Source wavelet correction for practical Marchenko imaging: A sub-salt field-data example from the Gulf of Mexico

Imaging a target zone below a salt body can be challenging because large velocity contrasts in the overburden between the salt and surrounding sediments generate internal multiples, which interfere with primary reflections from the target level in the imaging process. This can lead to an erroneous interpretation of reflections in the sub-salt area if multiples are misinterpreted as primaries. The Marchenko redatuming method may enable imaging of the sub-salt target area where the effect of the multiply-scattering overburden is removed. This is achieved by creating a redatumed reflection response where virtual sources and receivers are located below the overburden using a macromodel of the velocity field and the surface reflection data. The accuracy of the redatumed data and the associated internal multiple removal, however, depends on the accurate knowledge of the source wavelet of the acquired reflection data. For the first time, we propose a method which can accurately and reliably correct the amplitudes of the reflection response in field data as required by the Marchenko method. Our method operates by iteratively and automatically updating the source function so as to cancel the most artefact energy in the focusing functions, which are also generated by the Marchenko method. We demonstrate the method on a synthetic dataset and successfully apply it to a field dataset acquired in a deep-water salt environment in the Gulf of Mexico. After the successful source wavelet estimation for the field dataset, we create sub-salt target-oriented images with Marchenko redatumed data. Marchenko images using the proposed source wavelet estimation show clear improvements, such as increased continuity of reflectors, compared to surface-based images and to conventional Marchenko images computed without the inverted source wavelet. Our improvements are corroborated by evidence in the literature and our own synthetic results.     

Point‐spread functions for interferometric imaging

Interferometric redatuming is a data‐driven method to transform seismic responses with sources at one level and receivers at a deeper level into virtual reflection data with both sources and receivers at the deeper level. Although this method has traditionally been applied by cross‐correlation, accurate redatuming through a heterogeneous overburden requires solving a multidimensional deconvolution problem. Input data can be obtained either by direct observation (for instance in a horizontal borehole), by modelling or by a novel iterative scheme that is currently being developed. The output of interferometric redatuming can be used for imaging below the redatuming level, resulting in a so‐called interferometric image. Internal multiples from above the redatuming level are eliminated during this process. In the past, we introduced point‐spread functions for interferometric redatuming by cross‐correlation. These point‐spread functions quantify distortions in the redatumed data, caused by internal multiple reflections in the overburden. In this paper, we define point‐spread functions for interferometric imaging to quantify these distortions in the image domain. These point‐spread functions are similar to conventional resolution functions for seismic migration but they contain additional information on the internal multiples in the overburden and they are partly data‐driven. We show how these point‐spread functions can be visualized to diagnose image defocusing and artefacts. Finally, we illustrate how point‐spread functions can also be defined for interferometric imaging with passive noise sources in the subsurface or with simultaneous‐source acquisition at the surface.     

基于Marchenko理论压制自由表面多次波方法研究

常规虚源点Marchenko自聚焦多次波预测方法只适用于预测不含自由表面的多次波模型,局限于压制层间多次波,该方法在构建上下行格林函数场前,必须从反射响应中去除所有与表面相关的多次波.本文对构建上下行Marchenko格林函数方程进行改进,得到了包含一次波、层间多次波和自由表面多次波的格林函数,利用改进的Marchenko自聚焦预测方法预测自由表面多次波.本文利用水平层状模型数据及SMARRT模型数据证明,改进后的Marchenko法预测海底相关的自由表面多次波效果较为理想,该方法避免了常规SRME自由表面多次波预测方法需要近道重构的缺陷,能够有效提高地震资料的信噪比和分辨率.     

Retrieving virtual reflection responses at drill‐bit positions using seismic interferometry with drill‐bit noise

In the field of seismic interferometry, researchers have retrieved surface waves and body waves by cross‐correlating recordings of uncorrelated noise sources to extract useful subsurface information. The retrieved wavefields in most applications are between receivers. When the positions of the noise sources are known, inter‐source interferometry can be applied to retrieve the wavefields between sources, thus turning sources into virtual receivers. Previous applications of this form of interferometry assume impulsive point sources or transient sources with similar signatures. We investigate the requirements of applying inter‐source seismic interferometry using non‐transient noise sources with known positions to retrieve reflection responses at those positions and show the results using synthetic drilling noise as source. We show that, if pilot signals (estimates of the drill‐bit signals) are not available, it is required that the drill‐bit signals are the same and that the phases of the virtual reflections at drill‐bit positions can be retrieved by deconvolution interferometry or by cross‐coherence interferometry. Further, for this case, classic interferometry by cross‐correlation can be used if the source power spectrum can be estimated. If pilot signals are available, virtual reflection responses can be obtained by first using standard seismic‐while‐drilling processing techniques such as pilot cross‐correlation and pilot deconvolution to remove the drill‐bit signatures in the data and then applying cross‐correlation interferometry. Therefore, provided that pilot signals are reliable, drill‐bit data can be redatumed from surface to borehole depths using this inter‐source interferometry approach without any velocity information of the medium, and we show that a well‐positioned image below the borehole can be obtained using interferometrically redatumed reflection responses with just a simple velocity model. We discuss some of the practical hurdles that restrict the application of the proposed method offshore.     

