Pre-stack Data Research Articles

Application of Reversible Jump Markov Chain Monte Carlo Algorithms to Elastic and Petrophysical Amplitude-Versus-Angle Inversions

We infer the elastic and petrophysical properties from pre-stack seismic data through a transdimensional Bayesian inversion. In this approach the number of model parameters (i.e. the number of layers) is treated as an unknown, and a reversible jump Markov Chain Monte Carlo (rjMCMC) algorithm is used to sample the variable-dimension model space. This inversion scheme provides a parsimonious solution, and reliably quantifies the uncertainties affecting the estimated model parameters. Parallel tempering, which employs a sequence of interacting Markov chains in which the likelihood function is successively relaxed, is used to improve the efficiency of the probabilistic sampling. In addition, the delayed rejection updating scheme is employed to speed up the convergence of the rjMCMC algorithm to the stationary regime. Both elastic and petrophysical inversions invert the amplitude versus angle responses and employ a convolutional forward modelling based on the exact Zoeppritz equations. First, synthetic tests are used to assess the reliability of the implemented rjMCMC algorithms, then their applicability is demonstrated by inverting field seismic data acquired onshore. In this case the inversion was aimed at inferring the elastic and petrophysical properties around a gas-saturated reservoir hosted in a shale-sand sequence. In this case, the final outcomes provided by the rjMCMC algorithms are also compared with the predictions of linear Bayesian elastic and petrophysical inversions. The synthetic and field data examples demonstrate that the implemented algorithms can successfully estimate model uncertainty, model dimensionality and subsurface parameters with an affordable computational cost.

Meet West Africa deep exploration challenge with geomorphology and targeted amplitude variation with offset inversion

Seismic amplitude has played a critical role in the exploration and exploitation of hydrocarbon in West Africa. Class 3 and 2 amplitude variation with offset (AVO) was extensively used as a direct hydrocarbon indicator and reservoir prediction tool in Neogene assets. As exploration advanced to deeper targets with class 1 AVO seismic character, the usage of seismic amplitude for reservoir presence and quality prediction became challenged. To overcome this obstacle, (1) we used seismic geomorphology to infer reservoir presence and precisely target geophysical analysis on reservoir prone intervals, (2) we applied rigorous prestack data preparation to ensure the accuracy and precision of AVO simultaneous inversion for reservoir quality prediction, and (3) we used lateral statistic method to sum up AVO behavior in regions of contrasts to infer reservoir quality changes. We have evaluated a case study in which the use of the above three techniques resulted in confident prediction of reservoir presence and quality. Our results reduced the uncertainty around the biggest risk element in reservoir among the source, charge, and trap mechanism in the prospecting area. This work ultimately made a significant contribution toward a confident resource booking.

Velocity Inversion with an Iterative Normal Incidence Point (NIP) Wave Tomography with Model-Based Common Diffraction Surface (CDS) Stack

Normal Incidence Point (NIP) wave tomography inversion has been recently developed to generate a velocity model using Common Reflection Surface (CRS) attributes, which is called the kinematic wavefield attribute. In this paper, we propose to use the model based Common Diffraction Surface (CDS) stack method attributes instead of data driven Common Reflection Surface attributes as an input data parameter. In this way, the effects of Normal wave on Normal Incidence Point wave calculation are removed. In the proposed method, the velocity model is updated iteratively by an interactive between Common Diffraction Surface attributes and the velocity model produced by Normal Incidence Point wave tomography inversion. We applied the proposed method on a 2D complex land data set in the northeast of Iran. The events in the Common Image Gathers (CIGs) become flat after migrating the pre stack data by using the obtained velocity. This is while the events on the same Common Image Gathers that are processed by the data driven Common Reflection Surface stake method are not well flatted. These results show a great capability of the proposed method to obtain the velocity model compared to the single step Normal Incidence Point wave tomography inversion with Common Reflection Surface attributes.

