Internal multiple prediction using inverse scattering series with sparsity promotion — Part 2: Application strategy and field data examples

Internal multiple adaptive subtraction using Huber norm

Linear inversion is defined as the linear approximation of a direct-inverse solution. This definition leads to data requirements and specific direct-inverse algorithms, which differ with all current linear and nonlinear approaches, and is immediately relevant for target identification and inversion in an elastic earth. Common practice typically starts with a direct forward or modeling expression and seeks to solve a forward equation in an inverse sense. Attempting to solve a direct forward problem in an inverse sense is not the same as solving an inverse problem directly. Distinctions include differences in algorithms, in the need for a priori information, and in data requirements. The simplest and most accessible examples are the direct-inversion tasks, derived from the inverse scattering series (ISS), for the removal of free-surface and internal multiples. The ISS multiple-removal algorithms require no subsurface information, and they are independent of earth model type. A direct forward method solved in an inverse sense, for modeling and subtracting multiples, would require accurate knowledge of every detail of the subsurface the multiple has experienced. In addition, it requires a different modeling and subtraction algorithm for each different earth-model type. The ISS methods for direct removal of multiples are not a forward problem solved in an inverse sense. Similarly, the direct elastic inversion provided by the ISS is not a modeling formula for PP data solved in an inverse sense. Direct elastic inversion calls for PP, PS, SS, … data, for direct linear and nonlinear estimates of changes in mechanical properties. In practice, a judicious combination of direct and indirect methods are called upon for effective field data application.

Seismic imaging is a significant technology to provide the image of the subsurface in several fields such as hydrocarbon exploration/production and civil engineering. A fundamental problem in seismic imaging is that both the depth reflectivity and velocity distribution of the subsurface have to be predicted by only seismic events observed at the surface, and it still remains a challenging research topic. Joint migration inversion (JMI) is one of the seismic waveform imaging algorithms that were recently proposed. JMI is capable of simultaneously estimating velocity and reflectivity models of the subsurface by exploiting reflected waves including internal multiples. The seismic modeling algorithm in the JMI process is a method termed full wavefield modeling (FWMod), which is a one-way propagator-based reflection modeling algorithm, including higher-order scattering and transmission effects. In this thesis, two directions to improve the accuracy of seismic imaging based on JMI are discussed. On one hand, an extension of FWMod is proposed to correctly deal with not only reflected waves but refracted/diving waves via one-way propagators in the horizontal direction, and this method is extended to a new JMI algorithm. On the other hand, we assume that only reflected waves including internal multiples are utilized in the imaging based on JMI and present two novel methods for the inversion and pre-processing: 1) iterative reflectivity-constrained velocity estimation, 2) surface amplitude correction via learning from synthetic models for land seismic data. The reflectivity-constrained velocity estimation is employed to improve the accuracy of the estimated velocity by exploiting the estimated reflectivity in the JMI process. The surface amplitude correction process is introduced to mitigate the influence of the amplitude variations caused by source/receiver response sensitivities and the difference of the features between observed land seismic data and the simulated data by the used imaging scheme. The numerical and field data examples for both land and marine cases demonstrate that the proposed approach is capable of effectively estimating reflectivity and velocity model, even though the low frequency components of the observed data are absent.

This work revisits and explores benefits and practical aspects of employing inverse scattering series (ISS) based algorithms to predict internal multiples under a new forward prediction parameterization framework. The intricate nature and rapid vertical and lateral variability of multiple generating reflectors pose a limitation for methods relying on prior information about formations and/or boundaries responsible for creating major internal multiples at the reservoir level.

