Internal Multiples Research Articles

Seismic Imaging of the Arctic Subsea Permafrost Using a Least-Squares Reverse Time Migration Method

High-resolution seismic imaging allows for the better interpretation of subsurface geological structures. In this study, we employ least-squares reverse time migration (LSRTM) as a seismic imaging method to delineate the subsurface geological structures from the field dataset for understanding the status of Arctic subsea permafrost structures, which is pertinent to global warming issues. The subsea permafrost structures in the Arctic continental shelf, located just below the seafloor at a shallow water depth, have an abnormally high P-wave velocity. These structural conditions create internal multiples and noise in seismic data, making it challenging to perform seismic imaging and construct a seismic P-wave velocity model using conventional methods. LSRTM offers a promising approach by addressing these challenges through linearized inverse problems, aiming to achieve high-resolution, subsurface imaging by optimizing the misfit between the predicted and the observed seismic data. Synthetic experiments, encompassing various subsea permafrost structures and seismic survey configurations, were conducted to investigate the feasibility of LSRTM for imaging the Arctic subsea permafrost from the acquired seismic field dataset, and the possibility of the seismic imaging of the subsea permafrost was confirmed through these synthetic numerical experiments. Furthermore, we applied the LSRTM method to the seismic data acquired in the Canadian Beaufort Sea (CBS) and generated a seismic image depicting the subsea permafrost structures in the Arctic region.

Seismic shear wave noise suppression and application to well tie

Abstract Seismic shear waves have been employed in oil and gas exploration for decades. A 2D seismic shear wave inline was acquired in Sanhu area, located in the Qaidam Basin in western China. Although the acquired shear wave data exhibits high resolution and comparable bandwidth to the compressional wave, it is contaminated by various types of noise, including linear noise, single-frequency noise, and especially internal multiples. Internal multiples seriously compromise the primary reflections at both near-offset and far-offset and are difficult to be suppressed. This paper presents a case study of noise attenuation for the seismic shear wave. Firstly, single-frequency noise and linear noise are attenuated through filtering methods. Then, two methods (the Radon transform and the frequency-wavenumber (F-K) filtering) are evaluated for their effectiveness in multiple suppression and amplitude preservation. The results indicate that both methods successfully reduce long-period multiples at far-offset, enhancing the signal-to-noise ratio. We show that F-K filtering retains the characteristic ‘strong-weak-strong’ amplitude variation in the SV-SV wave data gather, making it preferable for subsequent AVO (amplitude variation with offset) analysis and inversion. Finally, a wave-equation-based MSI (multiple suppression inversion) method is used to suppress near-offset internal multiples. This involves iteratively predicting internal multiples and adaptively subtracting them from the original data. Stacked sections of different offsets are compared to demonstrate de-multiple result, and the result is also validated by the improvement of well calibration with the seismic shear wave data.

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.

One‐way waveform inversion: Real marine data application

AbstractThe reflection waveform inversion is a powerful technique to build a large‐scale velocity model of the subsurface by fitting the reflected recorded seismic waves. The reflection waveform inversion is designed based on the pillar concept of model and data‐scale separation. Therefore, its success is related to the ability of its forward modelling engine to separate reflected events distinctly from other propagation modes (diving waves, multiples, etc.). However, the standard Born modelling based on the two‐way wave equation may generate internal multiples in case of an insufficient smooth background model. These internal multiples may lead to a distorted sensitivity kernel, which adds more non‐linearity to the inverse problem. In addition, simulating the wave equation using two‐way propagators is still an overburden step of the algorithm especially in large three‐dimensional real surveys. In this proposal, we introduce an alternative to the two‐way wave equation by using a one‐way approach for the reflection waveform inversion. The Born modelling based on one‐way propagators significantly reduces the computational cost and I think it should be allows to relax the smooth background velocity model assumption by restricting the forward modelling to primary reflected waves. After a brief theoretical description of the one‐way waveform inversion, we present an application of the algorithm on the real marine dataset to review its promises and pitfalls. Our approach produces an acceptable large‐scale velocity model whose accuracy is confirmed by the migrated image and the offset gathers.

