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In physical acoustic laboratories, wave propagation experiments often suffer from unwanted reflections at the boundaries of the experimental setup. We propose using multidimensional deconvolution (MDD) to post-process recorded experimental data such that the scattering imprint related to the domain boundary is completely removed and only the Green's functions associated with a scattering object of interest are obtained. The application of the MDD method requires in/out wavefield separation of data recorded along a closed surface surrounding the object of interest, and we propose a decomposition method to separate such data for arbitrary curved surfaces. The MDD results consist of the Green's functions between any pair of points on the closed recording surface, fully sampling the scattered field. We apply the MDD algorithm to post-process laboratory data acquired in a two-dimensional acoustic waveguide to characterize the wavefield scattering related to a rigid steel block while removing the scattering imprint of the domain boundary. The experimental results are validated with synthetic simulations, corroborating that MDD is an effective and general method to obtain the experimentally desired Green's functions for arbitrary inhomogeneous scatterers., The Journal of the Acoustical Society of America, 149 (3), ISSN:0001-4966, ISSN:1520-8524

As a result of the world-wide interest in carbon storage and geothermal energy production, increased emphasis is nowadays placed on the development of reliable microseismic monitoring techniques for hazard monitoring related to fluid movement and reactivation of faults. In the process of developing and benchmarking these techniques, the incorporation of realistic noise into synthetic datasets is of vital importance to predict their effectiveness once deployed in the real world. Similarly, the recent widespread use of Machine Learning in seismological applications calls for the creation of synthetic seismic datasets that are indistinguishable from the field data to which they will be applied. Noise generation procedures can be split into two categories: model-based and data-driven. The distributed surface sources approach is the most common method in the first category: however, it is well-known that this fails to capture the complexity of recorded noise (Dean et al., 2015). Pearce and Barley (1977)’s convolutional approach offers a data-driven procedure that has the ability to accurately capture the frequency content of noise however imposes that noise must be stationary. Birnie et al. (2016)’s covariance-based approach removes the stationarity requirement accurately capturing spatio-temporal characterisations of noise, however, like all other data-driven approaches it is constrained to the survey geometry in which the noise data has been collected. In this work, we propose an extension of the covariance-based noise modelling workflow that aims to generate a noise model over a user-defined geometry. The extended workflow comprises of two steps: the first step is responsible for the characterisation of the recorded noise field and the generation of multiple realisations with the same statistical properties, constrained to the original acquisition geometry. Gaussian Process Regression (GPR) is subsequently applied over each time slice of the noise model transforming the model into the desired geometry.The workflow is initially validated on synthetically generated noise with a user-defined input covariance matrix. This allows us to prove that the noise statistics (i.e., covariance and variogram) can be kept almost identical between the noise extracted from the synthetic dataset and the various steps of the noise model procedure. The workflow is further applied to the openly available ToC2ME passive dataset from Alberta, Canada consisting of 69 geophones arranged in a pseudo-random pattern. The noise is modelled and transformed into a 56-sensor, gridded array, which is shown to a very close resemblance to the recorded noise field. Whilst the importance of using realistic noise in synthetic datasets for benchmarking algorithms or training ML solutions cannot be overstated, the ability to transform such noise models into arbitrary receiver geometries opens up a host of new opportunities in the area of survey design. We argue that by coupling the noise generation and monitoring algorithms, the placement of sensors can be optimized based on the expected microseismic signatures as well as the surrounding noise behaviour. This could be of particular interest for geothermal and CO2 storage sites where processing plants are likely to be in close proximity to the permanent monitoring stations.

Seismic reflection data can be redatumed to a specified boundary in the subsurface by solving an inverse (or multidimensional deconvolution) problem. The redatumed data can be interpreted as an extended image of the subsurface at the redatuming boundary, depending on the subsurface offset and time. We retrieve target-enclosed extended images by using two redatuming boundaries, which are selected above and below a specified target volume. As input, we require the upgoing and downgoing wavefields at both redatuming boundaries due to impulsive sources at the earth’s surface. These wavefields can be obtained from actual measurements in the subsurface, they can be numerically modeled, or they can be retrieved by solving a multidimensional Marchenko equation. As output, we retrieved virtual reflection and transmission responses as if sources and receivers were located at the two target-enclosing boundaries. These data contain all orders of reflections inside the target volume but exclude all interactions with the part of the medium outside this volume. The retrieved reflection responses can be used to image the target volume from above or from below. We found that the images from above and below are similar (given that the Marchenko equation is used for wavefield retrieval). If a model with sharp boundaries in the target volume is available, the redatumed data can also be used for two-sided imaging, where the retrieved reflection and transmission responses are exploited. Because multiple reflections are used by this strategy, seismic resolution can be improved significantly. Because target-enclosed extended images are independent on the part of the medium outside the target volume, our methodology is also beneficial to reduce the computational burden of localized inversion, which can now be applied inside the target volume only, without suffering from interactions with other parts of the medium.

reflection measurements at the Earth's surface and an estimate of the direct wave from a focusing point in the subsurface to the acquisition level in order to retrieve the Green’s function between the two. However, the method suffers when an erroneous scaling of the amplitudes and/or a constant phase-shift is introduced to the reflection response, and artifacts caused by internal multiples are not fully suppressed in the retrieved subsurface wave fields. We propose a workflow to calibrate the reflection response, prior to Green's function retrieval via Marchenko focusing, using additional information in the form of a VSP dataset. First a virtual VSP dataset is estimated via Marchenko focusing, to subsequently compare its upgoing component to the upgoing part of the recorded VSP. Thereby, making it possible to correct for a constant phase shift applied to the reflection data. By identifying the minimum residual energy between the virtual VSP and the recorded VSP wave fields, an erroneous scaling of the reflection response can also be corrected. This workflow leads to a more robust Marchenko focusing, where the reflection response can be redatumed to a target zone in the subsurface and used for ghost-free imaging.

