Detailed reconstruction of deep crustal targets by seismic methods remains a long-standing challenge. One key to address this challenge is the joint development of new seismic acquisition systems and leading-edge processing techniques. In marine environments, controlled-source seismic surveys at a regional scale are typically carried out with sparse arrays of ocean bottom seismometers (OBSs), which provide incomplete and down-sampled subsurface illumination. To assess and minimize the acquisition footprint in high-resolution imaging process such as full waveform inversion, realistic crustal-scale benchmark models are clearly required. The deficiency of such models prompts us to build one and release it freely to the geophysical community. Here, we introduce GO_3D_OBS – a 3D high-resolution geomodel representing a subduction zone, inspired by the geology of the Nankai Trough. The

To make a step change in our understanding of the geodynamical processes that shape the earth's crust, we need to improve our ability to build 3D high-resolution multi-parameter models of geological targets at the regional scale. This deep target reconstruction is typically beyond the range of the streamer-based data acquisition due to the limited length of the streamer cable (

During the last decades, a vast majority of deep-crustal seismic experiments carried out in academia were performed in two dimensions (namely, along profiles), mainly due to the financial cost of such experiments and the lack of suitable equipments. They often combine a short-spread towed-streamer acquisition with sparse 4C (four-component) OBS (ocean bottom seismometer) deployments. The data recorded by these two types of acquisition conceptually provide complementary information on the subsurface, which is processed with different imaging techniques

Regarding streamer acquisition, to date only a few 3D academic multi-streamer experiments have been conducted

For stationary-receiver surveys, coarse 3D passive- or active-source OBS experiments have begun to emerge in academia

In terms of imaging, processing of streamer data interlaces two tasks under a scale-separation assumption: reconstruction of the reflectivity by depth migration (from ray-based Kirchhoff migration to two-way wave equation reverse-time migration, RTM) and velocity model building by reflection or slope tomography. Stable velocity model building with those techniques can be performed down to a maximum depth of the order of the streamer length. In turns, reflectivity imaging by migration may be performed at greater depths if reliable deep velocity information is provided (e.g. from complementary OBS data) and the deep reflection are recorded with an acceptable signal-to-noise ratio. Higher-resolution velocity models can also be built from streamer data by FWI

All these approaches have been designed to deal with the limited aperture illumination provided by short-spread streamer acquisition, which generates a null space between the low wavenumbers of the velocity macro-model and the high wavenumbers of the reflectivity image, hence justifying the explicit above-mentioned scale separation during seismic imaging

FWI is a brute-force nonlinear waveform matching procedure which allows for building broadband subsurface models – provided that the structure is illuminated by a variety of waves propagating from the transmission to the reflection regime

As reviewed above, advanced deep-crustal seismic imaging raises different frontier methodological issues in terms of acquisition design, inverse problem theory and high-performance computing. Addressing these challenges can be done by establishing a geologically meaningful 3D marine regional model amenable to exploring the pros and cons of different acquisition geometries, wave propagation requirements, and processing techniques. Indeed, most of the geomodels in the imaging community have been designed to fit the specifications of the exploration scale (Marmousil

The proposed geomodel is intended to serve as an experimental setting for various imaging approaches with a special emphasize on multi-parameter waveform inversion techniques. For this purpose, the size of geological features we introduce shall be detectable by seismic waves and span tens of kilometres (major structural units building mantle, crust, volcanic ridges, etc.) to tens of metres – namely to the order of the smallest seismic wavelengths (sedimentary cover, subducting channel, thrusts, and faults, etc.).
The structural complexity of the model is complemented by a broad range of physical parameters.
Our approach incorporates deterministic, stochastic and empirical components at various stages of the model building. The deterministic components cover the shape of the main geological units, as well as their projection into the third dimension. The stochastic components include small-scale perturbations and random structure warping – introducing further spatial variation

This article is organized as follows. We start with the description of the geological units, which build the 2D curvilinear structural skeleton of the model. Then, we review how we project the 2D initial structure into the third dimension and how we introduce the viscoelastic properties in each structural unit. Third, we describe the implementation of the stochastic components designed to introduce more structural heterogeneity. Finally, we present some simulations of OBS data in the 3D model with the finite-difference and spectral-element methods, and we summarize the article with a discussion and conclusion.

In the following sections we present, step by step, the workflow that was designed to create the seismologically representative model of the subduction zone. The whole procedure was implemented in a MATLAB environment.

The overall geological setup of our model is mainly (but not only) inspired by the features interpreted in the Nankai Trough area. However, these structures can also be found in different convergent margins around the world combined in various configurations. Therefore, our model is not intended to replicate a particular subduction zone and its related geology for geodynamic studies of the targeted region. On the contrary, it was designed to comprise broad range of features one may encounter in these tectonic environments. Such a quantitative subsurface description should challenge performances of high-resolution crustal-scale imaging from the complex waveforms generated in this model.

