Waveform inversion based on least-squares reverse time migration (LSRTM) usually involves Born modeling, which models the primary-only data. As a result the inversion process handles only primaries and corresponding multiple elimination pre-processing of the input data is required prior to imaging and inversion. Otherwise, multiples left in the input data are mapped as false reflectors, also known as crosstalk, in the final image. At the same time the developed full wavefield migration (FWM) methodology can handle internal multiples in an inversion-based imaging process. However, because it is based on the framework of the one-way wave equation, it cannot image dips close to and beyond 90°. Therefore, we aim at upgrading the LSRTM framework by bringing in the functionality of FWM to handle internal multiples. We inject the secondary source term, as used in the original formulation of FWM to define a wavefield relationship that allows to model multiple scattering via reflectivity. The secondary source term is based on the estimated reflectivity and can be injected into the pressure component when simulating the two-way wave equation using finite-difference modeling. We use this modified forward model for estimating the reflectivity model in a FWM-type manner and validate the method on both synthetic and field data containing visible internal multiples.

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An important imaging challenge is creating reliable seismic images without internal multiple crosstalk, especially in cases with strong overburden reflectivity. Several data-driven methods have been proposed to attenuate the internal multiple crosstalk, for which fully sampled data in the source and receiver side are usually required. To overcome this acquisition constraint, model-driven full-wavefield migration (FWM) can automatically include internal multiples and only needs dense sampling in either the source or receiver side. In addition, FWM can correct for transmission effects at the reflecting interfaces. Although FWM has been shown to work effectively in compensating for transmission effects and suppressing internal multiple crosstalk compared to conventional least-squares primary wavefield migration (PWM), it tends to generate relatively weaker internal multiples during modeling. Therefore, some leaked internal multiple crosstalk can still be observed in the FWM image, which tends to blend in the background and can be misinterpreted as real geology. Thus, we adopted a novel framework using local primary-and-multiple orthogonalization (LPMO) on the FWM image as a postprocessing step for leaked internal multiple crosstalk estimation and attenuation. Due to their opposite correlation with the FWM image, a positive-only LPMO weight can be used to estimate the leaked internal multiple crosstalk, whereas a negative-only LPMO weight indicates the transmission effects that need to be retained. Application to North Sea field data validates the performance of the proposed framework for removing the weak but misleading leaked internal multiple crosstalk in the FWM image. Therefore, with this new framework, FWM can provide a reliable solution to the long-standing issue of imaging primaries and internal multiples automatically, with proper primary restoration.

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The Full Wavefield Migration (FWM) algorithm has some additional features comparing to conventional least-squares imaging. It requires to store wavefields from previous iterations to take into account multiple scattering. We revise this approach and propose to recompute the wavefields instead of keeping them in the memory. It allows us to reduce the memory requirements and makes the algorithm more fault-tolerant and suitable for distributed computing. We apply the modified algorithm use the modified code on one of the public cloud providers.@en

Combination of Full Waveform Inversion (FWI) with wavefield tomography (WT) methods is a known and robust approach which is used to avoid the local minima problem, mostly due to so-called cycle-skipping. It is proposed to supplement FWI the image-domain joint migration inversion (IDJMI). The former method extends model-domain wavefield tomography (WT) in terms of introducing multiple scattering and transmission effects. Thus, joint inversion of FWI together with ID-JMI - instead of WT - becomes more robust, as in this configuration both methods handle multiple scattering in a natural way.

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Least-squares reverse-time migration (LSRTM) nowadays is a standard inversion-based seismic imaging method. One of the advantages of this approach is a high accuracy of the forward propagator, with which it is easy to handle large variations in the medium and to image vertical structures via diving waves. LSRTM estimates perturbations of the background model under a linear assumption (the Born approximation), therefore only single scattering generated in the subsurface is addressed and internal multiples are considered as noise, which results in image artifacts (crosstalk). In this paper we investigate an option to include internal multiple scattering in the forward model of LSRTM, while still using a smooth background model. This is achieved by introducing two-way scattering sources from the concept of Full Wavefield Migration, which will generate the higher-order scattering due to the imaged reflection structures. The methodology is demonstrated on synthetic and field data, showing its capabilities in properly handling internal multiples.

