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Seismic response from porous sediments can be used in reservoir characterization and fluid detection. Reflection coefficient at the isotropic/poroelastic interface is essential to reveal seismic response from the fluid‐saturated deposits. The exact normal incidence reflection coefficient is given by complex mathematic expression and not very clear relations with solid and fluid properties. Therefore, we derive the reflection coefficient approximate formula in series with respect to the square root of the imaginary unit multiplying by the ratio between angular frequency and the characteristic angular frequency. Compared to the exact reflection coefficient, the proposed approximate formula has a more concise mathematical form and clearer relationship with the moduli and densities. Meanwhile, there is no need to calculate the complex wavenumbers of poroelastic media from the dispersion equation as the exact reflection coefficient. When the frequency tends to zero, the approximate formula is consistent with reflection coefficient for the isotropic/isotropic interface. The proposed formula's applicability is verified through two models with an interface separating the mudstone and fully fluid‐saturated sandstone with pore fluids as water or carbon dioxide. [ABSTRACT FROM AUTHOR]

Cumulative oil predictions are made from stochastically inverted earth attributes. The inverted attributes are from the SEAM Life of Field model and an offshore field in West Africa. To perform the prediction, we use a naïve Bayesian classifier for its transparency in methodology, computational efficiency and flexibility. The inverted properties we use for classification consist of porosity, P‐S wave velocity ratio (Vp/Vs), acoustic impedance and density which are extracted from within a set radius around the well‐path. The production from the wells in both SEAM and the West African field serve as the labels for the naïve Bayesian classifier, which are ultimately placed into two classes: the 'high' and 'low' producers. For calculating the accuracy of the classifier, we perform full cross‐validation with a set number of training wells. The cross‐validation accuracy is 78.0% and 83.3% for the SEAM model and the West African Field respectively. The classifier's sensitivity to the chosen radius around the wells and its inherent independence assumption are investigated and shown to change the bulk accuracy by less than 3.0%. We implement full reservoir classifications on SEAM to highlight potential drilling locations and show the capability of the classifier. Overall, we demonstrate how the naïve Bayesian classifier can efficiently and transparently synthesize the entire distribution of stochastic inversions of seismic data to predict oil production. [ABSTRACT FROM AUTHOR]

Markov 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. [ABSTRACT FROM AUTHOR]

Seismically derived amplitude‐versus‐angle attributes along with well constraints are the base inputs into inverting seismic into subsurface properties. Conditioning the common image gathers is a common workflow in quantitative inversion and leads to a more accurate inversion product due to the removal of post‐migration artefacts. Here, we apply a neural network to condition the post‐migration gathers. The network is a cycle generative adversarial network, CycleGAN, which was designed for image‐to‐image translation. This can be considered the same problem as translating an artefact rich seismic gather to an artefact free seismic gather. To assess the feasibility of applying the network to pre‐stack conditioning, synthetic data sets were generated to train different networks for different tasks. The networks were trained to remove white noise, residual de‐multiples, gather flattening and a combination of the above for conditioning. The results show that a trained network was able remove white noise providing a more robust amplitude‐versus‐offset calculation. Another network trained using synthetic gathers with and without multiples assisted in multiple removal. However, instability around primary preservation has been observed so the network works better as a residual de‐multiple method. For gather conditioning, a network was trained with the unpaired artefact‐rich and artefact‐free training data where the artefacts included complex moveout, noise and multiples. When applied to the test data sets, the networks cleaned the artefact‐rich test data and translated complex moveout into flat gathers whilst preserving the amplitude response. Finally, two networks are applied to real data where a gather based on the well logs is used to quantify the match between the conditioned gathers and the raw gathers. The first network used synthetic data to train the network and, when applied to real data, provided a better tie with the well. The second network was trained with synthetic gathers whose properties were constrained by real seismic gathers from near the well. As anticipated, the network trained on the representative training data outperforms the network trained using the unconstrained data. However, the ability of the first network to condition the gather indicates that a sweep of networks can be trained without the need for real data and applied in a manner analogous to the way parameters are adjusted in traditional geophysical methods. The results show that the different neural networks can offer an alternative or augmentation to the existing geophysical workflow for conditioning pre‐stack seismic gathers. [ABSTRACT FROM AUTHOR]