The skeleton of the initial 2D model is presented in Fig.

To create an overall skeleton of the model, we start from the interfaces that shape the mantle and the crust. In Fig.

In the next step, we cut the subducting oceanic crust and mantle by series of interfaces (blue dashed lines in Fig.

On top of the oceanic crust, we place two layers of subducting sediments (grey dashed and solid lines in Fig.

Just between the edge of the continental crust and the subducting slab, we add a stack of relatively thin sheets corresponding to progressively underplated material (dashed black lines in Fig.

The accretionary wedge consists of two parts. The landward part is formed by large deformed stacked thrusts sheets (solid blue lines in Fig.

Finally, the frontal prism is fed by the layers of incoming sediments (black lines in Fig.

The next step in our scheme is the geologically guided projection of the initial skeleton (Fig.

Once the nodes defining a given interface are projected in the crossline direction, we interpolate the piecewise cubic polynomials between the new nodes in the inline direction. In this way we create a new interface, which is slightly shifted with respect to that of the previous inline section. The functions used to project each of the node from the subset of nodes defining a given interface are designed such that they are similar but not exactly the same. This means that the interface is not only shifted (as if exactly the same projection function was used for all the nodes defining the interface) but its geometry can also be modified. In Fig.

It is worth mentioning that some nodes can belong to several interfaces – for example, when they are at the junction of two interfaces. In such a case, these nodes are projected only once with the function assigned to the first interface in order to guarantee a conform space warp of the polygons. Therefore, the projection function applied to the second interface must be partially determined by the fact that one of the nodes (which belongs also to the first interface) was already projected. In such a way, the structural skeleton we create can be viewed as a system of interfaces that are implicitly coupled via the dependencies between the position of the nodes which define them. Therefore, adding new features to the model or modifying existing ones requires careful design of the corresponding projection functions, which will honour the previous dependencies between interfaces.

We assumed that the model will be 100 km in width, therefore we generate 4001 2D inline sections spaced 25 m apart. To highlight the lateral variability of the structure generated during the projection, we show the skeleton of the inline sections in a perspective view extracted every 20 km (Fig.

In Fig.

Once the inline section has been projected in the crossline direction, the newly generated structural skeletons are further mapped into uniform 2D Cartesian grids of the dimension

On top of the index matrix, we implement another matrix, referred to as gradient matrix, which allows us to introduce spatial variations in the physical parameters in each large-scale unit and around the main fault planes (Fig.

In practice, the index matrix and the gradient matrix are combined to implement any physical parameter in each geological formation. To do so, we extract a given geological unit (based on the index matrix) and assign to it a constant parameter value

To better illustrate how the index and gradient matrix can be used to produce a physical model, we consider the following example. Let us imagine that we want to assign

We also use the gradient matrix to implement variations in the parameters within the subducting sediments, fault-related damage zones, and subducting channel, which result from small-scale geological processes (fluid migrations, lithological variations, tectonic compaction, mass wasting, etc.;

Finally, the gradient matrix also describes two additional types of perturbations. The first type is implemented around the regions of thickened oceanic crust mimicking subducting volcanic ridges

From the index and gradient matrices described in the previous section, we can now implement the seismic properties in the structural units. In practice, this requires some constraints on the parameters, which might come from field experiments and laboratory measurements. Regional seismic studies often lack resolution to directly map the reconstructed properties into the fine-scale structures of our model. Moreover, they often ignore second-order parameters such as density (

Comparison of the

From the

We also implement attenuation effects in our model through the

In the final step of our model-building procedure, we consider various types of stochastic components, which are intended to introduce perturbations of a random character into the model. We design two types of such random components: (i) small-scale parameter perturbations and (ii) spatial warping of the final 3D cube.

In Figs.

In Fig.

Looking at the stochastic matrix in Fig.

In Fig.

To analyse what the designed stochastic perturbations mean in terms of the spatial resolution of the model, we compute the 2D wavenumber spectrum (displayed in logarithmic amplitude scale in Fig.

Finally, we apply a second type of stochastic components to the model after projection, parameterization, and application of small-scale stochastic perturbations. The aim of this step is to perform a small-scale pointwise warping of the input 3D grid using a distribution of random shifts. By small-scale we mean that the structural changes introduced by warping are in general much smaller than those incorporated during the projection step. Their impact on the shape of the wavefield will therefore be weaker than the one induced by the geological structure itself but more pronounced than that resulting from the small-scale perturbations described in the previous section. The idea was inspired by dynamic image warping (DIW)

In our case, we use DIW in a forward sense. This means we build a matrix of smoothly varying random spatial shifts of a desired scale and magnitude. Then, we warp each of the inline section from the 3D model grid using those shifts. Figure

First, for each of the 4001 inline sections, we extract from the distribution shown in Fig.