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Although considered as noise in the past, multiples are being increasingly seen as a tool for better illumination of the subsurface. We explore the different strategies of exploiting the surface-related multiples specifically in the case of large acquisition gaps. Surface-related multiples travel via different propagation paths compared to the primaries and hence, illuminate a wider area. This property makes them valuable in cases of limited illumination. Existing migration methods incorporate surface-related multiples in imaging by re-injecting the total measured data as a downgoing wavefield; this makes the method dependent on a dense receiver configuration and, therefore, sensitive to missing data. Using 3D synthetic examples we will illustrate a `non-linear' inversion approach in which all multiples are modeled from the original source field. This makes the method less dependent on the receiver geometry, therefore, helping us in case of limited illumination. We also discuss a `hybrid' method on the same 3D model that utilises the benefits of both `linear' and `non-linear' methods. The results indicate substantial reduction of migration holes compared to the `linear' inversion methods, which is demonstrated on a 3D synthetic data with an obstruction zone from the platform.

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Although seismic sources typically consist of identical broadband units alone, no physical constraint dictates the use of only one kind of device. We propose an acquisition method that involves the simultaneous exploitation of multiple types of sources during seismic surveys. It is suggested to replace (or support) traditional broadband sources with several devices individually transmitting diverse and reduced frequency bands and covering together the entire temporal and spatial bandwidth of interest. Together, these devices represent a so-called dispersed source array. As a consequence, the use of simpler sources becomes a practical proposition for seismic acquisition. In fact, the devices dedicated to the generation of the higher frequencies may be smaller and less powerful than the conventional sources, providing the acquisition system with increased operational flexibility and decreasing its environmental impact. Offshore, we can think of more manageable boats carrying air guns of different volumes or marine vibrators generating sweeps with different frequency ranges. On land, vibrator trucks of different sizes, specifically designed for the emission of particular frequency bands, are preferred. From a manufacturing point of view, such source units guarantee a more efficient acoustic energy transmission than today's complex broadband alternatives, relaxing the low- versus high-frequency compromise. Furthermore, specific attention can be addressed to choose shot densities that are optimum for different devices according to their emitted bandwidth. In fact, since the sampling requirements depend on the maximum transmitted frequencies, the appropriate number of sources dedicated to the lower frequencies is relatively small, provided the signal-to-noise ratio requirements are met. Additionally, the method allows to rethink the way to address the ghost problem in marine seismic acquisition, permitting to tow different sources at different depths based on the devices' individual central frequencies. As a consequence, the destructive interference of the ghost notches, including the one at 0 Hz, is largely mitigated. Furthermore, blended acquisition (also known as simultaneous source acquisition) is part of the dispersed source array concept, improving the operational flexibility, cost efficiency, and signal-to-noise ratio. Based on theoretical considerations and numerical data examples, the advantages of this approach and its feasibility are demonstrated.

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Nowadays, there is a strong emphasis on explaining the full seismic wavefield for obtaining detailed subsurface information, which is indeed the way forward to improve the final resolution of images and – after that – reservoir properties. Within the full waveform inversion (FWI) community there is a strong bias towards one type of modelling, which is the finite-difference based solutions of the wave equation. However, one issue associated with FWI is that it does not yet provide a full strategy towards a broadband elastic reservoir inversion process. Traditionally, FWI is used for estimating the velocity model that is used as input for standard migration-inversion approaches, thereby losing the advantages of the full waveform approach, such as including the effect of multiples. As an alternative, the Joint Migration Inversion process, with an operator-based modelling engine, provides an open framework that can include many physical features (such as anisotropy, elastic angle-dependent reflectivity), without having to re-implement a certain wave equation. By using one-way propagators in combination with reflectivity operators, a full two-way response can be built. It provides consistent full wavefield outputs that can lead to accurate elastic parameters in the reservoir, while fully removing the overburden imprint.@en

