Internal Multiple Elimination Research Articles

Three-dimensional internal multiple elimination in complex structures using Marchenko autofocusing theory

Internal multiples are commonly present in seismic data due to variations in velocity or density of subsurface media. They can reduce the signal-to-noise ratio of seismic data and degrade the quality of the image. With the development of seismic exploration into deep and ultradeep events, especially those from complex targets in the western region of China, the internal multiple eliminations become increasingly challenging. Currently, three-dimensional (3D) seismic data are primarily used for oil and gas target recognition and drilling. Effectively eliminating internal multiples in 3D seismic data of complex structures and mitigating their adverse effects is crucial for enhancing the success rate of drilling. In this study, we propose an internal multiples prediction algorithm for 3D seismic data in complex structures using the Marchenko autofocusing theory. This method can predict the accurate internal multiples of time difference without an accurate velocity model and the implementation process mainly consists of several steps. Firstly, simulating direct waves with a 3D macroscopic velocity model. Secondly, using direct waves and 3D full seismic acquisition records to obtain the upgoing and downgoing Green’s functions between the virtual source point and surface. Thirdly, constructing internal multiples of the relevant layers by upgoing and downgoing Green’s functions. Finally, utilizing the adaptive matching subtraction method to remove predicted internal multiples from the original data to obtain seismic records without multiples. Compared with the two-dimensional (2D) Marchenko algorithm, the performance of the 3D Marchenko algorithm for internal multiple predictions has been significantly enhanced, resulting in higher computational accuracy. Numerical simulation test results indicate that our proposed method can effectively eliminate internal multiples in 3D seismic data, thereby exhibiting important theoretical and industrial application value.

Internal-multiple-elimination with application to migration using two-way wave equation depth-extrapolation scheme

Internal multiple interference, affecting both seismic data processing and interpretation, has been observed for long time. Although great progress has been achieved in developing a variety of internal-multiple-elimination (IME) methods, how to increase accuracy and reduce cost of IME still poses a significant challenge. A new method is proposed to effectively and efficiently eliminate internal multiples, along with its application in internal-multiple-eliminated-migration (IMEM), addressing this issue. This method stems from two-way wave equation depth-extrapolation scheme and associated up/down wavefield separation, which can accomplish depth-extrapolation of both up-going and down-going wavefields simultaneously, and complete internal-multiple-elimination processing, adaptively and efficiently. The proposed method has several features: (1) input data is same as that for conventional migration: source signature (used for migration only), macro velocity model, and receiver data, without additional requirements for source/receiver sampling; (2) method is efficient, without need of iterative calculations (which are typically needed for most of IME algorithms); and (3) method is cost effective: IME is completed in the same depth-extrapolation scheme of IMEM, without need of a separate processing and additional cost. Several synthesized data models are used to test the proposed method: one-dimensional model, horizontal layered model, multi-layer model with one curved layer, and SEG/EAGE Salt model. Additionally, we perform a sensitivity analysis of velocity using smoothed models. This analysis reveals that although the accuracy of velocity measurements impacts our proposed method, it significantly reduces internal multiple false imaging compared to traditional RTM techniques. When applied to actual seismic data from a carbonate reservoir zone, our method demonstrates superior clarity in imaging results, even in the presence of high-velocity carbonate formations, outperforming conventional migration methods in deep strata.

Inverse-Scattering Theory Guided U-Net Neural Networks for Internal Multiple Elimination

Deep neural networks can automatically fetch specific features from seismic data, which can be used in the process of multiple elimination. An extended single-sided autofocusing guided by inverse-scattering theory is introduced to remove internal multiples in a data-driven manner, which can be used as labels in deep neural networks. In this research, we have developed a novel workflow to explore the potential of neural networks in identifying the internal multiples with the guidance of inverse-scattering theory. In particular, we use the U-net with a self-attention block during the training process, which could extract features from seismic data effectively. The neural network is fed with training data pairs, consisting of the shot records with internal multiples, and the primary-only datasets as labels, which are generated by an extended single-sided autofocusing method. The testing pairs show that internal multiple elimination via the neural network takes the advantage of the extended single-sided autofocusing method and is cheaper when the neural network is well-trained. The numerical results demonstrate promising performances of the self-attention U-net method in terms of the noise resistance, internal multiples elimination, and the reverse time migration (RTM) images, in comparison with the extended single-sided autofocusing method.