Free-surface multiples travel different paths and illuminate different volumes of the subsurface than primaries. When used jointly with primaries to image the subsurface by means of forward and backward extrapolation of separated down- and up-going wave components respectively, free-surface multiples havebeen shown to improve the continuity of shallow parts of the subsurface image by suppressing acquisition related footprints.We show that by carefully combining the full pressure and particle velocity data by means of newly developed, vector-acoustic boundary conditions, wavefronts can be forward and backward propagated without ambiguity in their propagation direction. Wavefield decomposition is thus naturally incorporated within the extrapolation procedure.Moreover, ocean-bottom acquisition geometries generally present source coverage that is wider than the receiver array. A strategy is proposed to incorporate in our imaging scheme energy of primary events whose direct source illumination lies outside of the receiver aperture. This is achieved by combining a directly modelled source illumination with the recorded (down-going) data.

Despite the close links between the fields of time-reversed acoustics, seismic interferometry and Marchenko imaging, a number of subtle differences exist. This paper reviews the various focusing conditions of these methods, the causality/acausality aspects of the corresponding focusing wavefields, and the requirements with respect to omnidirectional/single-sided acquisition.

Standard seismic processing steps such as velocity analysis and reverse time migration (imaging) usually assume that all reflections are primaries: Multiples represent a source of coherent noise and must be suppressed to avoid imaging artifacts. Many suppression methods are relatively ineffective for internal multiples. We show how to predict and remove internal multiples using Marchenko autofocusing and seismic interferometry. We first show how internal multiples can theoretically be reconstructed in convolutional interferometry by combining purely reflected, up- and downgoing Green’s functions from virtual sources in the subsurface. We then generate the relevant up- and downgoing wavefields at virtual sources along discrete subsurface boundaries using autofocusing. Then, we convolve purely scattered components of up- and downgoing Green’s functions to reconstruct only the internal multiple field, which is adaptively subtracted from the measured data. Crucially, this is all possible without detailed modeled information about the earth’s subsurface. The method only requires surface reflection data and estimates of direct (nonreflected) arrivals between subsurface virtual sources and the acquisition surface. The method is demostrated on a stratified synclinal model and shown to be particularly robust against errors in the reference velocity model used.

Conventional (linear) migration algorithms use only a small portion of recorded seismic data (primary reflections) because they rely on single-scattering assumptions. Nonlinear imaging methods also use reflected multiply-scattered waves, benefiting from their additional illumination and sensitivity to the model. Primary and multiple reflections are, however, just part of the energy generated during a seismic experiment - transmitted waves are also generated but are usually not recorded by one-sided (surface seismic) acquisition systems. In theory only two-sided illumination of the imaging target would allow this energy to be recorded and used in migration. Here we use a synthetic example of subsalt imaging to show the nature of improvements to the seismic image (and extended image) from the use of multiples and transmitted waves. We then suggest a practical approach to construct the additional fields required by nonlinear two-sided imaging without the need of a velocity model with sharp contrasts and receivers (and/or sources) in the subsurface.

Enabling nonlinear, elastic imaging using multicomponent seismic data is a key step in moving towards 'true-amplitude' imaging of the subsurface. Nonlinearity here refers both to the fact that even single-scattering interactions are in reality nonlinear (often ignored in Born-scattering migration methods), and to the nonlinearity introduced by the multiple interactions of reverberating waves with the structure to be imaged. Multiples are usually considered as noise in traditional linear imaging methods, and the nonlinearities of individual scattering events are simply ignored. We derive two new, nonlinear elastic imaging conditions based on reciprocity theory that are suitable for reverse-time imaging of land and marine ocean-bottom data. A synthetic example shows that these outperform the best existing elastic imaging conditions, highlighting the importance of handling interactions between multiply scattered and converted waves properly. Focusing such energy in the new methods better illuminates the target and reduces imaging artifacts.

Physical experiments are set up to study acoustic wave propagation in a laboratory. However, wave propagation experiments carried out in a size-limited volume often suffer from unwanted reflections at the boundaries of the experimental domain. We propose a method of multidimensional deconvolution (MDD) to process recorded data such that the undesired imprint of the laboratory boundary is completely removed from the data. The MDD results consist of Green's functions between any pair of points on a mathematically closed receiver surface, sampling the scattering wavefield related to an object of interest with a full aperture. We apply the MDD algorithm to process data recorded in a 2D acoustic waveguide in which a rigid steel block is placed inside of a circular recording array. The scattering imprint of the waveguide boundary is removed from the data, and the scattering Green’s functions only related to this steel block are obtained. The MDD methodology used for the physical experiment is also validated using synthetic simulations; this further corroborates the effectiveness of MDD in obtaining the desired Green's functions associated with arbitrary scatterers in unbounded domains.