Joint Migration Inversion Research Articles

Joint Migration Inversion Based on a Full-Wavefield Acoustic Wave Equation With Vector Reflectivity

Joint Migration Inversion Based on a Full-Wavefield Acoustic Wave Equation With Vector Reflectivity

Advanced Elastic and Reservoir Properties Prediction through Generative Adversarial Network

The prediction of subsurface properties such as velocity, density, porosity, and water saturation has been the main focus of petroleum geosciences. Advanced methods such as Full Waveform Inversion (FWI), Joint Migration Inversion (JMI) and ML-Rock Physics are able to produce better predictions than their predecessors, but they still require tedious manual interpretation that is prone to human error. The research on these methods remains open as they suffer from technical limitations. As computing resources are becoming cheaper, the use of a single deep-generative adversarial network is feasible in predicting all these properties in a completely data-driven manner. In our proposed method of multiscale pix2pix applied to SEG SEAM salt data, we have managed to map from one input, which is seismic post-stack data, to several outputs of reservoir and elastic properties such as porosity, velocity, and density by using only one trained model and without having to manually interpret or pre-process the input data. With 90% accuracy of the results in the synthetic data testing, the method is worthy of being explored by the petroleum geoscience fraternity.

An effective scheme of joint migration inversion in the pseudo‐time domain

AbstractTraditional full‐waveform inversion is a non‐linear and ill‐posed inversion problem. To reduce the non‐linearity of it, joint migration inversion (joint migration inversion) was proposed as an alternative. Joint migration inversion tries to minimize the mismatch between measured and modelled reflection data. One key feature of joint migration inversion is its parameterization: two separate parameters, reflectivity (for the amplitudes of reflected events) and propagation velocity (for the phase effects). This separation helps to reduce the non‐linearity of the inversion. During joint migration inversion, with the velocity being updated, the reflectors in the updated image are also shifting in depth accordingly, this phenomenon is called depth–velocity ambiguity. This interaction between the two parameters during inversion is desired to keep the image time consistent with the measured data but may lead to non‐robustness of joint migration inversion due to the presence of local minima. Therefore, we propose a more robust joint migration inversion scheme, which parameterizes the models with vertical time, termed pseudo‐time joint migration inversion. In pseudo‐time, the updates of velocity will not result in the associated vertical location changes of reflectors in the estimated image. Instead, the reflectors are mainly getting more focused. One limitation is that the depth‐pseudo‐time conversion process assumes a simple linear relationship between depth and pseudo‐time, which might cause some artefacts in the converted models when there exist strong lateral velocity variations. One subsequent round of depth joint migration inversion is recommended to resolve this issue. We demonstrate the effectiveness of our proposed method with a two‐dimensional synthetic example in an extreme scenario, where the initial velocity model is homogeneous, a realistic offshore two‐dimensional synthetic example, a two‐dimensional field example from the Vøring basin in Norway and a simple three‐dimensional synthetic example. In all examples, pseudo‐time joint migration inversion manages to recover more reasonable updates in the inverted velocity and invert more focused reflectors in the inverted image, compared to depth joint migration inversion.

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

ABSTRACTThe 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.

Introduction of the Hessian in joint migration inversion and improved recovery of structural information using image-based regularization

Joint migration inversion (JMI) is a method based on one-way wave equations that aims at fitting seismic reflection data to estimate an image and a background velocity. The depth-migrated image describes the high spatial-frequency content of the subsurface and, in principle, is true amplitude. The background velocity model accounts mainly for the large spatial-scale kinematic effects of the wave propagation. Looking for a deeper understanding of the method, we briefly review the continuous equations that compose the forward-modeling engine of JMI for acoustic media and angle-independent scattering. Then, we use these equations together with the first-order adjoint-state method to arrive at a new formulation of the model gradients. To estimate the image, we combine the second-order adjoint-state method with the truncated-Newton method to obtain the image updates. For the model (velocity) estimation, in comparison to the image update, we reduce the computational cost by adopting a diagonal preconditioner for the corresponding gradient in combination with an image-based regularizing function. Based on this formulation, we build our implementation of the JMI algorithm. Our image-based regularization of the model estimate allows us to carry over structural information from the estimated image to the jointly estimated background model. As demonstrated by our numerical experiments, this procedure can help to improve the resolution of the estimated model and make it more consistent with the image.