Seismic Bayesian evidential learning: estimation and uncertainty quantification of sub-resolution reservoir properties

We present a framework that enables estimation of low-dimensional sub-resolution reservoir properties directly from seismic data, without requiring the solution of a high dimensional seismic inverse problem. Our workflow is based on the Bayesian evidential learning approach and exploits learning the direct relation between seismic data and reservoir properties to efficiently estimate reservoir properties. The theoretical framework we develop allows incorporation of non-linear statistical models for seismic estimation problems. Uncertainty quantification is performed with approximate Bayesian computation. With the help of a synthetic example of estimation of reservoir net-to-gross and average fluid saturations in sub-resolution thin sand reservoir, several nuances are foregrounded regarding the applicability of unsupervised and supervised learning methods for seismic estimation problems. Finally, we demonstrate the efficacy of our approach by estimating posterior uncertainty of reservoir net-to-gross in sub-resolution thin sand reservoir from an offshore delta dataset using 3D pre-stack seismic data.

Improving Seismic Data Resolution With Deep Generative Networks

Noisy traces, gaps in coverage, or irregular/inadequate trace spacing are common problems in both land and marine surveys, possibly hindering the geological interpretation of an area of interest. This problem has been typically addressed in the literature using prestack data; however, prestack data are not always available. As an alternative, poststack interpolations may aid the geological interpretation by increasing the spatial density of a seismic section and can also be used to reconstruct entire sections by interpolating neighboring traces, reducing field costs. In this letter, we evaluate the performance of conditional Generative Adversarial Networks (cGANs) as an interpolation tool for improving seismic data resolution on a public poststack seismic data set and compare our results with the traditional cubic interpolation. To perform the comparisons, we used structural similarity (SSIM), mean squared error (mse), and local binary patterns (LBPs) texture descriptor. The results show that cGANs outperform traditional algorithms by up to 72% and that the texture descriptor was able to better capture image similarities, producing results more coherent with the visual perception.

Random noise attenuation of 2D seismic data based on sparse low-rank estimation of the seismic signal

Attenuation of noise in seismic data is a crucial and difficult task in analyzing seismic data. We propose a new noise suppression algorithm in which the noise can be suppressed; meanwhile, the seismic signal is preserved. In the proposed algorithm, first we analyze each seismic trace using a linear time–frequency method, i.e., the short-time Fourier transform, then we estimate the sparse low-rank matrix from the obtained noisy matrix. To this aim, an objective function comprising of a data-faithfulness term and two parameterized non-convex penalty functions is proposed. Finally, the denoised signal is synthesized using the obtained semi-low-rank matrix. We assess the proposed technique considering a synthetic seismic trace and seismic section. We have also assessed the proposed technique using pre-stack real data collected from a hydrocarbon field located in the southwest area of Iran. The performance of the proposed method is evaluated and compared with other state-of-the-art techniques such as the synchrosqueezed wavelet transform and low-rank signal matrix approximation by Semi-Soft GoDec (WSST-GoDec) algorithm, classical f−x singular spectrum analysis (f−x SSA) and the sparse signal estimation and extraction low-rank component by optimum singular value estimation (SLR-OptShrink). The results indicate the advantage of the proposed method over the selected methods.

Target-oriented Gaussian beam migration using a modified ray tracing scheme

For large-scale 3D seismic data, target-oriented reservoir imaging is more attractive than conventional full-volume migration, in terms of computation efficiency. Gaussian beam migration (GBM) is one of the most robust depth imaging method, which not only keeps the advantages of ray methods, such as high efficiency and flexibility, but also allows us to solve caustics and multipathing problems. But conventional Gaussian beam migration requires slant stack for prestack data, and ray tracing from beam center location to subsurface, which is not easy to be directly applied for target-oriented imaging. In this paper, we modify the conventional Gaussian beam migration scheme, by shooting rays from subsurface image points to receivers to implement wavefield back-propagation. This modification helps us to achieve a better subsurface illumination in complex structure and allows simple implementation for target reservoir imaging. Significantly, compared with the wavefield-based GBM, our method does not reconstruct the subsurface snapshots, which has higher efficiency. But the proposed method is not as efficient as the conventional Gaussian beam migration. Synthetic and field data examples demonstrate the validity and the target-oriented imaging capability of our method.

