsets to the imposed current measure the electromagnetic response of the Earth. In the marine environment, the application often uses only inline electric field receivers that, for a 50% duty‐cycle current waveform, include both step‐on and step‐off signals. Here, forward and inverse 1D modelling is used to demonstrate limited sensitivity towards shallow resistive layers in the step‐off electric field when transmitter and receivers are surrounded by conductive seawater. This observation is explained by a masking effect of the direct current signal that flows through the seawater and primarily affects step‐off data. During a step‐off measurement, this direct current is orders of magnitude larger than the inductive response at early and intermediate times, limiting the step‐off sensitivity towards shallow resistive layers in the seafloor. Step‐on data measure the resistive layer at times preceding the arrival of the direct current signal leading to higher sensitivity compared to step‐off data. Such dichotomous behaviour between step‐on and step‐off data is less obvious in onshore experiments due to the lack of a strong overlying conductive zone and corresponding masking effect from direct current flow. Supported by synthetic 1D inversion studies, we conclude that time‐domain controlled source electromagnetic measurements on land should apply both step‐on and step‐off data in a combined inversion approach to maximize signal‐to‐noise ratios and utilize the sensitivity characteristics of each signal. In an isotropic marine environment, step‐off electric fields have inferior sensitivity towards shallow resistive layers compared to step‐on data, resulting in an increase of non‐uniqueness when interpreting step‐off data in a single or combined inversion.
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Three‐dimensional electrical structure of the northwestern margin of the Karamay region, China, revealed by magnetotelluric data
Authors Yixin Ye, Shengping Gong, Hui Yu, Zhibing Feng and Wenyu LiuABSTRACTIn order to investigate the three‐dimensional structures of intrusive granite and the deep structure of the Darbut fault in the northwestern margin of the Karamay region, western Junggar Basin, China, new magnetotelluric data were collected along six profiles across the Darbut fault. The magnetotelluric data were processed using a robust estimation technique to obtain the magnetotelluric impedance. Then the off‐diagonal components of the impedance tensor were inverted using a three‐dimensional nonlinear conjugate gradient inversion technique, which was performed using open‐source three‐dimensional electromagnetic inversion software. The final three‐dimensional model includes two major low‐resistivity anomalies and two major high‐resistivity anomalies. The first low‐resistivity anomaly corresponds to the location of the Darbut fault, which indicates that metallic elements are abnormally enriched there. The second one is located beneath the Darbut fault, and it is most likely a magma channel in the middle crust. The two major high‐resistivity anomalies are distributed on either side of the Darbut fault. We interpret them as Karamay rocks and Akebasitao rocks and suggest that they were formed in an extensional setting. The cross sections of three‐dimensional magnetotelluric inversion result reveal that the Darbut fault has been reformed by the later magmatism, leading to the variation of its downward extent along its strike. Moreover, our inversion result also indicates that a magma channel exists in the middle crust of the region.
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Research Note: A workaround for the corner problem in numerically exact non‐reflecting boundary conditions
By W.A. MulderABSTRACTSimulations of wave propagation in the Earth usually require truncation of a larger domain to the region of interest to keep computational cost acceptable. This introduces artificial boundaries that should not generate reflected waves. Most existing boundary conditions are not able to completely suppress all the reflected energy, but suffice in practice except when modelling subtle events such as interbed multiples. Exact boundary conditions promise better performance but are usually formulated in terms of the governing wave equation and, after discretization, still may produce unwanted artefacts. Numerically exact non‐reflecting boundary conditions are instead formulated in terms of the discretized wave equation. They have the property that the numerical solution computed on a given domain is the same as one on a domain enlarged to the extent that waves reflected from the boundary do not have the time to reach the original truncated domain. With a second‐ or higher‐order finite‐difference scheme for the one‐dimensional wave equation, these boundary conditions follow from a recurrence relation. In its generalization to two or three dimensions, a recurrence relation was only found for a single non‐reflecting boundary on one side of the domain or two of them at opposing ends. The other boundaries should then be zero Dirichlet or Neumann. If two non‐reflecting boundaries meet at a corner, translation invariance is lost and a simple recurrence relation could not be found.
Here, a workaround is presented that restores translation invariance by imposing classic, approximately non‐reflecting boundary conditions on the other sides and numerically exact ones on the two opposing sides that otherwise would create the strongest reflected waves with the classic condition. The exact ones can also be applied independently. As a proof of principle, the method is applied to the two‐dimensional acoustic wave equation, discretized on a rectangular domain with a second‐order finite‐difference scheme and first‐order Enquist–Majda boundary conditions as approximate ones. The method is computationally costly but has the advantage that it can be reused on a sequence of problems as long as the time step and the sound speed values next to the boundary are kept fixed.
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Volumes & issues
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Volume 72 (2023 - 2024)
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