Simultaneous joint migration inversion as a high‐resolution time‐lapse imaging method: Feasibility and robustness study

ABSTRACTThe conventional time‐lapse processing workflow is usually sensitive to the non‐repeatable uncertainties between different vintages caused by noise, acquisition designs and independent processing. Therefore, in order to reduce these non‐repeatable uncertainties, all the datasets are usually acquired from well‐sampled and well‐repeated acquisition surveys, and the independent processing is always carefully tailored to maximally reduce the non‐repeatable uncertainties during processing. Moreover, the conventional time‐lapse analysis method, based on a time‐shift map, is not always a good indicator of the actual velocity differences due to its local one‐dimensional subsurface assumption. In order to relax these rigid requirements and have a better velocity change indicator, a robust high‐resolution simultaneous joint migration inversion was proposed as an effective time‐lapse tool for reservoir monitoring. The method combines a simultaneous data‐processing strategy with the joint migration inversion method. Joint migration inversion is a full wavefield inversion method with a parameterization in terms of reflectivity and propagation velocity. The simultaneous strategy allows the baseline and monitor parameters to communicate and compensate with each other dynamically during inversion, thus, suppressing the non‐repeatable uncertainties during the time‐lapse processing. To investigate the feasibility of using high‐resolution simultaneous joint migration inversion in practice, some numerical experiments are conducted to test the dependence of high‐resolution simultaneous joint migration inversion on the quality of the time‐lapse datasets including the following aspects: random noise; sparse surveys; ocean bottom node versus streamer (different types of monitoring surveys); non‐repeated sources, including source positioning errors and non‐repeated source wavelets; spatial weighting operators in the L2‐norm penalty terms; and sensitivity to weak time‐lapse effects. All the experiments are carried on the basis of a realistic synthetic time‐lapse model based on the Grane field offshore Norway. These experiments show that high‐resolution simultaneous joint migration inversion is robust to random noise, survey sparsity, survey non‐repeatability, source positioning errors and source wavelet discrepancies. Furthermore, high‐resolution simultaneous joint migration inversion remains effective when the spatial weighting operators in the L2‐norm penalty terms are largely relaxed, and high‐resolution simultaneous joint migration inversion is capable of detecting weak time‐lapse changes (e.g. velocity changes down to 35 m/s).

Simultaneous joint migration inversion with calendar-time constraints as a processing tool for semi-continuous surveys

Nowadays, to obtain a better understanding of dynamic time-lapse changes, frequent seismic monitoring is necessary, although it will generate a considerable cost increase. Therefore, low-cost frequent monitoring, e.g., sparse and/or nonrepeated surveys, is desired. The simultaneous inversion-based method allows the baseline and monitor parameters to communicate and compensate with each other during inversion via constraints and helps to reduce the artifacts caused by sparse acquisition. These features make it largely independent of the used low-cost acquisition geometry and suitable for inexpensive frequent monitoring surveys. Therefore, we have used this simultaneous inversion-based method as an effective time-lapse processing tool for data sets acquired from inexpensive, semi-continuous time-lapse monitoring surveys, which are based on the so-called instantaneous 4D (i4D) technology. We choose a specific simultaneous inversion method called simultaneous joint migration inversion (S-JMI), which combines a simultaneous processing strategy with the JMI method. In i4D technology, inexpensive localized/sparse surveys, called i4D surveys, are deployed frequently between the conventional full-field surveys. This technology can be treated as a special case of changing geometries during monitoring. In this case, the simultaneous strategy allows the information of the full-field survey to compensate for the insufficient illumination of the localized/sparse i4D surveys during processing. Furthermore, we apply constraints on the reflectivity and velocity differences between the baseline and monitor vintages along the calendar-time axis called calendar-time constraints. These constraints take advantage of the feature that time-lapse effects develop (semi-)continuously along the calendar-time axis, when the monitoring surveys are deployed (semi-)continuously over calendar time. Based on a complex synthetic example, we determined that S-JMI is a promising tool to process the data sets from the semi-continuous monitoring surveys based on i4D technology. Finally, we found that the calendar-time constraints significantly improve the quality of time-lapse effects.