A practical workflow using quantitative interpretation of seismic amplitudes to derisk infill wells in deepwater Gulf of Mexico: The Auger example

Seismic direct hydrocarbon indicators (DHIs) are routinely used in the identification of hydrocarbon reservoirs and in the positioning of drilling targets. Understanding seismic amplitude reliability and character, including amplitude variation with offset (AVO), is key to correct interpretation of the DHI and to enable confident assessment of the commercial viability of the reservoir targets. In many cases, our interpretation is impeded by limited availability of data that are often less than perfect. Here, we present a seismic quantitative interpretation (QI) workflow that made the best out of imperfect data and managed to successfully derisk a multiwell drilling campaign in the Auger and Andros basins in the deepwater Gulf of Mexico. Data challenges included azimuthal illumination effects caused by the presence of the Auger salt dome, sand thickness below tuning, and long-term production effects that are hard to quantify without dedicated time-lapse seismic. In addition, seismic vintages with varying acquisition geometries led to different QI predictions that further complicated the interpretation story. Given these challenges, we implemented an amplitude derisking workflow that combined ray-based illumination assessments and prestack data observations to guide selection of the optimal seismic data set(s) for QI analysis. This was followed by forward modeling to quantify the fluid saturation and sand thickness effects on seismic amplitude. Combined with structural geology analysis of the well targets, this workflow succeeded in significantly reducing the risk of the proposed opportunities. The work also highlighted potential pitfalls in AVO interpretation, including AVO inversion for the characterization of reservoirs near salt, while providing a workflow for prestack amplitude quality control prior to inversion. The workflow is adaptable to specific target conditions and can be executed in a time-efficient manner. It has been applied to multiple infill well opportunities, but for simplicity reasons here, we demonstrate the application on a single well target.

A physical modelling study of the reservoir scale effect on amplitude variation with incidence angle

Abstract The 3D pre-stack seismic data from a physical modeling experiment were employed to investigate the effect of reservoir scales on AVO (amplitude variation with offset or incidence angle). Eight cuboid samples simulating cavernous reservoirs with different widths and the same thickness and elastic parameters were set within a 3D model. 3D seismic data acquisition and processing were conducted. To get the AVO responses of the samples with different widths, trough amplitudes corresponding to the sample tops at different incidence angles were extracted from the pre-stack angle gathers. Amplitude calibration for transducer radiation patterns was conducted on the extracted amplitudes at different angles. AVO analysis was conducted to quantitatively demonstrate the effect of sample scales on AVO characteristics. The effect of sample width was weak when the width was less than 60 m, which was 3/5 of the wavelength. When the width was larger than 60 m, both AVO intercept and gradient gradually increased with the sample width. The AVO gradient peaked at 150 m, which was 1.5 times the wavelength. Cross-plot analysis of AVO intercept and gradient showed the samples were aligned in a straight line when the sample width was less than twice the seismic wavelength. The result in this study partially verified the conclusions of reservoir scale effect on AVO responses drawn from previous numerical modelling studies. For a heterogeneous rectangular reservoir, the effect of reservoir scales on AVO responses could potentially be used to quantitatively estimate reservoir scale.