An improved method for internal multiple elimination using the theory of virtual events

Compared with first-order surface-related multiples from marine data, the onshore internal multiples are weaker and are always combined with a hazy and occasionally strong interference pattern. It is usually difficult to discriminate these events from complex targets and highly scattering overburdens, especially when the primary energy from deep layers is weaker than that from shallow layers. The internal multiple elimination is even more challenging due to the fact that the velocity and energy difference between primary reflections and internal multiples is tiny. In this study, we propose an improved method which formulates the elimination of the internal multiples as an optimization problem and develops a convolution factor T. The generated internal multiples at all interfaces are obtained using the convolution factor T through iterative inversion of the initial multiple model. The predicted internal multiples are removed from seismic data through subtraction. Finally, several synthetic experiments are conducted to validate the effectiveness of our approach. The results of our study indicate that compared with the traditional virtual events method, the improved method simplifies the multiple prediction process in which internal multiples generated from each interface are built through iterative inversion, thus reducing the calculation cost, improving the accuracy, and enhancing the adaptability of field data.

Surface-Related and Internal Multiple Elimination Using Deep Learning

Multiple elimination has always been a key, challenge, and hotspot in the field of hydrocarbon exploration. However, each multiple elimination method comes with one or more limitations at present. The efficiency and success of each approach strongly depend on their corresponding prior assumptions, in particular for seismic data acquired from complex geological regions. The multiple elimination approach using deep learning encodes the input seismic data to multiple levels of abstraction and decodes those levels to reconstruct the primaries without multiples. In this study, we employ a classic convolution neural network (CNN) with a U-shaped architecture which uses extremely few seismic data for end-to-end training, strongly increasing the neural network speed. Then, we apply the trained network to predict all seismic data, which solves the problem of difficult elimination of global multiples, avoids the regularization of seismic data, and reduces massive amounts of calculation in traditional methods. Several synthetic and field experiments are conducted to validate the advantages of the trained network model. The results indicate that the model has the powerful generalization ability and high calculation efficiency for removing surface-related multiples and internal multiples effectively.

Internal Multiple Removal and Illumination Correction for Seismic Imaging

Marchenko equation-based imaging methods have been proved as an effective way to remove the internal multiples. Conventional Marchenko imaging needs the reflection response at the surface and an estimate of the direct arrival times from the virtual source point to the acquisition surface. It contains the procedure of redatuming and imaging. The redatuming process is valid only for layered media with a moderately curved interface. We rederive the single reflection retrieval by a focusing source method based on the scattering theory and avoid the use of redatuming plane and the upgoing/downgoing decomposition. This scheme reproduces a new data free from internal multiples for complex structures, such as salt dome. Our theory/method expands the application range of Marchenko imaging and internal multiple elimination. With an artifact-free image obtained by this procedure, an illumination compensation can be further applied to obtain a high-fidelity image, especially in the subsalt area. Numerical examples using the 2-D SEG/EAGE salt model are shown to validate this method.

An application of the Marchenko internal multiple elimination scheme formulated as a least-squares problem

Images produced by migration of seismic data related to complex geology are often contaminated by artifacts due to the presence of internal multiple reflections. These reflections are created when the seismic wave is reflected more than once in a source-receiver path and can be interpreted as the main coherent noise in seismic data. Several schemes have been developed to predict and subtract internal multiple reflections from measured data, such as the Marchenko multiple elimination (MME) scheme that eliminates the referred events without requiring a subsurface model or an adaptive subtraction approach. The MME scheme is data-driven, can remove or attenuate most of these internal multiples, and was originally based on the Neumann series solution of Marchenko’s projected equations. However, the Neumann series approximate solution is conditioned to a convergence criterion. We reformulate the MME as a least-squares problem (LSMME) in such a way that it can provide an alternative that avoids a convergence condition as required in the Neumann series approach. To demonstrate the LSMME scheme performance, we apply it to 2D numerical examples and compare the results with those obtained by the conventional MME scheme. In addition, we evaluate the successful application of our method through the generation of in-depth seismic images, by applying reverse time migration (RTM) to the original data set and to those obtained through MME and LSMME schemes. From the RTM results, we found that the application of both schemes on seismic data allows the construction of seismic images free of artifacts related to internal multiple events.

Internal multiple elimination: Can we trust an acoustic approximation?

Correct handling of strong elastic internal multiples remains a challenge for seismic imaging. Methods aimed at eliminating them are currently limited by monotonicity violations, a lack of a-priori knowledge about mode conversions, or unavailability of multicomponent sources and receivers for not only particle velocities but also the traction vector. Most of these challenges vanish in acoustic media such that Marchenko-equation-based methods are able, in theory, to remove multiples exactly (within a certain wavenumber-frequency band). In practice, however, when applied to (elastic) field data, mode conversions are unaccounted for. Aiming to support a recently published marine field data study, we build a representative synthetic model. For this setting, we demonstrate that mode conversions can have a substantial impact on the recovered multiple-free reflection response. Nevertheless, the images are significantly improved by acoustic multiple elimination. Moreover, after migration the imprint of elastic effects is considerably weaker and unlikely to alter the seismic interpretation.