Design, implementation and application of the Marchenko plane-wave algorithm

The Marchenko algorithm can suppress the disturbing effects of internal multiples that are present in seismic reflection data. To achieve this, a set of coupled equations with four unknowns is solved. These coupled equations are separated into a set of two equations with two unknowns using a time window. The two unknown focusing functions can be resolved by an iterative or direct method. These focusing functions, when applied to reflection data, create virtual point-sources inside the medium. Combining individual virtual point-sources into a plane-wave leads to an efficient computation of images without internal multiples. In this study the internal multiples are eliminated in a redatuming step which is part of the imaging algorithm. To use the Marchenko algorithm with plane-wave focusing functions, the time window that separates the unknowns must be adapted. The design of the plane-wave Marchenko algorithm is explained and illustrated with numerically modeled and measured reflection data.

Full-Wavefield Migration Using an Imaging Condition of Global Normalization Multi-Order Wavefields: Application to a Synthetic Dataset

In marine seismic exploration, seismic signals comprise primaries that undergo first-order scattering, as well as multiples resulting from multi-order scattering events. Surface-related multiples involve multi-order scattering at the free surface interface between seawater and air and exhibit a smaller reflection angle and broader illumination compared to primaries. Internal multiples, originating from multi-order scattering among stratified layers, provide additional illumination compensation beneath the reflecting interface. However, in conventional primary migration, different-order wavefields may result in crosstalk artifacts. To address this issue, we developed a least-squares migration (LSM) method based on the multi-order wavefield global normalization condition. This methodology investigates the illumination effects and crosstalk artifacts associated with different-order surface-related and internal multiples, and then modifies the global normalization condition by incorporating an illumination compensation perspective. Virtual sources, represented by surface-related multiples and internal multiples, are integrated into the source compensation term, ultimately yielding a multi-order wavefield normalization condition. This normalization condition is subsequently combined with least-squares full-wavefield migration (LSFWM). Numerical experiments demonstrate that the normalization condition of multi-order wavefields can resolve the problem of weak deep imaging energy and promote the suppression of multiple crosstalk artifacts in the least-squares algorithm.

Marchenko imaging assisted by vertical seismic profiling data for land seismic data in the Middle East

Attenuating interference from internal multiples has challenged seismic data imaging in the Middle East basins. The challenge results from the strong short-period internal multiples that exhibit nearly indistinguishable characteristics from the primaries reflected from the underlying reservoirs due to predominantly horizontal strata and occasional low-relief structures, as indicated in the Jurassic formations in Kuwait. To address the internal-multiple issues, multiple prediction followed by adaptive subtraction is the most common approach in the industry. However, due to the similarities between primaries and multiples, applying adaptive subtraction poses a high risk of primary-amplitude damage, preventing quantitative seismic data interpretation. Therefore, we examine the Marchenko method that retrieves Green’s functions from surface seismic data for target-oriented imaging without applying adaptive subtraction. Marchenko imaging has produced promising results on several offshore seismic data sets, but an onshore application is still needed. To better understand the effects of internal multiples and implement Marchenko imaging, we perform integrated analysis through well-log, vertical seismic profiling (VSP), and seismic data from a hydrocarbon field in Kuwait. In addition, we use VSP data to cross-check the retrieved Green’s functions and estimate the scaling factor of the Marchenko method. The results indicate that (1) the poor imaging at the center of the field is due to the destructive interference of internal multiples, (2) the reverberation of internal multiples between the evaporite formations of the overburden is the most likely candidate that affects the seismic images of the Jurassic reservoirs, (3) the retrieved Green’s functions conform to the recorded Green’s functions from VSP data, and (4) Marchenko imaging provides a means to improve the seismic images of the Jurassic formations in Kuwait.

Joint Reverse Time Migration of Primaries and Internal Multiples Based on Imaging Constraint

Joint Reverse Time Migration of Primaries and Internal Multiples Based on Imaging Constraint

Time‐lapse applications of the Marchenko method on the Troll field

AbstractThe data‐driven Marchenko method is able to redatum wavefields to arbitrary locations in the subsurface, and can, therefore, be used to isolate zones of specific interest. This creates a new reflection response of the target zone without interference from over‐ or underburden reflectors. Consequently, the method is well suited to obtain a clear response of a subsurface reservoir, which can be advantageous in time‐lapse studies. The isolated responses of a baseline and monitor survey can be more effectively compared; hence, the retrieval of time‐lapse characteristics is improved. This research aims to apply Marchenko‐based isolation to a time‐lapse marine data set of the Troll field in Norway in order to acquire an unobstructed image of the primary reflections and retrieve small time‐lapse traveltime difference in the reservoir. It is found that the method not only isolates the primary reflections but can also estimate internal multiples outside the recording time. Both the primaries and the multiples can then be utilized to find time‐lapse traveltime differences. More accurate ways of time‐lapse monitoring will allow for a better understanding of dynamic processes in the subsurface, such as observing saturation and pressure changes in a reservoir or monitoring underground storage of hydrogen and CO2.