Application of very fast simulated annealing and differential evolution in the search for FO-CRS wavefield attributes

The finite-offset common-reflection-surface (FO-CRS) stack method can be used to simulate any common-offset (CO) seismic section by stacking prestack seismic data along the surfaces defined by the paraxial hyperbolic traveltime approximation. In two dimensions, the FO-CRS stacking operator depends on five kinematic wavefield attributes for every time sample of the target CO section. The main problem with this method is identifying a computationally efficient data-driven search strategy for accurately determining the best set of FO-CRS attributes that produce the optimal coherence measure of the seismic signal in the prestack data. Identifying a global optimization algorithm with the best performance is a challenge when solving this optimization problem. This is because the objective function is multimodal and involves a large volume of data, which leads to high computational costs. We introduced a comparative and competitive study through the application of two global optimization algorithms that simultaneously search the FO-CRS attributes from the prestack seismic data, very fast simulated annealing (VFSA) and the differential evolution (DE). By applying this FO-CRS stack to the Marmousi synthetic seismic data set, we have compared the performances of the two optimization algorithms with regard to their efficiency and effectiveness in estimating the five FO-CRS attributes. To analyze the robustness of the two algorithms, we apply them to real land seismic data and show their ability to find the near-optimal attributes and to improve reflection events in noisy data with a very low fold. We reveal that VFSA is efficient in reaching the optimal coherence value with the lowest computational costs, and that DE is effective and reliable in reaching the optimal coherence for determining the best five searched-for attributes. Regardless of the differences, the FO-CRS stack produces enhanced and regularized high-quality CO sections using both global optimization methods.

Deep learning for 3D seismic compressive-sensing technique: A novel approach

A deep-learning-based compressive-sensing technique for reconstruction of missing seismic traces is introduced. The agility of the proposed approach lies in its ability to perfectly resolve the optimization limitation of conventional algorithms that solve inversion problems. It demonstrates how deep generative adversarial networks, equipped with an appropriate loss function that essentially leverages the distribution of the entire survey, can serve as an alternative approach for tackling compressive-sensing problems with high precision and in a computationally efficient manner. The method can be applied on both prestack and poststack seismic data, allowing for superior imaging quality with well-preconditioned and well-sampled field data, during the processing stage. To validate the robustness of the proposed approach on field data, the extent to which amplitudes and phase variations in original data are faithfully preserved is established, while subsurface consistency is also achieved. Several applications to acquisition and processing, such as decreasing bin size, increasing offset and azimuth sampling, or increasing the fold, can directly and immediately benefit from adopting the proposed technique. Furthermore, interpolation based on generative adversarial networks has been found to produce better-sampled data sets, with stronger regularization and attenuated aliasing phenomenon, while providing greater fidelity on steep-dip events and amplitude-variation-with-offset analysis with migration.

Prestack and poststack inversion using a physics-guided convolutional neural network

An inversion algorithm is commonly used to estimate the elastic properties, such as P-wave velocity ([Formula: see text]), S-wave velocity ([Formula: see text]), and density ([Formula: see text]) of the earth’s subsurface. Generally, the seismic inversion problem is solved using one of the traditional optimization algorithms. These algorithms start with a given model and update the model at each iteration, following a physics-based rule. The algorithm is applied at each common depth point (CDP) independently to estimate the elastic parameters. Here, we have developed a technique using the convolutional neural network (CNN) to solve the same problem. We perform two critical steps to take advantage of the generalization capability of CNN and the physics to generate synthetic data for a meaningful representation of the subsurface. First, rather than using CNN as in a classification type of problem, which is the standard approach, we modified the CNN to solve a regression problem to estimate the elastic properties. Second, again unlike the conventional CNN, which is trained by supervised learning with predetermined label (elastic parameter) values, we use the physics of our forward problem to train the weights. There are two parts of the network: The first is the convolution network, which takes the input as seismic data to predict the elastic parameters, which is the desired intermediate result. In the second part of the network, we use wave-propagation physics and we use the output of the CNN to generate the predicted seismic data for comparison with the actual data and calculation of the error. This error between the true and predicted seismograms is then used to calculate gradients, and update the weights in the CNN. After the network is trained, only the first part of the network can be used to estimate elastic properties at remaining CDPs directly. We determine the application of physics-guided CNN on prestack and poststack inversion problems. To explain how the algorithm works, we examine it using a conventional CNN workflow without any physics guidance. We first implement the algorithm on a synthetic data set for prestack and poststack data and then apply it to a real data set from the Cana field. In all the training examples, we use a maximum of 20% of data. Our approach offers a distinct advantage over a conventional machine-learning approach in that we circumvent the need for labeled data sets for training.