Effects of aperture on Marchenko focussing functions and their radiation behaviour at depth

A focussing function is a specially constructed field that focusses on to a purely downgoing pulse at a specified subsurface position upon injection into the medium. Such focussing functions are key ingredients in the Marchenko method and in its applications such as retrieving Green's functions, redatuming, imaging with multiples and synthesizing the response of virtual sources/receiver arrays at depth. In this study, we show how the focussing function and its corresponding focussed response at a specified subsurface position are heavily influenced by the aperture of the source/receiver array at the surface. We describe such effects by considering focussing functions in the context of time-domain imaging, offering explicit connections between time processing and Marchenko focussing. In particular, we show that the focussed response radiates in the direction perpendicular to the line drawn from the centre of the surface data array aperture to the focussed position in the time-imaging domain, that is, in time-migration coordinates. The corresponding direction in the Cartesian domain follows from the sum (superposition) of the time-domain direction and the directional change due to time-to-depth conversion. Therefore, the result from this study provides a better understanding of focussing functions and has implications in applications such as the construction of amplitude-preserving redatuming and imaging, where the directional dependence of the focussed response plays a key role in controlling amplitude distortions.     

Utilization of multiple scattering: the next big step forward in seismic imaging

Surface removal and internal multiple removal are explained by recursively separating the primary and multiple responses at each depth level with the aid of wavefield prediction error filtering. This causal removal process is referred to as “data linearization.” The linearized output (primaries only) is suitable for linear migration algorithms. Next, a summary is given on the migration of full wavefields (primaries + multiples) by using the concept of secondary sources in each subsurface gridpoint. These secondary sources are two‐way and contain the gridpoint reflection and the gridpoint transmission properties. In full wavefield migration, a local inversion process replaces the traditional linear imaging conditions. Finally, Marchenko redatuming is explained by iteratively separating the full wavefield response from above a new datum and the full wavefield response from below a new datum. The redatuming output is available for linear migration (Marchenko imaging) or, even better, for full wavefield migration. Linear migration, full wavefield migration, and Marchenko imaging are compared with each other. The principal conclusion of this essay is that multiples should not be removed, but they should be utilized, yielding two major advantages: (i) illumination is enhanced, particularly in the situation of low signal‐to‐noise primaries; and (ii) both the upper side and the lower side of reflectors are imaged. It is also concluded that multiple scattering algorithms are more transparent if they are formulated in a recursive depth manner. In addition to transparency, a recursive depth algorithm has the flexibility to enrich the imaging process by inserting prior geological knowledge or by removing numerical artefacts at each depth level. Finally, it is concluded that nonlinear migration algorithms must have a closed‐loop architecture to allow successful imaging of incomplete seismic data volumes (reality of field data).     

Scattering diagrams in seismic imaging: More insights into the construction of virtual events and internal multiples

The key processes in marine seismic imaging include (i) removing from seismic data all seismic events (free-surface multiples and ghosts) which contain at least one reflection at the sea surface in their wave-propagation path, and leaving those with no reflection at the free surface (internal multiples and primaries), (ii) removing events with at least two reflections in the subsurface (internal multiples), and leaving events with only one reflection in the subsurface (primaries), and then (iii) locating the scattering points and reflectors inside the subsurface which are the sources of primaries and internal multiple events. All these processes are here explained, derived, and optimized via scattering diagrams (diagrammatica) in a way similar to the way the quantum field theory is often explained via Feynman diagrams. Our discussion of the removal of events with free-surface reflections from the data will be brief, as the diagrammatica of these events are now well understood.The main focus of this paper is the diagrammatica of internal multiples and primaries. Although these events do not contain any reflection at the sea surface, it is important to reconstruct them with scattering points near the sea surface, where seismic data are recorded. So our diagrammatica of primaries and internal multiples include events which are not directly recorded in seismic data but which can be constructed from seismic data. These events have allowed us to construct scattering diagrams of primaries and internal multiples with scattering points near the sea surface. Furthermore, these new diagrammatica of internal multiples and primaries can be used to remove internal multiples from the data.     