Generalized internal multiple prediction for low relief structures

Correlation- and convolution-based internal multiple prediction is one of the most common methods to predict and subsequently attenuate internal multiples. This technique requires the convolution of two seismic events from the deep section followed by the correlation with an event from the shallow part section to satisfy the so-called deep-shallow-deep (late-early-late) condition; otherwise, nonphysical seismic events can be predicted. To comply with this condition, seismic data are separated into shallow and deep portions according to a given phantom horizon. Internal multiples whose raypaths pass through the phantom horizon four times are predicted for one trial. In this way, only a portion of internal multiples are predicted. To address this limitation, a novel algorithm called the generalized internal multiple prediction (GIMP) algorithm is proposed. This algorithm is founded upon the adaptation of the deep-shallow correlation and deep-deep convolution techniques, constrained by specific integration boundaries. The GIMP method effectively accommodates the deep-shallow-deep (late-early-late) mode, without necessitating the segmentation of the seismic data set into shallow and deep segments via a user-defined phantom horizon. Notably, this approach is comprehensive in nature and has the capability to predict all potential internal multiples concurrently. Considering the computational cost, the current implementation focus of GIMP is primarily on 1D or 1.5D; however, GIMP is applicable to 2D and 3D scenarios.

Multiple and Coherent Noise Removal from X-Profile 2D Seismic Data of Southern Iraq Using Normal Move Out-Frequency Wavenumber Technique

Multiple eliminations (de-multiple) are one of seismic processing steps to remove their effects and delineate the correct primary refractors. Using normal move out to flatten primaries is the way to eliminate multiples through transforming these data to frequency-wavenumber domain. The flatten primaries are aligned with zero axis of the frequency-wavenumber domain and any other reflection types (multiples and random noise) are distributed elsewhere. Dip-filter is applied to pass the aligned data and reject others will separate primaries from multiple after transforming the data back from frequency-wavenumber domain to time-distance domain. For that, a suggested name for this technique as normal move out- frequency-wavenumber domain method for multiple eliminations. The method is tested on a fake reflection event to authorize their validity, and applied to a real field X-profile 2D seismic data from southern Iraq. The results ensure the possibility of internal multiple types existing in the deep reflection data in Iraq and have to remove. So that the interpretation for the true reflectors be valid. The final processed stacked seismic data using normal move out- frequency-wavenumber domain technique shows good, clear, and sharp reflectors in comparison with the conventional normal move out stack data. Open-source Madagascar reproducible package is used for processing all steps of this study and the package is very efficient, accurate, and easy to implement normal move out, frequency-wavenumber domain, Dip-filter programs. The aim of the current study is to separate internal multiples and noise from the real 2D seismic data.

Multiple and Coherent Noise Removal from X-Profile 2D Seismic Data of Southern Iraq Using Common Depth Point Muting Procedures and Depending on Madagascar Open-Source Package

This article describes how to predict different types of multiple reflections in pre-track seismic data. The characteristics of multiple reflections can be expressed as a combination of the characteristics of primary reflections. Multiple velocities always come in lower magnitude than the primaries, this is the base for separating them during Normal Move Out correction. The muting procedure is applied in Time-Velocity analysis domain. Semblance plot is used to diagnose multiples availability and judgment for muting dimensions. This processing procedure is used to eliminate internal multiples from real 2D seismic data from southern Iraq in two stages. The first is conventional Normal Move Out correction and velocity auto picking and stacking, and the second stage is muting. Many Common Depth Point gathers are tested to select the proper muting dimension, later on; the auto pick for the muted semblance is done for the whole 2D seismic data. The following step is to stack the Normal Move Out corrected data. Differences are calculated between the two stages of the process which greatly help to determine the eliminated multiple locations within the sedimentary secession. This will reduce the risk of interpreting these sequences as primary reflectors spatially within deep thin layers. Madagascar open source package is used in these processing steps. Madagascar open source package is very efficient, accurate, and easy to correct any part of the Python code used in the two stages of processing.