Azimuthally variation of elastic impedances for fracture estimation

Fracture parameters including fracture orientation and fracture density, work as significant information in the fields of the engineering and exploration geophysics. However, it nowadays still remains challenging to concisely and stably estimate those fracture parameters from seismic data due to the limited signal to noise ratio of the azimuthal seismic data. A method based on azimuthally anisotropic elastic impedance (azimuthal AEI) in terms of Fourier series variation with azimuth is proposed to characterize the fracture distribution. Firstly, the azimuthal AEI equation in terms of truncated Fourier series is derived to reduce the number of unknown parameters in the fracture parameters estimation. In addition, KL (Karhunen-Loève) transformation is used to extract the primary feature of reflection amplitude variation with azimuth and weaken the random noise for azimuthal pre-stack seismic data. And then the azimuthal AEI is estimated from KL transformed azimuthal pre-stack seismic data with the constrained sparse spike inversion method. The fracture orientation without 90° ambiguity can be estimated by an innovative azimuthal AEI equation incorporating the azimuthal AEI equation in terms of Fourier series and the fracture orientation prior information. And the biased estimate for the anisotropic gradient of the azimuthal AEI can be estimated from the second order Fourier coefficient to forecast the fracture density. Besides, we introduce a more convenient way, which is employing the standard deviation of the nature logarithm (SDNL) of the azimuthal AEI in the azimuth domain, than that based on the anisotropic gradient in the fracture density estimation. The synthetic cases demonstrate the rationality and robustness of the innovative primary wave azimuthal AEI equation and the fracture parameters estimation method even with sparse 30° sampling interval in the azimuth. A field data example demonstrates that the proposed method is effective and efficient in the fracture parameters prediction.

Reliability of data-driven wavefront attributes in laterally heterogeneous media

3D wavefront attributes play a major role in many processing steps, such as prestack data enhancement, diffraction separation, and wavefront tomography. For the determination of the 3D wavefront attributes, various stacking operators can be used by adopting semblance optimization. These operators are derived for laterally homogeneous media. In praxis, however, they are applied in real geologic environments with even strong lateral velocity variations such as salt structures. This leads to the question of the quality of the 3D wavefront attributes using these operators when determined in the presence of strong lateral velocity changes. We compared the 3D wavefront attributes determined by 3D common-reflection-surface (CRS) operator (called data-driven wavefront attributes) with the 3D wavefront attributes computed by 3D kinematic and dynamic ray tracing (called model-driven wavefront attributes). For the determination of the 3D CRS wavefront attributes, we have developed a global optimization scheme based on differential evolution. Reflection seismic data of the laterally heterogeneous 3D SEG C3WA salt model are considered, and the model-driven wavefront attributes are computed for a smoothed version of the 3D SEG salt model. The comparison reveals that the wavefront attributes for the normal-incidence-point ray indicate a very good match not only in areas of mild lateral velocity variation but even in regions with strong lateral velocity variations. Approximately 80%–90% of the total picks indicate the good match with a relative error of less than 10% when a semblance threshold of 0.1 is considered in the automatic picking process. This confirms the validity of the determined wavefront attributes even in the presence of strong lateral velocity changes. Using a higher semblance threshold in the automatic picking leads to fewer picks but with an even better match between model- and data-driven wavefront attributes.