Joint migration inversion: features and challenges

Abstract Joint migration inversion is a recently proposed technology, accommodating velocity model building and seismic migration in one integrated process. Different from the widely accepted full waveform inversion technology, it uses imaging parameters, i.e. velocities and reflectivities of the subsurface, to parameterize its solution space. The unique feature of this new technology is its explicit capability to exploit multiples in its inversion scheme, which are treated as noise by most current technologies. In this paper, we comprehensively evaluate the state-of-the-art joint migration inversion technology from various angles: we first benchmark its performance, on both velocity model building and seismic imaging, against that of the well-accepted workflow comprising full waveform inversion and reverse-time migration using a fully controlled 2D realistic synthetic dataset. Next, we demonstrate its application on a 2D field dataset. Last, we use another 2D synthetic dataset to clearly illustrate the challenges the current joint migration inversion technology is facing. With this paper, we transparently reveal the pros of cons of the current joint migration inversion, and we will also point out the imminent research directions joint migration inversion technology should focus on in the next phase for it to be more widely accepted by the geophysics community.

Simultaneous joint migration inversion for high‐resolution imaging/inversion of time‐lapse seismic datasets

ABSTRACTThe current time‐lapse practice is to exactly repeat well‐sampled acquisition geometries to mitigate acquisition effects on the time‐lapse differences. In order to relax the rigid requirements on acquisition effects, we propose simultaneous joint migration inversion as an effective time‐lapse tool for reservoir monitoring, which combines a joint time‐lapse data processing strategy with the joint migration inversion method. Joint migration inversion is a full‐wavefield inversion method that explains the measured reflection data using a parameterization in terms of reflectivity and propagation velocity. Both the inversion process inside the imaging/inversion scheme and the extra illumination provided by including multiples in joint migration inversion makes the obtained velocity and reflectivity operator largely independent of the utilized acquisition geometry and, thereby, relaxes the strong requirement of non‐repeatability during the monitoring. Because simultaneous joint migration inversion inverts for all datasets simultaneously and utilizes various constraints on the estimated reflectivities and velocity, the obtained time‐lapse differences have much higher accuracy compared to inverting each dataset separately. It allows the baseline and monitor parameters to communicate with each other dynamically during inversion via a user‐defined spatial weighting operator. In order to get more localized time‐lapse velocity differences, we further extend the regular simultaneous joint migration inversion to a robust high‐resolution simultaneous joint migration inversion process using the time‐lapse reflectivity difference as an extra constraint for the velocity estimation during inversion. This constraint makes a link between the reflectivity‐ and the velocity difference by exploiting the relationship between them. We demonstrate the feasibility of the proposed method with a highly realistic synthetic model based on the Grane field offshore Norway and a time‐lapse field dataset from the Troll Field.

From surface seismic data to reservoir elastic parameters using a full-wavefield redatuming approach

SUMMARY Traditionally, reservoir elastic parameters inversion suffers from the overburden multiple scattering and transmission imprint in the local input data used for the target-oriented inversion. In this paper, we present a full-wavefield approach, called reservoir-oriented joint migration inversion (JMI-res), to estimate the high-resolution reservoir elastic parameters from surface seismic data. As a first step in JMI-res, we reconstruct the fully redatumed data (local impulse responses) at a suitable depth above the reservoir from the surface seismic data, while correctly accounting for the overburden interal multiples and transmission losses. Next, we apply a localized elastic full waveform inversion on the estimated impulse responses to get the elastic parameters. We show that JMI-res thus provides much more reliable local target impulse responses, thus yielding high-resolution elastic parameters, compared to a standard redatuming procedure based on time reversal of data. Moreover, by using this kind of approach we avoid the need to apply a full elastic full waveform inversion-type process for the whole subsurface, as within JMI-res elastic full waveform inversion is only restricted to the reservoir target domain.