In geophysical inverse problems, the posterior model can be analytically assessed only in case of linear forward operators, Gaussian, Gaussian mixture, or generalized Gaussian prior models, continuous model properties, and Gaussian‐distributed noise contaminating the observed data. For this reason, one of the major challenges of seismic inversion is to derive reliable uncertainty appraisals in cases of complex prior models, non‐linear forward operators and mixed discrete‐continuous model parameters. We present two amplitude versus angle inversion strategies for the joint estimation of elastic properties and litho‐fluid facies from pre‐stack seismic data in case of non‐parametric mixture prior distributions and non‐linear forward modellings. The first strategy is a two‐dimensional target‐oriented inversion that inverts the amplitude versus angle responses of the target reflections by adopting the single‐interface full Zoeppritz equations. The second is an interval‐oriented approach that inverts the pre‐stack seismic responses along a given time interval using a one‐dimensional convolutional forward modelling still based on the Zoeppritz equations. In both approaches, the model vector includes the facies sequence and the elastic properties of P‐wave velocity, S‐wave velocity and density. The distribution of the elastic properties at each common‐mid‐point location (for the target‐oriented approach) or at each time‐sample position (for the time‐interval approach) is assumed to be multimodal with as many modes as the number of litho‐fluid facies considered. In this context, an analytical expression of the posterior model is no more available. For this reason, we adopt a Markov chain Monte Carlo algorithm to numerically evaluate the posterior uncertainties. With the aim of speeding up the convergence of the probabilistic sampling, we adopt a specific recipe that includes multiple chains, a parallel tempering strategy, a delayed rejection updating scheme and hybridizes the standard Metropolis–Hasting algorithm with the more advanced differential evolution Markov chain method. For the lack of available field seismic data, we validate the two implemented algorithms by inverting synthetic seismic data derived on the basis of realistic subsurface models and actual well log data. The two approaches are also benchmarked against two analytical inversion approaches that assume Gaussian‐mixture‐distributed elastic parameters. The final predictions and the convergence analysis of the two implemented methods proved that our approaches retrieve reliable estimations and accurate uncertainties quantifications with a reasonable computational effort. [ABSTRACT FROM AUTHOR]

ABSTRACT: Extracting true amplitude versus angle common image gathers is one of the key objectives in seismic processing and imaging. This is achievable to different degrees using different migration techniques (e.g., Kirchhoff, wavefield extrapolation, and reverse time migration techniques) and is a common tool in exploration, but the costs can vary depending on the selected migration algorithm and the desired accuracy. Here, we investigate the possibility of combining the local‐shift imaging condition, specifically the time‐shift extended imaging condition, for angle gathers with a Kirchhoff migration. The aims are not to replace the more accurate full‐wavefield migration but to offer a cheaper alternative where ray‐based methods are applicable and to use Kirchhoff time‐lag common image gathers to help bridge the gap between the traditional offset common image gathers and reverse time migration angle gathers; finally, given the higher level of summation inside the extended imaging migration, we wish to understand the impact on the amplitude versus angle response. The implementation of the time‐shift imaging condition along with the computational cost is discussed, and results of four different datasets are presented. The four example datasets, two synthetic, one land acquisition, and a marine dataset, have been migrated using a Kirchhoff offset method, a Kirchhoff time‐shift method, and, for comparison, a reverse time migration algorithm. The results show that the time‐shift imaging condition at zero time lag is equivalent to the full offset stack as expected. The output gathers are cleaner and more consistent in the time‐lag‐derived angle gathers, but the conversion from time lag to angle can be considered a post‐processing step. The main difference arises in the amplitude versus offset/angle distribution where the responses are different and dramatically so for the land data. The results from the synthetics and real data show that a Kirchhoff migration with an extended imaging condition is capable of generating subsurface angle gathers. The same disadvantages with a ray‐based approach will apply using the extended imaging condition relative to a wave equation angle gather solution. Nevertheless, using this approach allows one to explore the relationship between the velocity model and focusing of the reflected energy, to use the Radon transformation to remove noise and multiples, and to generate consistent products from a ray‐based migration and a full‐wave equation migration, which can then be interchanged depending on the process under study. [ABSTRACT FROM AUTHOR]

ABSTRACT Existing and commonly used in industry nowadays, closed-form approximations for a P-wave reflection coefficient in transversely isotropic media are restricted to cases of a vertical and a horizontal transverse isotropy. However, field observations confirm the widespread presence of rock beds and fracture sets tilted with respect to a reflection boundary. These situations can be described by means of the transverse isotropy with an arbitrary orientation of the symmetry axis, known as tilted transversely isotropic media. In order to study the influence of the anisotropy parameters and the orientation of the symmetry axis on P-wave reflection amplitudes, a linearised 3D P-wave reflection coefficient at a planar weak-contrast interface separating two weakly anisotropic tilted tranversely isotropic half-spaces is derived. The approximation is a function of the incidence phase angle, the anisotropy parameters, and symmetry axes tilt and azimuth angles in both media above and below the interface. The expression takes the form of the well-known amplitude-versus-offset 'Shuey-type' equation and confirms that the influence of the tilt and the azimuth of the symmetry axis on the P-wave reflection coefficient even for a weakly anisotropic medium is strong and cannot be neglected. There are no assumptions made on the symmetry-axis orientation angles in both half-spaces above and below the interface. The proposed approximation can be used for inversion for the model parameters, including the orientation of the symmetry axes. Obtained amplitude-versus-offset attributes converge to well-known approximations for vertical and horizontal transverse isotropic media derived by Rüger in corresponding limits. Comparison with numerical solution demonstrates good accuracy. [ABSTRACT FROM AUTHOR]