Three-dimensional Marchenko internal multiple attenuation on narrow azimuth streamer data of the Santos Basin,Brazil

In 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.     

Kirchhoff scattering series for sources and receivers located in an elastic medium: Another insight into the concept of virtual events

The convolution-type and correlation-type representation theorems are building blocks of wave-scattering theory whose usefulness expands in many seismological applications. For example, the Kirchhoff scattering series currently used for attenuating free-surface multiples has been derived from the convolution-type representation theorem. The recently introduced concept of virtual events, which allows us to put virtual sources and virtual receivers inside the subsurface based on the data collected at the sea surface, has been derived by a combined use of the convolution-type and correlation-type representation theorems. The formulation of inverse Kirchhoff scattering series and virtual events has been limited so far to the cases in which sources or receivers, or both, are located in the water. Unfortunately, this assumption is not valid, especially in the context of virtual events, in which both sources and receivers will often be located in a solid. We here redescribe the Kirchhoff scattering series and reformulate the concept of virtual events for the cases in which sources and receivers are in a solid. Moreover, we describe a new form of Kirchhoff series based on the correlation-type representation theorem and new formulae for computing virtual events which do not include the complex renormalization operation of the previous formulation.     

地震多次波成像

地震资料含有各种类型多次波,而传统成像方法仅利用地震一次反射波成像,在地震成像前需将多次波去除.然而,多次波携带了丰富的地下结构信息,多次波偏移能够提供除反射波外的额外地下照明.修改传统逆时偏移方法,用包含一次反射波和多次波的原始记录代替震源子波,将SRME方法预测的表面多次波代替一次反射波作为输入数据,可将表面多次波成像.多次波成像的挑战和困难在于大量串扰噪声的产生,针对表面多次波成像中的成像噪声问题,将最小二乘逆时偏移方法与多次波分阶思想结合起来,发展可控阶数的表面多次波反演成像方法,有望初步实现高精度的表面多次波成像.在消除原始记录中的表面多次波后,通过逆散射级数方法预测得到层间多次波,将层间多次波作为逆时偏移方法的输入数据可将其准确归位到地下反射位置.数值实验表明,多次波成像能够有效地为地下提供额外照明,而可控阶表面多次波最小二乘逆时偏移成像方法几乎完全避免成像噪声.     

基于低频信息补偿的数据驱动Marchenko成像

基于常规地震干涉法和地震超越干涉法,提出了SI和BSI的结合方法SIBSI,即在SI被动源低频信息提取的基础上,重构主动源BSI地震数据,并利用BSI进行格林函数重构和面向目标的Marchenko成像.研究了基于频率优势的主动源低频重构方法,在完整保留了主动源信号高频信息的基础上,有效重构了低频信息,拓宽了地震数据的频带范围.讨论了含有自由表面多次波的地震数据在Marchenko成像中应用的方法.设计了一个含有高阻抗地层的模型,在该模型上使用SI低频信息重构BSI主动源地震数据,最后与纯主动源地震数据的格林函数重构和Marchenko成像进行了对比,证明了本文所提出方法的有效性、抗噪性以及在提高成像效果中的优势.     

Imaging pre‐existing natural fractures using microseismic data

In hydraulic fracturing treatments, locating not only hydraulic fractures but also any pre‐existing natural fractures and faults in a subsurface reservoir is very important. Hydraulic fractures can be tracked by locating microseismic events, but to identify the locations of natural fractures, an additional technique is required. In this paper, we present a method to image pre‐existing fractures and faults near a borehole with virtual reverse vertical seismic profiling data or virtual single‐well profiling data (limited to seismic reflection data) created from microseismic monitoring using seismic interferometry. The virtual source data contain reflections from natural fractures and faults, and these features can be imaged by applying migration to the virtual source data. However, the imaging zone of fractures in the proposed method is strongly dependent on the geographic extent of the microseismic events and the location and direction of the fracture. To verify our method, we produced virtual reverse vertical seismic profiling and single‐well profiling data from synthetic microseismic data and compared them with data from real sources in the same relative position as the virtual sources. The results show that the reflection travel times from the fractures in the virtual source data agree well with travel times in the real‐source data. By applying pre‐stack depth migration to the virtual source data, images of the natural fractures were obtained with accurate locations. However, the migrated section of the single‐well profiling data with both real and virtual sources contained spurious fracture images on the opposite side of the borehole. In the case of virtual single‐well profiling data, we could produce correct migration images of fractures by adopting directional redatuming for which the occurrence region of microseismic events is divided into several subdivisions, and fractures located only on the opposite side of the borehole are imaged for each subdivision.     