Joint imaging of angle-dependent reflectivity and estimation of the migration velocity model using multiple scattering

Migration velocity analysis is an important method for providing an accurate velocity model for seismic imaging, which is crucial for correct focusing and localization of subsurface information. Conventionally, only primaries are considered as a source of information for both methods. The use of surface multiples in imaging is becoming more common due to the use of inversion-based approaches, which allow us to handle the crosstalk associated with multiples. However, including internal multiples in imaging and velocity estimation is not straightforward using the standard combination of reverse time migration in combination with image-domain velocity tomography. Incorporating internal multiples in imaging and velocity estimation is possible with the joint migration inversion (JMI) methodology, in which internal multiples are explicitly modeled using the estimated reflectivity via a data-domain objective function. However, to correctly match the observed data, the angle-dependent reflectivity and the migration velocity model need to be determined, which provide an over-parameterization of the inversion problem. Therefore, we have extended the JMI methodology to carry out velocity analysis via the extended image domain, in which the angle-dependent reflectivity is updated via data-domain matching. Examples of synthetic and field data with strong internal multiples demonstrate the validity of our method.

Acquisition design for direct reflectivity and velocity estimation from blended and irregularly sampled data

ABSTRACTBlended acquisition along with efficient spatial sampling is capable of providing high‐quality seismic data in a cost‐effective and productive manner. While deblending and data reconstruction conventionally accompany this way of data acquisition, the recorded data can be processed directly to estimate subsurface properties. We establish a workflow to design survey parameters that account for the source blending as well as the spatial sampling of sources and detectors. The proposed method involves an iterative scheme to derive the survey design leading to optimum reflectivity and velocity estimation via joint migration inversion. In the workflow, we extend the standard implementation of joint migration inversion to cope with the data acquired in a blended fashion along with irregular detector and source geometries. This makes a direct estimation of reflectivity and velocity models feasible without the need of deblending or data reconstruction. During the iterations, the errors in reflectivity and velocity estimates are used to update the survey parameters by integrating a genetic algorithm and a convolutional neural network. Bio‐inspired operators enable the simultaneous update of the blending and sampling operators. To relate the choice of survey parameters to the performance of joint migration inversion, we utilize a convolutional neural network. The applied network architecture discards suboptimal solutions among newly generated ones. Conversely, it carries optimal ones to the subsequent step, which improves the efficiency of the proposed approach. The resultant acquisition scenario yields a notable enhancement in both reflectivity and velocity estimation attributable to the choice of survey parameters.

Full-waveform inversion and joint migration inversion with an automatic directional total variation constraint

As full-waveform inversion (FWI) is a nonunique and typically ill-posed inversion problem, it needs proper regularization to avoid cycle skipping. To reduce the nonlinearity of FWI, we have developed joint migration inversion (JMI) as an alternative, explaining the reflection data with decoupled velocity and reflectivity parameters. However, the velocity update may also suffer from being trapped in local minima. To optimally include geologic information, we have developed FWI/JMI with directional total variation (TV) as an L1-norm regularization on the velocity. We design the directional TV operator based on the local dip field, instead of ignoring the local structural direction of the subsurface and only using horizontal and vertical gradients in the traditional TV. The local dip field is estimated using plane-wave destruction based on a raw reflectivity model, which is usually calculated from the initial velocity model. With two complex synthetic examples, based on the Marmousi model, we determine that our method is much more effective compared with FWI/JMI without regularization and FWI/JMI with the conventional TV regularization. In the JMI-based example, we also determine that L1 directional TV works better than L2 directional Laplacian smoothing. In addition, by comparing these two examples, it can be seen that the impact of regularization is larger for FWI than for JMI because in JMI the velocity model only explains the propagation effects and, thereby, makes it less sensitive to the details in the velocity model.

Research note: derivations of gradients in angle‐independent joint migration inversion

ABSTRACTAlthough joint migration inversion has been proposed for several years, a thorough derivation and description of the involved gradients was not published. In this paper, we derive the gradient of both the angle‐independent reflectivity and the velocity in a framework of acoustic angle‐independent joint migration inversion. With some further approximations taken, the conclusions shown in previous publications can also be reached from our new derivation.

