Low-wavenumber noise attenuation of seismic reverse time migration with deep learning

We present the theory of the element-free method (EFM) and its numerical applications in seismic modelling and reverse time migration. The absence of elements makes the method cheaper and more flexible than the finite element method (FEM). The shape function in the EFM only needs to satisfy the moving-least-squares (MLS) criterion, so it can be generated easily. Besides, it is convenient to deal with the local problems using weight functions and influence domains. Due to the MLS fitting method, the dependent variable and its derivative are both continuous and precise in the EFM. However, as a result of its heavy cost burden, this method seems difficult to be developed in seismic modelling and reverse time migration. The cost is mainly caused by improper storage of some large sparse matrices such as the mass matrix and the stiffness matrix, and improper operations (multiplication and inversion) on them. In this paper we compress the sparse matrices by the compressed sparse column (CSC) format and solve the linear equations instead of inverting sparse matrices, with the help of Intel linear sparse solver ‘PARDISO’. By these strategies, we have saved computer resources significantly. In the end, we show some applications of the improved method in seismic modelling and reverse time migration.

Wave equation solutions based on finite-differences is a standard technique and has been widely used for seismic forward modeling and reverse-time migration. However, the time step for the explicit method is restricted by the stability condition and to obtain good results both the spatial and time derivatives need to be computed with accurate operators. This can be achieved using higher order finite-difference schemes or very fine computational grids. However, both approaches increase the computational cost. On the other hand, numerical dispersion normally appears in the finite-difference results and can contaminate the signals of interest. Numerical dispersion noise is a very well known problem in finite-difference methods and several algorithms have being proposed to obtain seismic modeling sections and migration results free from this noise. In this paper, we propose to use the finite-difference technique together with a predictor-corrector method to obtain an efficient algorithm for seismic modeling and reverse time migration. First, we derive a new wave equation which we call the anti-dispersion wave equation. Then, we present some numerical results to demonstrate that the finite difference scheme based on this new anti-dispersion wave equation can be used as a new tool for seismic modeling and migration, producing little numerical dispersion compared with the original wave equation but requiring slightly more computational cost.

3C-3D tunnel seismic reverse time migration imaging: A case study of Pearl River Delta Water Resources Allocation Project

The Role of Reverse Time Migration in Imaging and Model Estimation Introduction The key depth imaging technology addressed in this article is Reverse Time Migration (RTM). It will be compared to Kirchhoff, beam and other wave equation migration (WEM) techniques. There will be an emphasis on reducing exploration cycle time and risk. Recent trends such as TTI anisotropy and wide azimuth applications will also be discussed. RTM is most suitable in geologic regimes that exhibit significant amounts of salt. Typically, there are contrasts in velocity and steeply dipping features in this setting. The key conclusion from this article will be that by using RTM throughout the imaging sequence, including model building, the total cycle time of the project can be significantly reduced. Exploration risk is also reduced by RTM because it produces images that are more accurate in terms of structure and amplitudes. Sub-Salt Imaging Challenges The challenges of subsalt imaging are daunting. Salt structures are formed when salt sheets intrude into the higher-density sediments deposited above them. The resulting domes, walls, pillows, ridges and fountains are complex. They can be free-floating or remain attached to the base salt layer as irregular, mushroom-shaped bodies called diapirs. The map in Figure 1 gives an indication of how common these highly complex salt bodies are in exploration. Imaging in salt rich domains is difficult since the seismic waves reflected off the steep flanks of subsurface features travel near horizontal so it is a problem for standard imaging algorithms to image them. Further the top of salt structures is often highly rugose, which causes the scattering of seismic waves into multiple paths. These factors, if not taken into consideration, can yield misleading information about the location and geometry of prospective formations. In the 80's, the Kirchhoff depth migration method was used to image seismic data. From the 1990's, wave equation migration methods were used in combination with Kirchhoff methods to try to fully resolve structures not adequately resolved with Kirchhoff migration. Starting in 2005, reverse time migration became commercially viable in all phases of the imaging sequence.