It is widely recognized that the first arrival seismic tomography is one of the robust ways to estimate the near surface velocity model. However, both the first arrival tomography itself and its application to static corrections are still less perfect. With regard to the first arrival seismic tomography, one of the challenges is the sparseness of the tomography matrix. This sparseness will cause the tomography matrix poorly conditioned. Although the model regularization can produce a well‐posed system for an ill‐posed system from the mathematic point of view, in principle, we had better to provide more information or reasonable physical constraints to the first arrival seismic tomography, if we want to get a more reliable result. In this paper, we introduce the fat‐ray into the first arrival seismic tomography in order to reduce the sparseness or the dimension of the null space of the tomography matrix. Thus, although the seismic tomography may be still partly underdetermined and partly over‐determined, it is possible to use the sparsely acquired seismic data to get reasonable near surface velocity model, or use part of the normally acquired seismic data or big cell size to perform seismic tomography to lower the computational cost. Synthetic data and field data examples shows that this method is feasible.

Internal multiples severely reduce seismic imaging quality and interpretation accuracy. With the continuous advancement of seismic imaging toward higher resolution, the accurate suppression of internal multiples has become increasingly critical. The concept of virtual events provides a fully data-driven approach for suppressing internal multiples. However, when energy interference occurs between internal multiples and primaries, the process of adaptive subtraction using matching filters may lead to damage to primaries. Building on the conventional virtual-events theory, an adaptive iterative method for the internal multiple suppression had been developed that reduces the dependency on the matching algorithm to some extent. Nonetheless, it remains unable to fundamentally prevent the loss of primary energy. To address this issue, we propose a waveform inversion-based internal multiple suppression method by constructing virtual events. Based on the theoretical foundation of the traditional virtual-events theory, we formulate an inversion objective function to estimate internal multiples via waveform inversion, thereby avoiding the requirement for the adaptive subtraction process. This approach achieves effective suppression of internal multiples while better preserving the primary energy. Comparing results with traditional methods, we demonstrate that the proposed method exhibits superior performance in both accuracy of multiple suppression and preservation of primary amplitude, providing a more reliable data foundation for subsequent seismic processing and geological interpretation.

The resolution of seismic data determines the ability to characterize individual geological structures in a seismic image. Sparse spike inversion (SSI) is an effective approach for improving the resolution of seismic data. However, the basic assumption of SSI is that the strong reflectivity of the formation is sparse, which may not be a reasonable fit for weak thin-layer reflections. In this study, we propose a deep learning-based method to reconstruct high-resolution seismic data by combining information from the longitudinal reflectivity distribution and lateral geological structure features in the field data. A U-shaped network that fuses residual block and attention mechanism is used to learn the relationship between low resolution and high resolution. In addition, we use a hybrid loss function that combines <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\ell _{1}}$ </tex-math></inline-formula> loss and structural similarity (SSIM) loss to optimize the network parameters for better distinguishing the geometrical features characterized by structural amplitude changes. To train the network, we adopt a workflow to automatically generate numerous 2-D low-resolution data and their corresponding high-resolution data. In this workflow, the prior information, such as statistical reflectivity distribution of well logs and structural features of the data are considered. The synthetic data and field data tests show that our method can work well compared to the traditional method even though only a few well logs are available. Especially in the field data example, our method recovers thin layers better and yields laterally more consistent high-resolution results.

Event detection is an essential component of microseismic data analysis. This process is typically carried out using a short- and long-term-average-ratio (STA/LTA) method, which is simple and computationally efficient but often yields inconsistent results for noisy data sets. We have aimed to optimize the performance of the STA/LTA method by testing different input forms of 3C waveform data and different characteristic functions (CFs), including a proposed [Formula: see text]-mean CF. These tests are evaluated using receiver operating characteristic (ROC) analysis and are compared based on synthetic and field data examples. Our analysis indicates that the STA/LTA method using a [Formula: see text]-mean CF improves the detection sensitivity and yields more robust event detection on noisy data sets than some previous approaches. In addition, microseismic events are detected efficiently on field data examples using the same detection threshold obtained from the ROC analysis on synthetic data examples. We recommend the use of the Youden index based on ROC analysis using a training subset, extracted from the continuous data, to further improve the detection threshold for field microseismic data.