Robust estimation of vertical symmetry axis models via joint migration inversion: Including multiples in anisotropic parameter estimation

Because the earth is predominately anisotropic, the anisotropy of the medium needs to be included in seismic imaging to avoid mispositioning of reflectors and unfocused images. Deriving accurate anisotropic velocities from the seismic reflection measurements is a highly nonlinear and ambiguous process. To mitigate the nonlinearity and trade-offs between parameters, we have included anisotropy in the so-called joint migration inversion (JMI) method, in which we limit ourselves to the case of transverse isotropy with a vertical symmetry axis. The JMI method is based on strictly separating the scattering effects in the data from the propagation effects. The scattering information is encoded in the reflectivity operators, whereas the phase information is encoded in the propagation operators. This strict separation enables the method to be more robust, in that it can appropriately handle a wide range of starting models, even when the differences in traveltimes are more than a half cycle away. The method also uses internal multiples in estimating reflectivities and anisotropic velocities. Including internal multiples in inversion not only reduces the crosstalk in the final image, but it can also reduce the trade-off between the anisotropic parameters because internal multiples usually have more of an imprint of the subsurface parameters compared with primaries. The inverse problem is parameterized in terms of a reflectivity, vertical velocity, horizontal velocity, and a fixed [Formula: see text] value. The method is demonstrated on several synthetic models and a marine data set from the North Sea. Our results indicate that using JMI for anisotropic inversion makes the inversion robust in terms of using highly erroneous initial models. Moreover, internal multiples can contain valuable information on the subsurface parameters, which can help to reduce the trade-off between anisotropic parameters in inversion.

Iterative reflectivity-constrained velocity estimation for seismic imaging

This paper proposes a reflectivity constraint for velocity estimation to optimally solve the inverse problem for active seismic imaging. This constraint is based on the velocity model derived from the definition of reflectivity and acoustic impedance. The constraint does not require any prior information of the subsurface and large extra computational costs, like the calculation of so-called Hessian matrices. We incorporate this constraint into the joint migration inversion algorithm, which simultaneously estimates both the reflectivity and velocity model of the subsurface in an iterative process. Using so-called full wavefield modelling, the misfit between forward modelled and measured data is minimized. Numerical and field data examples are given to demonstrate the validity of our proposed algorithm in case accurate initial models and the low-frequency components of observed seismic data are absent.

Seismic input optimisation for Joint Migration Inversion on complex structures, Malay Basin

The field of seismic imaging has made a recent breakthrough in migration technique with the introduction of Joint Migration Inversion to aid the imaging process by incorporating multiple scattering into the algorithm. Initially, seismic multiples have been regarded as noise and should be removed prior to migration, but today these multiples could be used to enhance the final seismic images since they carry a vast percentage of energy that was generated from the source during acquisition phase. This new technique could be used to improve the final image of complex structures such as the steeply fractured basement reservoir in Anding Utara Field in Malay Basin. As of now, the efforts of improving the steeply-fractured basement image have been done without the incorporation of multiple scattering. Thus, the application of JMI might shed some light on the potential of this technique. Joint Migration Inversion make use of a Closed-Loop imaging process which means that less wave energy is wasted during processing making the final image more consistent with the input data. In conventional migration process, multiple scattering is removed thus vast amount of energy is wasted that leads to a poor final subsurface image. The two main elements in Joint Migration Inversion are Full-Wavefield Migration and Full-Wavefield Inversion. Apart from including seismic multiples in the imaging process, Joint Migration Inversion also allows the user to automatically update the velocity model of the area under investigation while maintaining very little user intervention.