An application of internal multiple prediction and primary reflection retrieval to salt structures

Irregular salt bodies complicate the seismic wavefield propagation and cause multipathing, leading to intricate internal multiples that cannot be easily suppressed during data processing. To investigate the performance of internal multiple removal in salt bodies, we compare two types of Marchenko-based internal multiple removal strategies. One focuses on internal multiple prediction (IMP) based on Marchenko redatuming and seismic interferometry. With the retrieved upgoing and downgoing Green’s functions, internal multiples can be reconstructed using convolutional interferometry. The second method emphasizes primary reflection retrieval (PRR) by capturing primary reflections without adaptive subtraction. It is derived from a modified method based on the Gel’fand-Levitan-Marchenko equation. Testing with the Pluto salt model, we find that for the IMP the critical point is obtaining the purely scattering components of the upgoing and downgoing Green’s functions from the complicated wavefield. Our complex salt model indicates that the predicted internal multiples’ adaptive subtraction also introduces an extra challenge for attenuation quality. We develop a layer-by-layer adaptive subtraction scheme for the IMP to obtain primary reflections. The constant-time truncation operator in the time domain makes the PRR independent of additional model information, which can exclude internal multiples from the primary reflections. However, selecting an appropriate smoothing window for truncation requires further investigation. We evaluate the weaknesses of these methods and enhance each method individually. Our numerical results indicate that these improved schemes can correctly handle internal multiples in salt structure scenarios. In the addition, we study the robustness of the IMP when an erroneous background velocity model is used to estimate the direct arrival and the effects of sampling on the virtual receiver/source lines in IMP.

Application of Iterative Virtual Events Internal Multiple Suppression Technique: A Case of Southwest Depression Area of Tarim, China

The seismic records in the Cambrian southwest depression of the Tarim Basin exhibit discrepancies when compared to the actual geological setting, which is caused by the presence of multiples. Despite the application of the Radon transform, multiple interferences persist beneath the Cambrian salt in the pre-stack data, with significant variations in energy and frequency across the horizontal direction. In addition, other multiple suppression methods are also difficult to handle this problem. To address this issue, we have developed an iterative virtual event internal multiple suppression method for post-stack data. This novel algorithm extends the traditional virtual event internal multiple suppression approach, eliminating the need for data regularization and avoiding the problem of the traditional virtual events method requiring sequential extraction of primaries from relevant layers, which greatly improves computational efficiency and simplifies the implementation steps of the traditional method. Numerical experiments demonstrate the efficacy of our method in suppressing internal multiples in both synthetic and field data while preserving primary signals. When applied to real seismic data profiles, the iterative method yields structural characteristics that align more closely with sedimentary laws and reduces disparities in energy and frequency of multiples along the horizontal axis. Consequently, our method provides a robust foundation for subsequent hydrocarbon source rock prediction.

Inverse Scattering Series Internal Multiple Attenuation in the Common-Midpoint Domain

Internal multiple prediction remains a high-priority problem in seismic data processing, such as subsurface imaging and quantitative amplitude analysis and inversion, particularly in the common-midpoint (CMP) gathers, which contain multicoverage reflection information of the subsurface. Internal multiples, generated by unknown reflectors in complex environments, can be reconstructed with certain combinations of seismic reflection events using the inverse scattering series internal multiple prediction algorithm, which is usually applied to shot records in source–receiver coordinates. The computational overhead is one of the major challenges limiting the strength of the multidimensional implementation of the prediction algorithm, even in the coupled plane-wave domain. In this paper, we first comprehensively review the plane-wave domain inverse scattering series internal multiple prediction algorithm, and we propose a new scheme of achieving 2D multiple attenuation using a 1.5D prediction algorithm in the CMP domain, which significantly reduces the computational burden. Moreover, we quantify the difference in behavior of the 1.5D prediction algorithm for the shot/receiver and the CMP gathers on tilted strata. Numerical analysis of prediction errors shows that the 1.5D algorithm is more capable of handling dipping generators in the CMP domain than in the shot/receiver gathers, and it is able to predict the accredited traveltimes of internal multiples caused by dipping reflectors with small inclinations. For more complex cases with large inclination, using the 1.5D prediction algorithm, internal multiple predictions fail both in the CMP domain and in the shot/receiver gathers, which require the full 2D prediction algorithm. To attenuate internal multiples in the CMP gathers generated by large-dipping strata, a modified version is proposed based on the full 2D plane-wave domain internal multiple prediction algorithm. The results show that the traveltimes of internal multiples caused by dipping generators seen in the simple benchmark example are correctly predicted in the CMP domain using the modified 2D prediction algorithm.