Processing of the seismic data acquired in areas of complex geology of the Dnieper-Donets basin, characterized by the salt tectonics, requires special attention to the salt dome interpretation. For this purpose, Kirchhoff Depth Imaging and Reverse Time Migration (RTM) were applied and compared. This is the first such experience in the Dnieper-Donets basin. According to international experience, RTM is the most accurate seismic imaging method for steep and vertical geological (acoustic contrast) boundaries. Application of the RTM on 3D WAZ land data is a great challenge in Dnieper-Donets Basin because of the poor quality of the data with a low signal-to-noise ratio and irregular spatial sampling due to seismic acquisition gaps and missing traces. The RTM algorithm requires data, organized to native positions of seismic shots. For KPSDM we used regularized data after 5D interpolation. This affects the result for near salt reflection. The analysis of KPSDM and RTM results for the two areas revealed the same features. RTM seismic data looked more smoothed, but for steeply dipping reflections, lateral continuity of reflections was much improved. The upper part (1000 m) of the RTM has shadow zones caused by low fold. Other differences between Kirchhoff data and RTM are in the spectral content, as the former is characterized by the full range of seismic frequency spectrum. Conversely, beneath the salt, the RTM has reflections with steep dips which are not observed on the KPSDM. It is possible to identify new prospects using the RTM seismic image. Reverse Time Migration of 3D seismic data has shown geologically consistent results and has the potential to identify undiscovered hydrocarbon traps and to improve salt flank delineation in the complex geology of the Dnieper-Donets Basin's salt domes.

Common-image gathers are an important output of prestack depth migration. They provide information needed for velocity model building and amplitude and phase information for subsurface attribute interpretation. Conventionally, common-image gathers are computed using Kirchhoff migration on common-offset/azimuth data volumes. When geologic structures are complex and strong contrasts exist in the velocity model, the complicated wave behaviors will create migration artifacts in the image gathers. As long as the gather output traces are indexed by any surface attribute, such as source location, receiver location, or surface plane-wave direction, they suffer from the migration artifacts caused by multiple raypaths. These problems have been addressed in a significant amount of work, resulting in common-image gathers computed in the reflection angle domain, whose traces are indexed by the subsurface reflection angle and/or the subsurface azimuth angle. Most of these efforts have concentrated on Kirchhoff and one-way wave-equation migration methods. For reverse time migration, subsurface angle gathers can be produced using the same approach as that used for one-way wave-equation migration. However, these approaches need to be revisited when producing high-quality subsurface angle gathers in three dimensions (reflection angle/azimuth angle), especially for wide-azimuth data. We have developed a method for obtaining 3D subsurface reflection angle/azimuth angle common-image gathers specifically for the amplitude-preserved reverse time migration. The method builds image gathers with a high-dimensional convolution of wavefields in the wavenumber domain. We have found a windowed antileakage Fourier transform method that leads to an efficient and practical implementation. This approach has generated high-resolution angle-domain gathers on synthetic 2.5D data and 3D wide-azimuth real data.

To avoid spatial aliasing problems in broad band high resolution seismic sections, I present a high density migration processing solution. I first analyze the spatial aliasing definition for stack and migration seismic sections and point out the differences between the two. We recognize that migration sections more often show spatial aliasing than stacked sections. Second, from wave propagation theory, I know that migration output is a new spatial sampling process and seismic prestack time migration can provide the high density sampling to prevent spatial aliasing on high resolution migration sections. Using a 2D seismic forward modeling analysis, I have found that seismic spatial aliasing noise can be eliminated by high density spatial sampling in prestack migration. In a 3D seismic data study for Daqing Oilfield in the Songliao Basin, I have also found that seismic sections obtained by high-density spatial sampling (10 × 10 m) in prestack migration have less spatial aliasing noise than those obtained by conventional low density spatial sampling (20 × 40 m) in prestack migration.