Joint migration inversion: Simultaneous determination of velocity fields and depth images using all orders of scattering

The future in seismic exploration and seismic monitoring is the inclusion of all orders of scattering in the imaging and inversion algorithms. Using the full wavefield in an inversion process allows us to surpass imprints provided by incomplete acquisition and provide more accurate information on the subsurface, as noise becomes signal. We describe an inversion process that does not use the standard parameters from finite-difference-type modeling (being local velocity and density) but that describes the seismic data in terms of elastic reflectivity operators and propagation operators. With these operators, our full-wavefield modeling process builds the complete two-way seismic response. A major advantage of our alternative to the traditional full-waveform inversion methodology is that reflectivity operators are traveltime-free and propagation operators are scattering-free, making the inversion problem significantly more linear. A major advantage of our algorithm is (1) that multiples are utilized to improve both image and velocity accuracy, and (2) that both image and velocities are utilized to make a contribution in the nonlinear migration process. Hence, in joint migration inversion, multiples have a twofold active role.

Review Paper: An outlook on the future of seismic imaging, Part III: Joint Migration Inversion

ABSTRACTThe next generation seismic imaging algorithms will consider multiple scattering as indispensable information, referred to as Full Wavefield Migration. In addition, these algorithms will also include autonomous velocity updating in the migration process, referred to as Joint Migration Inversion. Full wavefield migration and joint migration inversion address the industrial needs of improving images of very complex reservoirs as well as the industry ambition of producing these images in a more automatic manner (‘automation in seismic processing’).In this vision paper on seismic imaging, full wavefield migration and joint migration inversion are formulated in terms of a closed‐loop, estimation algorithm that can be physically explained by an iterative double focusing process (full wavefield Common‐Focus‐Point technology). A critical module in this formulation is forward modelling, allowing feedback from migrated output to unmigrated input (‘closing the loop’). For this purpose a full wavefield modelling module has been developed that utilizes an operator description of complex geology. Full wavefield modelling module is pre‐eminently suited to function in the feedback path of a closed‐loop migration algorithm.‘The Future of Seismic Imaging’ is presented as a coherent trilogy, proposing in three consecutive parts the migration framework of the future. In part I it was shown that the proposed full wavefield modelling module algorithm differs fundamentally from finite difference modelling, as velocities and densities need not be provided. Instead, full wavefield modelling module uses an operator description of the subsurface. In Part II it was shown how the theory of Primary Wavefield Migration can be extended to Full Wavefield Migration by correcting for elastic transmission effects and by utilizing multiple scattering. In Part III it is shown how the full wavefield migration technology can be extended to Joint Migration Inversion, allowing full wavefield migration of blended data without knowledge of the velocity. Velocities are part of the joint migration inversion output, being obtained by an operator‐driven parametric inversion process. The potential of the proposed joint migration inversion algorithm is illustrated with numerical examples.

Review Paper: An outlook on the future of seismic imaging, Part I: forward and reverse modelling

ABSTRACTThe next generation of seismic imaging algorithms will use full wavefield migration, which regards multiple scattering as indispensable information. These algorithms will also include autonomous velocity‐updating in the migration process, called joint migration inversion. Full wavefield migration and joint migration inversion address industrial requirements to improve the images of highly complex reservoirs as well as the industrial ambition to produce these images more automatically (automation in seismic processing).In these vision papers on seismic imaging, full wavefield migration and joint migration inversion are formulated in terms of a closed‐loop, estimation algorithm that can be physically explained by an iterative double‐focusing process (full wavefield Common Focus Point technology). A critical module in this formulation is forward modelling, allowing feedback from the migrated output to the unmigrated input (‘closing the loop’). For this purpose, a full wavefield modelling module has been developed, which uses an operator description of complex geology. Full wavefield modelling is pre‐eminently suited to function in the feedback path of a closed‐loop migration algorithm.‘The Future of Seismic Imaging’ is presented as a coherent trilogy of papers that propose the migration framework of the future. In Part I, the theory of full wavefield modelling is explained, showing the fundamental distinction with the finite‐difference approach. Full wavefield modelling allows the computation of complex shot records without the specification of velocity and density models. Instead, an operator description of the subsurface is used. The capability of full wavefield modelling is illustrated with examples. Finally, the theory of full wavefield modelling is extended to full wavefield reverse modelling (FWMod−1), which allows accurate estimation of (blended) source properties from (blended) shot records.