Cost-Effective Seismic Exploration: 2D Reflection Imaging at the Kylylahti Massive Sulfide Deposit, Finland

We show that by using an advanced pre-stack depth imaging algorithm it is possible to retrieve meaningful and robust seismic images with sparse shot points, using only 3–4 source points per kilometer along a seismic profile. Our results encourage the use of 2D seismic reflection profiling as a reconnaissance tool for mineral exploration in areas with limited access for active seismic surveys. We used the seismic data acquired within the COGITO-MIN project comprising two approximately 6 km long seismic reflection profiles at the polymetallic Kylylahti massive sulfide mine site in eastern Finland. The 2D seismic data acquisition utilized both Vibroseis and dynamite sources with 20 m spacing and wireless receivers spaced every 10 m. For both source types, the recorded data show clear first breaks over all offsets and reflectors in the raw shot gathers. The Kylylahti area is characterized by folded and faulted, steeply dipping geological contacts and structures. We discuss post-stack and pre-stack data processing and compare time and depth imaging techniques in this geologically complex Precambrian hardrock area. The seismic reflection profiles show prominent reflectors at 4.5–8 km depth utilizing different migration routines. In the shallow subsurface, steep reflectors are imaged, and within and underneath the known Kylylahti ultramafic body reflectivity is prominent but discontinuous.

Amplitude Variation with Offset Inversion Analysis in One of the Western Oilfields of the Persian Gulf

Reservoir characterization has a leading role in the reservoir geophysics and reservoir management. Since the interests of the reservoir geophysics and reservoir managements are the elastic properties and reservoir properties of the subsurface rock for their purposes, a robust method is required for converting seismic data into elastic properties. Accordingly, by employing a rock physics model and using the inverted seismic data, one can describe the reservoir for purposes such as improvement in the production of the reservoir. In the present study, we employ one of the methods for converting the seismic data into the elastic properties. This method of inversion is known as simultaneous inversion, which is grouped in amplitude-variation-with-offset (AVO) inversion category. In this method, unlike the other methods of AVO inversion, the pre-stack seismic data are directly inverted into the elastic properties of the rock and an excellent lithology and fluid indicator (VP/VS) are provided. Then, this indicator is tested on one of the oilfields of the Persian Gulf. Moreover, by means of this method, one can locate the fluids contact and the lithological interlayers; also, by the inversion results, which are the cubes of the seismic properties of the rock, one can generate sections of the elastic properties of the rock such as Poisson’s ratio and Young modulus which are useful for geomechanical analysis. Therefore, this kind of method is a quick way for the prior analysis of the studied area.

Automatic events extraction in pre-stack seismic data based on edge detection in slant-stacked peak amplitude profiles

— Events picking is one of the fundamental tasks in interpreting seismic data. To extract the correct travel-time of reflected waves, picking events in a wide range of source-receiver offsets is needed. Compared to post-stack seismic data, pre-stack seismic data has an accurate horizon and abundant travel-time, amplitude, and frequency while the waveform of post-stack data is damaged by normal move-out (NMO) applications. In this paper, we focus on automatic event extraction from pre-stack reflection seismic data. With the deep development of oil-gas exploration, the difficulty of petroleum exploration is being increased. Auto recognition and picking of seismic horizon is presented as the basis for oil-gas detection. There is a correspondence between the real geology horizon and events of seismic profiles. As a result, firstly, recognizing and tracing continuous events from real seismic records are needed to acquire significant horizon locations. Picking events is in this context the recognition and tracing of waves reflected from the same interfaces according to kinematics and dynamic characteristics of seismic waves. Current extraction algorithms are well able to trace these events of the seismic profile and are undergoing great development and utilization. In this paper, a method is proposed to pick travel-time and local continuous events based on edges obtained by slant-stacked peak amplitude section (SSPA). How to calculate the SSPA section is discussed in detail. The new method can improve the efficiency and accuracy without windowing and manual picking of seed points. The event curves obtained from both the synthetic layered model and field record have validated the high accuracy and efficiency of the proposed methodology.