Migration imaging is a key step in tunnel seismic data processing. Due to the limitation of tunnel space, tunnel seismic data are small-quantity, multi-component, and have a small offset. Kirchhoff migration based on the ray theory is limited to the migration aperture and has low migration imaging accuracy. Kirchhoff migration can no longer meet the requirements of high-precision migration imaging. The reverse time migration (RTM) method is used to realize cross-correlation imaging by reverse-time recursion principle of the wave equation. The 3-D RTM method cannot only overcome the effect of small offset, but also realize multi-component data imaging, which is the most accurate migration method for tunnel seismic data. In this paper, we will study the 3-D RTM method for multi-component tunnel seismic data. Combined with the modeled data and the measured data, the imaging accuracy of the 3-D Kirchhoff migration and 3-D RTM is analyzed in detail. By comparing single-component and multi-component Kirchhoff migration and RTM profile, the advantages of the multi-component RTM method are summarized. Compared with the Kirchhoff migration method, the 3-D RTM method has the following advantages: (1) it can overcome the effect of small offset and expand the range of migration imaging; (2) multi-component data can be realized to improve the energy of anomalous interface; (3) it can make full use of multiple waves to realize migration imaging and improve the resolution of the anomalous interface. The modeled data and the measured data prove the advantages of the 3-D multi-component RTM method.

Marine controlled source electromagnetic (CSEM) survey is a novel complementary geophysical method for exploring structure below the seafloor. In this research, the processing of marine CSEM data is investigated for monitoring of hydrocarbon reservoirs in the offshore. Due to highly conductive seawater and shallow conductive layers, the attenuation of any EM signals is one of the most crucial problems that has prevented the application of imaging technologies (e.g. migrations) regularly adopted in exploration seismology. Inspired by the similarity of seismic and electromagnetic data, we investigate an innovative approach by applying two popular seismic imaging methods on CSEM data for monitoring of hydrocarbon reservoirs in conductive (attenuating) media: reverse time migration (RTM) and Kirchhoff migration (KM). The synthetic marine CSEM data is calculated for a model including a hydrocarbon reservoir in an attenuating medium. We used the realistic values for sedimentary rocks that are common for attenuating media. Then, we apply RTM and KM methods to CSEM data in the real-time diffusive domain to monitor the hydrocarbon reservoir. In marine CSEM surveys it is important to consider the direction of source implementation and here we model the effects of source implementation directions in terms of reservoir monitoring. Maxwell's equations were solved in the fictitious wave domain, a scheme allows faster calculations than conventional methods, reducing the computational cost. However, the wavefields calculated using this fictitious method are not real and should transferred to the real-time diffusive domain. The results confirm the RTM handles both the vertical and horizontal edges and defines the hydrocarbon reservoir in attenuating media much better than KM since the RTM does not introduce any approximations of the physics of wave propagation. The main drawback of RTM, its expensive computational cost, has been significantly reduced by advent of new powerful computers., The results also show that the horizontal source implementation is a better scheme for reservoir monitoring using a marine CSEM survey.

Using compact representations of Green’s functions we derive a common framework for reverse time migration (RTM) and Kirchhoff migration. These compact Green’s functions (CGFs) are 3D volumes containing traveltimes and amplitudes for the N most representative events in the upcoming/downgoing decomposed 4D wavefields originating from a point source. Within this framework, we implement an RTM algorithm using a multivalued excitation time/amplitude imaging condition. This new approach produces four complementary imaging volumes (different combinations of source and receiver decomposed wavefields) and angle/azimuth gathers with computational effort less than 15% greater than that of plain (one image and no gathers) RTM algorithms. The advantages of separating the image volume into four complementary volumes are well established in the literature (low-frequency noise separation and turning wave imaging); however, its use has been limited by the computational cost. Despite using two source propagations to decompose the source wavefield, we reduce the computations to less than 20% of a single source propagation by performing finite-difference propagation with half the frequency limit used in the receiver wavefield propagation. The combination of CGF and an excitation time/amplitude imaging condition allows receiver wavefield decomposition with only one wavefield propagation. Our RTM algorithm constructs angle/azimuth gathers using a postmigration computation of the source and receiver wavefield’s propagation directions. To compute the propagation directions after migration, we use a new concept: the cumulative wavefield volumes, which are 3D, imaging-condition-guided compressions, of the 4D source and receiver wavefields. We also use CGF to implement a Kirchhoff migration algorithm that produces four complementary image volumes with RTM-like quality. Furthermore, we present synthetic and field data examples to clarify the new concepts and illustrate the results obtained using these methods.