Production through wellbores in petroleum industry involves multi-phase flow of oil, gas and water. It is necessary to capture the effects of varying composition of phases to represent wellbore hydraulics accurately. However, a majority of current wellbore simulators prefer a ‘black-oil’ formulation due to its higher speed as compared to a compositional approach. In this work, a neuro-simulation protocol is developed for fast and accurate simulation of wellbore hydraulics in vertical non-isothermal systems. The proposed toolbox is capable of predicting the pressure profile along a production tubing containing flow of pure hydrocarbons (C1 through C45) and water. The tool can operate within a range of flow rates, well depths, pipe diameters, inlet fluid compositions, wellhead pressures and geothermal gradients. The data for training the expert system is generated from a numerical simulator that computes wellbore hydraulics. The numerical simulator is a compositional model, which uses a two-phase equilibrium flash calculation for determining the distribution of hydrocarbon components in oil and gas phases. A two-phase drift flux model accounts for the variation in gas and liquid velocities under various flow regimes. The compositional mass balance and momentum equations are simultaneously solved using a fully implicit scheme, while the temperature profile of the well is taken into consideration in computations. The results provided by both the numerical simulator and the tool described in this paper are compared against field data as well as numerical simulation results reported in the literature. It is observed that the average relative deviation of the results generated in this study from the field data example is 2.2 %. The average relative deviation between the numerical simulator developed and field data example is 2.4 %, showing that the expert system is capable of capturing the related physics and thermodynamics of the wellbore hydraulics phenomena. The average relative deviation between the results generated by the proposed tool and numerical simulation examples from literature data is observed to be between 3.3 and 7.1 %. The average relative deviations between results from the numerical simulator developed in the current work and simulation results reported in literature are found to be between 2.3 and 8.1 %. The variation between predictions provided by various models for wellbore hydraulics in the literature lie within the ranges mentioned above. It is observed that the tool discussed in this paper is a fast, accurate and robust model for predicting wellbore hydraulics for compositional systems. The proposed tool also overcomes the stability issues associated with compositional numerical wellbore simulation models. Such a versatile tool can also be used for generating tubing intake curves for an unrestricted set of scenarios and for quick selection of optimal gas lift design parameters.

Shallow-seismic Rayleigh waves are attractive for geotechnical site investigations. They exhibit a high signal to noise ratio in field data recordings and have a high sensitivity to the S-wave velocity, an important lithological and geotechnical parameter to characterize the very shallow subsurface. In recent years we studied the applicability of the two-dimensional elastic FWI method using numerous synthetic reconstruction tests and two field data examples. Some important challenges are reported here: (1) the accurate correction of the geometrical spreading, (2) the estimation of the source wavelet, (3) the importance of an-elastic attenuation in the forward simulations. We found that Important pre-processing steps for the application of 2-D elastic FWI to shallow-seismic field data are the 3D to 2D correction of geometrical spreading and the estimation of a priori Q-values that must be used as a passive medium parameter during the FWI. Furthermore, a source-wavelet correction filter should be applied during the FWI process. Smooth initial models obtained from the analysis of the first arrivals of body waves are important and seem to be sufficient. Our field data examples indicate that FWI is able to resolve lateral variations of S-wave velocities in the very shallow subsurface.

ABSTRACTIn recent years, a variety of Marchenko methods for the attenuation of internal multiples has been developed. These methods have been extensively tested on two‐dimensional synthetic data and applied to two‐dimensional field data, but only little is known about their behaviour on three‐dimensional synthetic data and three‐dimensional field data. Particularly, it is not known whether Marchenko methods are sufficiently robust for sparse acquisition geometries that are found in practice. Therefore, we start by performing a series of synthetic tests to identify the key acquisition parameters and limitations that affect the result of three‐dimensional Marchenko internal multiple prediction and subtraction using an adaptive double‐focusing method. Based on these tests, we define an interpolation strategy and use it for the field data application. Starting from a wide azimuth dense grid of sources and receivers, a series of decimation tests are performed until a narrow azimuth streamer geometry remains. We evaluate the effect of the removal of sail lines, near offsets, far offsets and outer cables on the result of the adaptive double‐focusing method. These tests show that our method is most sensitive to the limited aperture in the crossline direction and the sail line spacing when applying it to synthetic narrow azimuth streamer data. The sail line spacing can be interpolated, but the aperture in the crossline direction is a limitation of the acquisition. Next, we apply the adaptive Marchenko double‐focusing method to the narrow azimuth streamer field data from the Santos Basin, Brazil. Internal multiples are predicted and adaptively subtracted, thereby improving the geological interpretation of the target area. These results imply that our adaptive double‐focusing method is sufficiently robust for the application to three‐dimensional field data, although the key acquisition parameters and limitations will naturally differ in other geological settings and for other types of acquisition.