Machine-Learning Approach Identifies Wolfcamp Reservoirs

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 193002, “Exploring for Wolfcamp Reservoirs, Eastern Shelf of the Permian Basin, Using a Machine-Learning Approach,” by Bruno de Ribet and Peter Wang, Emerson; Monte Meers, independent geologist; Howard Renick, independent geophysicist; Russ Creath, Hardin International; and Ryan McKee, RAM Imaging, prepared for the 2018 SPE Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, 11–14 November. The paper has not been peer reviewed. This paper discusses a project with the objective of leveraging prestack and poststack seismic data in order to reconstruct 3D images of thin, discontinuous, oil-filled packstone pay facies of the Upper and Lower Wolfcamp formation. The classification results were created by neural networks, which can be used as a substitute for traditional amplitude-vs.-offset, inversion, and cross-plotting techniques for seismic reservoir characterization. Introduction The problem encountered by the operator in this oil field is that the reservoir, an oil-filled packstone, is thin and laterally discontinuous. Despite having collected a high-resolution, state-of-the-art 3D seismic survey with usable frequencies up to 138 Hz, and despite having generated seismic attribute volumes in order to assist interpretation, the operator was unable to generate an interpretation manually that matched the rock-type interpretation at the wells. Therefore, the decision was taken to supplement the human interpretation with a machine-learning methodology. Geological Setting The East Soldier Mount (ESM) study area is approximately 200 km northeast of Midland, Texas, USA, on the eastern shelf of the Permian Basin. The study area contains both Upper and Lower Wolfcamp oil-filled packstones, which are thin and laterally discontinuous. Bioturbation and oolitic shoals caused the initial porosity; however, much of the porosity was occluded by cementation after burial. The porosity was enhanced by fracturing that occurred after burial, caused by differential compaction beneath and tectonic faulting in the deeper formations. Many millions of years after burial, oil leaked into the Tannehill sand (Middle Wolfcamp) detrital, then migrated up the detrital zone into the delta, which is located 2 km west of the study area. Then, the oil migrated out of the delta and into the study area itself. Middle Wolfcamp deltaic sands are not collocated with the seismic survey and thus are not part of this study. They were, however, the conduit for oil migration into the ESM wells. The total drilled depth for these vertical wells is approximately 1500 m. Each successful well produces approximately 3–4 million bbl of reserves. These wells flow naturally, without the need for hydraulic fracturing. Theory and Definitions The technique developed in this paper assumes the existence of a relation-ship between a seismic response at a given point and the rock-type distribution around this point. However, no model has been established yet and the mathematical formulation of such an operator is complex. Its determination would imply the need for a long empirical process to evaluate the consequence of rock-type distribution on seismic response. Estimating the number of parameters is challenging and is a function of the geological context, measurement constraints, and experimental design. Therefore, the work flow is to create an operator by using learning techniques.

Simultaneous prestack inversion of variable-depth streamer seismic data

Variable-depth streamer seismic data are characterized by low and high frequencies and can be used to obtain high-quality and resolution images of complex subsurface structures. Taking advantage of the frequency range in the variable-depth streamer data, we propose the simultaneous inversion of prestack data from variable-offset stack gathers to obtain the P-wave impedance, S-wave impedance, and density. Next, we validate the method by using model and actual variable-depth streamer data from the Huizhou block. The results suggest that the broadband data recorded by variable-depth streamers improve the signal-to-noise ratio and quality of the inversion results and outperform the constant-depth streamer data in delineating the underground stratigraphy.

3D edge-diffraction coefficients in the azimuth and emergence domain

The conventional equation for 3D edge diffractions in the Cartesian coordinate system lacks angle information for studying the energy patterns in 3D seismic prestack data. Here, a new calculation method is presented for determining 3D edge-diffraction coefficients in a spherical coordinate system that can formulate the coefficients according to the azimuth and emergence angles. To avoid the singularity phenomenon, a Haar wavelet operator matrix is used for this new method. Analysis of the edge-diffraction coefficients variations with azimuth in the common-shot domain, common-receiver domain, and common-midpoint domain reveals that the variation curves of the coefficients can be used to identify the trend of a fault. The phenomenon of polarity reversal of the edge-diffraction coefficients is observed in the different domains, and the coefficients in the common-shot domain are more sensitive than in other domains.