Seismic modelling plays an important role in the estimation of subsurface parameters by waveform inversion. Modelling methods based on a two-way wave equation are well known for their high accuracy, however by using them explicitly when solving inverse problems is very nonlinear, yielding local minima issues. One of the possibilities to overcome this is splitting the governing two-way wave equation into a set of one-way wave equations that define propagation along the preferred (vertical) direction and that are coupled by a special term that includes transmission and reflection functions. In this case, the scattering is mainly driven by the coupling term whereas the velocity model is responsible for the propagation, which simplifies the inversion and also puts more control on the modelling. We demonstrate that this system of equations can be discretized and solved numerically using a frequency-domain finite-difference (FDFD) approach. Numerical examples demonstrate the validity of such modelling as a forward model in full wavefield migration (FWM) – an inversion-based imaging method that includes multiple scattering and transmission effects.
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Accurate estimation of the local reservoir responses - including the AVO information - is crucial for correctly estimating the elastic parameters from the target area. In this paper the estimation of the target reflection responses
is implemented as part of the full wavefield imaging algorithm that handles multiple scattering not only by suppressing undesired overburden imprints but also by using its information for obtaining a better estimate of the responses. The newly obtained inversion problem includes the two main components — full wavefield migration (FWM) of the overburden - yielding its reflectivity properties - combined with the estimation of the local reflection impulse responses of the target area located below. Both sets of parameters are included in the forward model and should simultaneously fit the observed surface data in the least-squares manner. The main advantage of this combined approach is that multiple scattering and transmission effects in the overburden are correctly accounted for, yielding high-quality target impulse responses. It is shown that estimating the responses in this manner is also suitable for the 3D case, where sparse acquisition geometries provide an additional challenge.@en

The joint migration inversion (JMI) approach is a very robust and effective method for simultaneously estimating reflectivity (imaging) and the propagation velocity model in a closed-loop process. Being a full waveform method, it utilizes multiple scattering for estimating both types of parameters. Usually, angle-independent reflectivity and velocity are estimated in a ”flip-flop” manner based on gradient descent scheme. Two new features are discussed in this paper. First, simultaneous estimation of angle-dependent reflectivity in the JMI framework is studied, which allows to handle data with strong amplitude versus offset (AVO) variations. Second, a quasi-Newton algorithm was tested to estimate both angle-independent and angle-dependent reflectivity. The method is demonstrated on numerical data, generated by it’s own forward modelling method, as well as data generated using finite difference modeling.@en

Multiple scattering is usually ignored in migration algorithms, although it is a genuine part of the physical reflection response. When properly included, multiples can add to the illumination of the subsurface, although their crosstalk effects are removed. Therefore, we introduce full-wavefield migration. It includes all multiples and transmission effects in deriving an image via an inversion approach. Since it tries to minimize the misfit between modeled and observed data, it may be considered a full waveform inversion process. However, full-wavefield migration involves a forward modelling process that uses the estimated seismic image (i.e., the reflectivities) to generate the modelled full wavefield response, whereas a smooth migration velocity model can be used to describe the propagation effects. This separation of modelling in terms of scattering and propagation is not easily achievable when finite-difference or finite-element modelling is used. By this separation, a more linear inversion problem is obtained. Moreover, during the forward modelling, the wavefields are computed separately in the incident and scattered directions, which allows the implementation of various imaging conditions, such as imaging reflectors from below, and avoids low-frequency image artefacts, such as typically observed during reverse-time migration. The full wavefield modelling process also has the flexibility to image directly the total data (i.e., primaries and multiples together) or the primaries and the multiples separately. Based on various numerical data examples for the 2D and 3D cases, the advantages of this methodology are demonstrated.

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In this chapter we demonstrate application of FWM on real data. We test the FWM
algorithm on various types of data: firstly we study using the surface multiples for
both shallow and deep water cases and moving towards the water bottom by using 3D ocean bottom nodes measurements. Next, we demonstrate how the impact of internal multiples on the resulted image can be eliminated if FWM is used as an imaging tool. Finally, we show the example of data prediction using the forward model of FWM for the field dataset.@en

In the previous chapter the forward model (FWMod) and the general inversion
scheme (FWM) has been described. This chapter discusses different implementation approaches that can be used via FWM. First of all, aspects of surface multiples imaging are discussed and a strategy to image them in an optimal way is introduced. Next, it is shown how surface multiples can be very helpful when imaging ocean bottom node (OBN) data. Furthermore, it is discussed, that imaging of surface multiples, after some adjustments, opens the possibility to efficiently estimate the effective source wavelet. Further, we show that the forward model of FWM can be used for predicting events. In this way missing data reconstruction, primaries/surface multiples separation or de-blending can be performed.@en