Seismic imaging from sparsely acquired data faces challenges such as low image quality, discontinuities, and migration swing artifacts. Existing convolutional neural network (CNN)-based methods struggle with complex feature distributions and cannot effectively assess uncertainty, making it hard to evaluate the reliability of their processed results. To address these issues, we propose a new method using a generative diffusion model (GDM). Here, in the training phase, we use the imaging results from sparse data as conditional input, combined with noisy versions of dense data imaging results, for the network to predict the added noise. After training, the network can predict the imaging results for test images from sparse data acquisition, using the generative process with conditional control. This GDM not only improves image quality and removes artifacts caused by sparse data but also naturally evaluates uncertainty by leveraging the probabilistic nature of the GDM. To overcome the decline in generation quality and the memory burden of large-scale images, we develop a patch fusion strategy that effectively addresses these issues. Synthetic and field data examples demonstrate that our method significantly enhances imaging quality and provides effective uncertainty quantification.

&lt;p&gt;Iterative substitution of the Marchenko equation has been introduced recently to integrate internal multiple reflection in the seismic and electromagnetic imaging process. In the so-called Marchenko imaging, solving the Marchenko equation at each imaging point is required to meet this objective. It makes the scheme seriously expensive. Inspired by this limitation, we present an Electromagnetic Marchenko equation based one dimensional scheme to eliminate the internal multiples of the single-sided lossless surface ground penetrating radar data layer by layer, such that the conventional imaging schemes can be applied to get the internal multiple related artifacts free imaging result without the need of solving Marchenko equation at each imaging point. We show with an example that the method works well for a sample in a synthetic waveguide that could be used for measurements in laboratory and field.&lt;/p&gt;

We report the first use of Green's theorem derived source and receiver deghosting on deep water Gulf of Mexico synthetic (SEAM) and field data. Green's theorem derived deghosting has several qualities which separate it from previous deghosting methods: (1) it accommodates a multi-dimensional earth, (2) it doesn't require a Fourier transform over space coordinates, (3) it works in every depth of water, (4) it allows for any shape of measurement surface (e.g., a corrugated water bottom), and (5) it is consistent with wave theory processing methods. The context of Green's theorem deghosting is placed within a single consistent Green's theorem preprocessing and inverse scattering series (ISS) processing chain. Green's theorem derived deghosting theory is presented, and an algorithm implementing the theory is discussed. The algorithm has been tested on field data and several kinds of synthetic data with positive and encouraging results.

Summary Wavefield separation is an important processing step to remove the interfering receiver ghost in seismic data. For ocean-bottom surveys, where typically both the pressure P (hydrophone) and particle velocity Vz (geophone) is measured, PZ-summation is a commonly used wavefield separation method. Although this method delivers excellent results, the required wavefield calibration makes it user-intensive to apply and QC. Supervised machine learning (ML) can offer a robust and user-friendly alternative to the industry-standard PZ-summation method. The convolutional neural network used in the proposed approach automatically calibrates the multi-component recordings and performs the wavefield separation without any user interaction required. A comparison study is conducted where the ML method is compared to the industry-standard PZ-summation method for a controlled shallow water data experiment and an OBN field data example with water depths ranging between 25m and 40m. After an easy to execute network training phase, the method delivers excellent wavefield separation results for both the complex synthetic and the shallow water field data example.