Subbasalt Marchenko imaging with offshore Brazil field data

Subbasalt imaging for hydrocarbon exploration faces challenges with the presence of multiple scattering, attenuation, and mode conversion as seismic waves encounter highly heterogeneous and rugose basalt layers. A combination of modern seismic acquisition that can record densely sampled data and advanced imaging techniques make imaging through basalt feasible. Yet, the internal multiples, if not properly handled during seismic processing, can be mapped to reservoir layers by conventional imaging methods, misguiding geologic interpretation. Traditional internal multiple elimination methods suffer from the requirement of picking horizons of multiple generators and/or a top-down adaptive subtraction process. Marchenko imaging provides an alternative solution to directly remove the artifacts due to internal multiples, without the need of horizon picking or subtraction. In this paper, we evaluate a successful application of direct Marchenko imaging for subbasalt demultiple and imaging with an offshore Brazil field data set. The internal multiples in this example are generated from the seabed and basalt layers, causing severe artifacts in conventional seismic images. We have determined that these artifacts are largely suppressed with Marchenko imaging, and we have developed a general workflow for data preprocessing and regularization of marine streamer data sets. We find that horizontally propagating waves also can be reconstructed by the Marchenko method at far offsets.

Internal Multiple Prediction Based on Imaging Profile Prediction and Kirchhoff Demigration

This paper introduces an internal multiple prediction method based on imaging profile prediction and Kirchhoff demigration. First, based on an inputted prestack time migration profile, the method predicts the prestack time migration profile that only includes internal multiples by inverse scattering series method. Second, the method uses velocity-weighted Kirchhoff demigration to create shot gathers that contains only internal multiples. Internal multiple prediction based on the prestack time migration profile effectively reduces the computational cost of multiple predictions, and the internal-multiple shot gathers created by Kirchhoff demigration remarkably reduces the complexity of the practical problem. Internal multiple elimination can be conducted through the combined adaptive multiple subtraction based on event tracing. Synthetic and field data tests show that the method effectively predicts internal multiples and possesses considerable potential in field data processing, particularly in areas where internal multiples develop seriously.

Data-driven internal multiple elimination and its consequences for imaging: A comparison of strategies

We have compared three data-driven internal multiple reflection elimination schemes derived from the Marchenko equations and inverse scattering series (ISS). The two schemes derived from Marchenko equations are similar but use different truncation operators. The first scheme creates a new data set without internal multiple reflections. The second scheme does the same and compensates for transmission losses in the primary reflections. The scheme derived from ISS is equal to the result after the first iteration of the first Marchenko-based scheme. It can attenuate internal multiple reflections with residuals. We evaluate the success of these schemes with 2D numerical examples. It is shown that Marchenko-based data-driven schemes are relatively more robust for internal multiple reflection elimination at a higher computational cost.

Free-surface and internal multiple elimination in one step without adaptive subtraction

We have derived a scheme for retrieving the primary reflections from the acoustic surface-reflection response by eliminating the free-surface and internal multiple reflections in one step. This scheme does not require model information and adaptive subtraction. It consists only of the reflection response as a correlation and convolution operator that acts on an intermediate wavefield from which we compute and capture the primary reflections. For each time instant, we keep one value for each source-receiver pair and store it in the new data set. The resulting data set contains only primary reflections, and from this data set, a better velocity model can be built than from the original data set. A conventional migration scheme can then be used to compute an artifact-free image of the medium. We evaluated the success of the method with a 2D numerical example. The method can have a wide range of applications in 3D strongly scattering media that are accessible from one side only.

Marchenko scheme based internal multiple reflection elimination in acoustic wavefield

Marchenko imaging is a methodology to image the subsurface with two important properties: (1)accurate amplitude and (2)free from free-surface and internal multiple artefacts. It requires an estimate of the first arrival of the focusing function which is commonly obtained from a macro velocity model. Inspired by this limitation, a projected Marchenko scheme has been introduced from which an internal multiple reflection elimination scheme has been derived. This internal multiple reflection elimination scheme requires an estimate of the two-way travel time surface of a selected horizon in the subsurface instead of a macro model. In order to make it totally model free we have rewritten the scheme by replacing the estimate of the two-way travel time surface by a fixed truncation for all traces. The output of the current scheme contains primary reflections without contamination from internal multiple reflections. We apply this scheme to a 2D numerical example to illustrate the procedure of this method and show how the internal multiple reflection eliminated data set can be retrieved and the migration image is improved.