Migration of multiples from the South China Sea

The South China Sea where water depth is up to 5000 m is the most promising oil and gas exploration area in China in the future.The seismic data acquired in the South China Sea contain various types of multiples that need to be removed before imaging can be developed.However,compared with the conventional reflection migration,multiples carry more information of the underground structure that helps provide better subsurface imaging.This paper presents a method to modify the conventional reverse time migration so that multiple reflections can migrate to their correct locations in the subsurface.This approach replaces the numerical impulsive source with the recorded data including primaries and multiples on the surface,and replaces the recorded primary reflection data with multiples.In the reverse time migration process,multiples recorded on the surface are extrapolated backward in time to each depth level,while primaries and multiples recorded on the surface are extrapolated forward in time to the same depth levels.By matching the difference between the primary and multiple images using an objective function,this algorithm improves the primary resultant image.Synthetic tests on Sigsbee2 B show that the proposed method can obtain a greater range and better underground illumination.Images of deep water in the South China Sea are obtained using multiples and their matching with primaries.They demonstrate that multiples can make up for the reflection illumination and the migration of multiples is an important research direction in the future.     

地震干涉技术被动源地震成像

被动源地震成像是基于地下反射波响应和透射波响应之间的关系,通过在地表接收由地下非人工震源发出的透射波响应,利用互相关运算来合成反射波响应的方法.合成的反射波响应,又称虚炮集记录等价于地表地震剖面记录.本文研究了由地下随机分布的被动源发出的透射波记录来合成虚炮集记录的基本原理,推导了反射波记录和透射波记录的关系公式;并通过数值模拟方法,分析了被动源成像的可行性.结果表明:利用被动源地震信息进行成像是可行的.     

Review paper: Virtual sources and their responses,Part I: time‐reversal acoustics and seismic interferometry

A focusing acoustic wave field, emitted into a medium from its boundary, converges to a focal spot around the designated focal point. Subsequently, the focused field acts as a virtual source that emits a field propagating away from the focal point, mimicking the response to a real source at the position of the focal point. In this first part of a two‐part review paper on virtual sources and their responses, we define the focusing wave field as the time reversal of an observed point‐source response. This approach underlies time‐reversal acoustics and seismic interferometry. We analyse the propagation of a time‐reversed point‐source response through an inhomogeneous medium, paying particular attention to the effect of internal multiples. We investigate the differences between emitting the focusing field from a closed boundary and from an open boundary, and we analyse in detail the properties of the virtual source. Whereas emitting the time‐reversed field from a closed boundary yields an accurate isotropic virtual source, emitting the field from an open boundary leads to a highly directional virtual source and significant artefacts related to multiple scattering. The latter problems are addressed in Part II, where we define the focusing wave field as an inverse filter that accounts for primaries and multiples.     

一阶多次波聚焦变换成像

将多次波转换成反射波并按传统反射波偏移算法成像,是多次波成像的一种方法.聚焦变换能准确的将多次波转换为纵向分辨率更高的新波场记录,其中一阶多次波转换为反射波.本文对聚焦变换提出了两点改进:1)提出局部聚焦变换,以减小存储量和计算量,增强该方法对检波点随炮点移动的采集数据的适应性;2)引入加权矩阵,理论上证明原始记录的炮点比检波点稀疏时,共检波点道集域的局部聚焦变换可以将多次波准确转换成炮点与检波点有相同采样频率的新波场记录.本文在第一个数值实验中对比了对包含反射波与多次波的原始记录做局部聚焦变换和直接对预测的多次波做局部聚焦变换两种方案,验证了第二种方案转换得到的波场记录信噪比更高且避免了第一个方案中切聚焦点这项比较繁杂的工作.第二个数值实验表明:在炮点采样较为稀疏时,该方法能有效的将一阶多次波转换成反射波;转换的反射波能提供更丰富的波场信息,成像结果更均衡、在局部有更高的信噪比,以及较高的纵向分辨率.     