The article discusses a high accuracy seismic modeling and reverse time migration (RTM) method. High-order finitedifference (FD) equation is used for modeling and RTM with fourth-order in time domain, eighth-order in x, y direction of space domain and sixteenth-order in z direction. This high-order FD solution can effectively reduce numerical dispersion. PML absorbing boundary conditions is used to effectively solve artificial boundary reflection problem. Thereby, the accuracy of modeling and RTM are significantly improved. By the advantage of GPU, the computation efficiency is largely increased. Research of theoretical data and real data shows this method is very applicable to the modeling and imaging for the media with complex surface and complex underground structure.

Reverse time migration: A prospect of seismic imaging methodology

We examine the performance of a 3D finite difference seismic reverse time migration (RTM) kernel on systems with Intel® Xeon® processors and Intel® Xeon Phi™ x200 processors. Using an identical tuned RTM TTI source code, an system with one Intel Xeon Phi 7250 processor outperforms a system with two-socket Intel Xeon 2697v4 processors by a factor of 1.5.

In recent years, fiber-optic distributed acoustic sensing (DAS) has been gradually applied to seismology because of its long-distance and dense observation capability. It is a great challenge to effectively process the massive seismic data recorded by DAS. At present, the seismic data processing methods based on deep learning have achieved great success, especially in the tasks of seismic detection and arrival-time picking. However, due to the differences between DAS and geophone, such as sensing principles, spatial and temporal sampling rates, and noise intensity. The seismic arrival time picking model based on deep learning, which is trained by geophone seismic data with low spatial and temporal sampling rates and low noise intensity, severely degrades in performance on DAS seismic data with high spatial and temporal sampling rates and high noise intensity. In addition, a new seismic arrival time picking model is trained by fully supervised learning, which usually requires a large number of seismic data with accurate labels. However, the huge cost of manual picking and the lack of effective automatic picking models make it very difficult to build large-scale DAS seismic data sets with accurate labels. Therefore, it is very difficult to build an arrival time picking model based on fully supervised learning for DAS seismic data.In this study, we propose a DAS seismic arrival time picking method based on fractional lower order statistics. Based on the difference of probability density function between noise and seismic signal, the proposed method uses alpha-stable distribution modeling noise (generally follow a Gaussian distribution) and seismic signal (generally follow a non-Gaussian distribution), and uses fractional lower order statistics under the assumption of alpha-stable distribution as the characteristic function to pick the arrival time.Synthetic and actual DAS data tests show that the proposed method has better performance and robustness to random noise than other methods based on characteristic functions, such as STA/LTA, AR-AIC and kurtosis. Since the actual DAS seismic data has no ground truth of arrival time, we have further the performance of the proposed method on the geophone seismic data set. The proposed method provides better results on geophone seismic data and the data after up-sampling them to the typical time sampling rate of DAS.

Salt model building is a key process for successful subsalt imaging. In complex areas, Reverse Time Migration (RTM) provides better images than One-way Wave Equation Migration (OWEM) or Kirchhoff Migration (KMIG). With a superior image, RTM can give improved solutions for delineation of salt geometry. The main obstacle in applying RTM to iterative salt model building is that RTM requires substantially more computing power than OWEM or KMIG. However, the cost of RTM can be reduced by localizing the imaging area. First, perform the redatuming of source and receiver wavefields to a certain depth just above the interested subsalt target area. Second, localize the image zone near the steep salt boundary. After then, update salt geometry iteratively using localized RTM (LRTM) images and an interactive salt modeling tool.