Surface-based Internal Multiple Elimination in the CMP Domain — Theory and Application Strategies on Land Seismic Data

The data-driven internal multiple elimination (IME) method based on feedback model, which includes CFP-based, surface-based and inversion- based methods, are successfully applied to marine datasets. However, these methods are computationally expensive and not always straightforward on land datasets. In this paper, we first proved that the surface-based IME method, which is the most computationally efficient method among the three methods, can be derived from the CFP theory. Then we extend it to CMP domain under the assumption of locally lateral invariance of the earth, which makes it more computationally efficient. In addition, we proposed applying a time-variant taper based on the first Fresnel zone to predict the multiples more percisely. Besides, the improved S/N ratio and dense offset distribution can be obtained by using the CMP supergather, which makes the CMP-oriented method more suitable for land data. Some practical processing strategies are proposed via case study. The effectiveness of the proposed method is demonstrated with the application to synthetic and field data.

Adaptive overburden elimination with the multidimensional Marchenko equation

Iterative substitution of the multidimensional Marchenko equation has been introduced recently to integrate internal multiple reflections in the seismic imaging process. In so-called Marchenko imaging, a macro velocity model of the subsurface is required to meet this objective. The model is used to back-propagate the data during the first iteration and to truncate integrals in time during all successive iterations. In case of an erroneous model, the image will be blurred (akin to conventional imaging) and artifacts may arise from inaccurate integral truncations. However, the scheme is still successful in removing artifacts from internal multiple reflections. Inspired by these observations, we rewrote the Marchenko equation, such that it can be applied early in a processing flow, without the need of a macro velocity model. Instead, we have required an estimate of the two-way traveltime surface of a selected horizon in the subsurface. We have introduced an approximation, such that adaptive subtraction can be applied. As a solution, we obtained a new data set, in which all interactions (primaries and multiples) with the part of the medium above the picked horizon had been eliminated. Unlike various other internal multiple elimination algorithms, the method can be applied at any specified target horizon, without having to resolve for internal multiples from shallower horizons. We successfully applied the method on synthetic data, where limitations were reported due to thin layers, diffraction-like discontinuities, and a finite acquisition aperture. A field data test was also performed, in which the kinematics of the predicted updates were demonstrated to match with internal multiples in the recorded data, but it appeared difficult to subtract them.

Study on internal multiple elimination method on Land Seismic Data

SUMMARY Multiple is a tough issue in recent years, especially the internal multiples in deep earth. In this paper we proposed to construct virtual events to predict internal multiples. Then adopt the mean value multi-channel adaptive subtraction method for matching the multiple model and seismic data. However, the results depend on the parameters closely. We propose to apply the dynamic time wrapping method in order to accomplish the precise matching. And the regression of multiples can effectively improve the internal multiple elimination results when internal multiples are interfered with effective signal.

Internal multiple adaptive subtraction using Huber norm

There are two steps in internal multiple elimination, the first step is multiple prediction (predicted multiple model by inverse scattering series (ISS) method from marine seismic data only), the second step is adaptive matching subtraction, subtract multiple from seismic data. Because of the complex generation mechanism of internal multiple, the second step is always the main challenge of internal multiple suppression. A new subtraction method using Huber norm is proposed to remove internal multiples in this paper, it can deal with the negative influence of amplitude and phase in internal multiple subtraction. In this approach, the multi-channel Huber norm function minimized by quasi-Newtonian method that has the potential for more accurate and robust multiple subtraction. Tests with synthetic and field data suggest that internal multiple adaptive subtraction using the Huber norm gives highly satisfactory result, and shows its effectiveness.

Comparing three feedback internal multiple elimination methods

Abstract Multiple reflections have posed a great challenge for current seismic imaging and inversion methods. Compared to surface multiples, internal multiples are more difficult to remove due to poorer move-out discrimination with primaries and we are left with wave equation-based prediction and subtraction methods. In this paper, we focus on the comparison of three data-driven internal multiple elimination (IME) methods based on the feedback model, where two are well established prediction-and-subtraction methods using back-propagated data and surface data, referred to as CFP-based method and surface-based method, respectively, and the third one, an inversion-based method, has been recently extended from estimation of primaries by sparse inversion (EPSI). All these three methods are based on the separation of events from above and below a certain level, after which internal multiples are predicted by convolutions and correlations. We begin with theory review of layer-related feedback IME methods, where implementation steps for each method are discussed, and involved event separation are further analyzed. Then, recursive application of the three IME methods is demonstrated on synthetic data and field data. It shows that the two well established prediction-and-subtraction methods provide similar primary estimation results, with most of the internal multiples being removed while multiple leakage and primary distortion have been observed where primaries and internal multiples interfere. In contrast, generalized EPSI provides reduced multiple leakage and better primary restoration which is of great value for current seismic amplitude-preserved processing. As a main conclusion, with adaptive subtraction avoided, the inversion-based method is more effective than the prediction-and-subtraction methods for internal multiple elimination when primaries and internal multiples overlap. However, the inversion-based method is quite computationally intensive, and more researches on efficient implementation need to be done in future.