Research note: Inverse propagation in 1.5-dimensional amplitude-versus-offset joint migration inversion

The state-of-the-art joint migration inversion faces the so-called amplitude-versus-offset challenge, due to adopting over-simplified one-way propagation, reflection and transmission operators to avoid over-parameterization in the inversion process. To overcome this challenge, we apply joint migration inversion to horizontally layered media (or 1.5-dimensional media) and parameterize the solution space via density and velocity models. In this scenario, one-way propagation, reflection and transmission operators required by the joint migration inversion process can be analytically and correctly derived from the subsurface models, so the amplitude-versus-offset challenge is successfully overcome. We introduce a new concept, which is named ‘inverse propagation’, into our 1.5-dimensional amplitude-versus-offset joint migration inversion. It can correctly reconstruct subsurface wavefields by using a surface-recorded receiver wavefield with all the influence of transmission, reflection and multiples accounted for. A synthetic example is used to demonstrate the correctness of the inverse propagation. This work is the foundation to further develop the 1.5-dimensional amplitude-versus-offset joint migration inversion technology.     

DECOMPOSITION OF MULTICOMPONENT SEISMIC DATA INTO PRIMARY P- AND S-WAVE RESPONSES1

Inversion of multicomponent seismic data can be subdivided in three main processes: (1) Surface-related preprocessing (decomposition of the multicomponent data into ‘primary’ P-and S-wave responses). (2) Prestack migration of the primary P- and S-wave responses, yielding the (angle-dependent) P-P, P-S, S-P and S-S reflectivity of the subsurface. (3) Target-related post-processing (transformation of the reflectivity into the rock and pore parameters in the target). This paper deals with the theoretical aspects of surface-related preprocessing. In a multicomponent seismic data set the P- and S-wave responses of the subsurface are distorted by two main causes: (1) The seismic vibrators always radiate a mixture of P- and S-waves into the subsurface. Similarly, the geophones always measure a mixture of P- and S-waves. (2) The free surface reflects any upgoing wave fully back into the subsurface. This gives rise to strong multiple reflections, including conversions. Therefore, surface-related preprocessing consists of two steps: (1)Decomposition of the multicomponent data (pseudo P- and S-wave responses) into true P- and S-wave responses. In practice this procedure involves (a) decomposition per common shot record of the particle velocity vector into scalar upgoing P- and S-waves, followed by (b) decomposition per common receiver record of the traction vector into scalar downgoing P- and S-waves. (2) Elimination of the surface-related multiple reflections and conversions. In this procedure the free surface is replaced by a reflection-free surface. The effect is that we obtain ‘primary’ P-and S-wave responses, that contain internal multiples only. An interesting aspect of the procedure is that no knowledge of the subsurface is required. In fact, the subsurface may have any degree of complexity. Both the decomposition step and the multiple elimination step are fully determined by the medium parameters at the free surface only. After surface-related preprocessing, the scalar P- and S-wave responses can be further processed independently by existing scalar algorithms.     

Combining two seismic experiments to attenuate free-surface multiples in OBC data*

The current inverse scattering solution used for multiple attenuation of marine seismic reflection data assumes that sources and receivers are located in the water. To adapt this solution to the ocean-bottom cable (OBC) experiment where receivers are located on the sea-floor, we have proposed combining the conventional marine surface seismic reflection data (streamer data) with OBC data. The streamer data add to the OBC data some of the wave paths needed for multiple attenuation. This combination has allowed us to develop a multiple attenuation method for OBC data which does not require any knowledge of the subsurface and which takes into account all free-surface multiples, including receiver ghosts. A non-linear synthetic data example consisting of pressure and particle velocity fields is used to illustrate the procedure.     

Correlation‐based reflection waveform inversion by one‐way wave equations

Reflection full waveform inversion can update subsurface velocity structure of the deeper part, but tends to get stuck in the local minima associated with the waveform misfit function. These local minima cause cycle skipping if the initial background velocity model is far from the true model. Since conventional reflection full waveform inversion using two‐way wave equation in time domain is computationally expensive and consumes a large amount of memory, we implement a correlation‐based reflection waveform inversion using one‐way wave equations to retrieve the background velocity. In this method, one‐way wave equations are used for the seismic wave forward modelling, migration/de‐migration and the gradient computation of objective function in frequency domain. Compared with the method using two‐way wave equation, the proposed method benefits from the lower computational cost of one‐way wave equations without significant accuracy reduction in the cases without steep dips. It also largely reduces the memory requirement by an order of magnitude than implementation using two‐way wave equation both for two‐ and three‐dimensional situations. Through numerical analysis, we also find that one‐way wave equations can better construct the low wavenumber reflection wavepath without producing high‐amplitude short‐wavelength components near the image points in the reflection full waveform inversion gradient. Synthetic test and real data application show that the proposed method efficiently updates the background velocity model.