Crosscorrelation-based Marchenko imaging with an optimal aperture

The Marchenko method can retrieve Green’s functions among virtual sources in the subsurface and receivers at the surface from single-sided reflection data. This process, called Marchenko redatuming, allows the estimation of the full-wavefield information in the inhomogeneous subsurface. The retrieved Green’s functions form the input for creating the subsurface image free of artifacts caused by internal multiples. However, when using the crosscorrelation imaging condition in Marchenko imaging, the shallower regions of the obtained image suffer from reduced resolution due to unwanted interference, which occurs in the crosscorrelation gathers at far offsets. With a simple model, we have found that the image resolution obtained using the crosscorrelation Marchenko imaging (CCMI) method is influenced by image position and the integral range of the crosscorrelation function. To overcome this problem, we develop an optimal aperture-bounded crosscorrelation imaging condition using only the constructive wavefields during integration. The optimal aperture is defined as an intercept at which the time difference between the first arrivals of up- and downgoing Green’s functions equals one wavelet period. The integration of the crosscorrelation function is then performed over the determined optimal range that varies with the image position rather than a fixed aperture. As a result, we exclude the unwanted destructive interference from the crosscorrelation gather, resulting in a high-resolution image. The effectiveness of our method has been validated with its applications to synthetic and field data tests.

Seismic wave propagation around subsurface igneous sill complexes

Imaging both within and beneath subsurface igneous sill complexes is a seismic exploration challenge. A significant aspect of this challenge is due to a lack of understanding of the interaction between the heterogeneous geological structures and the seismic wavefield, which includes the seismic response to sub-resolution ‘thin’ sills. This study aims to provide some insight into the effect subsurface sills have on the observed seismic wavefield. This is achieved through high-resolution full-waveform elastic seismic modelling, using a realistic geological model developed from interpreted seismic data and statistics of sills from wireline logs and conceptual understanding from sill complexes in outcrop. We find that little energy penetrates through the sill complex to a target reflector below the sill complex, which is consistent with real-world observations. This is due to a number of factors, including energy lost to strong internal multiples (stratigraphic filtering), converted modes and leaky guided waves within the sills. These processes remove energy from the primary transmitted wavefront, contributing to degraded seismic imaging. Whilst these are all fundamental physical limitations that cannot be overcome, further work should focus on the processing of seismic data to ensure that these aspects of the seismic wave-field around sill complexes are optimally treated within processing workflows.

Data-driven suppression of short-period multiples from laterally varying thin-layered overburden structures

Marchenko multiple elimination methods remove all orders of overburden-generated internal multiples in a data-driven way. In the presence of thin beds, however, these methods have been shown to underperform. This is because the underlying inverse problem requires the information about short-period internal multiple (SPIM) imprint on the inverse transmission to be correctly constrained. This has been addressed in 1.5D media with energy conservation and minimum-phase reconstruction. Extending the applications to two dimensions and, hence, making the step toward field data were believed to be hampered by the need for a multidimensional minimum-phase reconstruction which is (1) not unique and (2) no algorithm has been found to perform this in practice on band-limited data. Here, we address both of these problems with an approach that includes solving the Marchenko equation with a trivial constraint, evaluating the energy conservation condition of its solutions to find the spatially dependent error syndrome, using the 1.5D minimum-phase reconstruction for each shot gather to find the spatially dependent constraint, and finally using that inside another run of the Marchenko equation solver to find a much-improved result. We find that the method works because in 2D media the expression of SPIMs in the inverse transmission coda is approximately 1.5D. We then investigate a class of models and synthetic data sets to verify where the 1.5D approximation starts breaking down. Our analysis indicates that this approach could perform very well in settings with moderate lateral variations, which also is where the (short-period) internal multiples are most difficult to differentiate from primary reflections.

Extracting small time-lapse traveltime changes in a reservoir using primaries and internal multiples after Marchenko-based target zone isolation

Geophysical monitoring of subsurface reservoirs relies on detecting small changes in the seismic response between a baseline and monitor study. However, internal multiples, related to the over- and underburden, can obstruct the view of the target response, hence complicating the time-lapse analysis. To retrieve a response that is free from the over- and underburden effects, the data-driven Marchenko method is used. This method effectively isolates the target response, which can then be used to extract more precise time-lapse changes. In addition, the method also reveals target-related multiples that probe the reservoir more than once, which further defines the changes in the reservoir. To verify the effectiveness of the method, a numerical example is constructed. This test finds that, when using the isolated target response, the observed time differences resemble the expected time differences in the reservoir. Moreover, the results obtained with target-related multiples also benefit from the Marchenko-based isolation of the reservoir. It is, therefore, concluded that this method has the potential to observe dynamic changes in the subsurface with increased accuracy.