Once we have the sub-matrix of shifts and the initial inline section

Once an inline section has been warped, we extract a sub-matrix of shifts for the next inline section from the distribution of shifts shown in Fig.

Three depth slices extracted at 5, 7.5, and 10 km depth from the 3D

In this section, we perform full wavefield modelling in a target of the GO_3D_OBS model to assess the footprint of the structural complexity and the heterogeneity of the physical parameters on the anatomy of these wavefields. Figure

The perspective view on the chair plot of the 3D

The first modelling test demonstrates the influence of the viscous effects on 2D acoustic P-wave modelling. We compare 2D wavefields that are computed without (

OBS gathers generated using 2D finite-difference

Figure

In Fig.

We assess now the footprint of 3D effects by comparing the synthetic seismograms computed by 2D and 3D wave modelling. The data resulting from both simulations are shown in Fig.

OBS gathers generated using finite-difference visco-acoustic

To better understand how the wavefield propagates within the 3D target during the simulation, we extract snapshots every 2.5 s at 10 km depth (see black dotted line in Fig.

Note that, although our 3D target contains part of the curved subduction front, the acquisition profile is still mainly aligned with the dip direction of the structures within the wedge. Nevertheless, the off-plane wavefield propagation is still remarkable. One can imagine that this effect can be further magnified when the geological setting contains more heterogeneities along the crossline direction.

The final modelling example that we present here shows the difference between 3D spectral-element acoustic (in the whole model) and acoustic–elastic (acoustic in water and elastic in solid) wavefield propagation. The solid–fluid coupling along the bathymetry is implemented by means of displacement potential

Figure

OBS gathers generated using 3D spectral-element

From the rms amplitude curves in Fig.

It is also worth to mention here, that the data simulated with the finite-difference scheme exhibit some evidence of so called “staircase effect” (see diffraction-like patterns in the short-offset data in Fig.

Our previous studies oriented on crustal-scale seismic imaging from OBS data were located in the Tokai area of the Nankai Trough

In the academic community of marine geosciences, sparse OBS acquisitions remain the primary tool for offshore lithospheric model reconstruction. The acquisition-related issues focus mainly on the shooting strategy and the optimal OBS spacing

To investigate the footprint of various acquisition settings on the imaged target, realistic synthetic models are necessary for the survey design. The processing of different datasets generated in such models would allow for the optimization of the acquisition setup to find the best compromise between deployment effort, image resolution, and target sampling. This was one of our main motivations behind the design of the GO_3D_OBS model. One of the ongoing projects now focuses on the investigations of the off-plane wavefield propagation during 2D crustal-scale FWI. From the modelling tests shown in this paper (Fig.

Although the processing method we pair the most with our model is FWI, there are no limits in terms of the application of other tomographic techniques, for example ray-theory-based modelling techniques such as ray-tracing or eikonal solvers. While FAT is typically producing rather smooth velocity models, the other variants of tomography have the potential to build models with improved resolution. An evaluation of those tomographic methods against GO_3D_OBS model can lead to their further development. Travel time tomography techniques are in general computationally much less intensive than waveform inversion methods. It is therefore worth pushing their efficiency to the resolution limits and validating them with complex benchmarks. This kind of development of tomographic methods indirectly contributes also to FWI popularization since the tomographic models are usually used as initial models for FWI.

Together with the development of different seismic imaging techniques, methods for the quantitative estimation of their uncertainty and resolution limits shall be proposed. Indeed, this subject is not trivial when facing real-data processing and therefore the issue is often skipped by authors. The obvious problem is that the true geological structure is never exactly known, and therefore the model of this structure has no direct reference point to compare. On the other hand, the resolution and accuracy of the seismic imaging methods are always limited. Therefore, it shall lead us to reflect on the potential pitfalls related to overinterpretations during real-data case studies.

Sparse OBS deployments combined with travel time tomography processing techniques lead to a wide range of similar smooth velocity models of the crust, which explain the travel time data equally well. In such a scenario, the Monte Carlo random sampling of the model space supported by the estimation of probability density of the model parameters

On the other hand, the high-resolution reconstruction methods relying on the inversion of the waveforms recorded by denser OBS acquisitions are also burdened with uncertainty. The fact that those techniques are waveform driven makes the reliability of the wavefield propagation simulation one of the key factors for the final model accuracy. The popular acoustic wavefield modelling and inversion can be precise enough for the overall reconstruction of the medium without, e.g., strong velocity contrasts, fluid-related attenuation zones, and anisotropic layers. However, in the case of the presence of such structures, the acoustic approximation can lead to significant reconstruction error in the final model. The significance of this error is poorly understood, and therefore the evaluation of the uncertainty of the inversion methods with realistic synthetic tests can bring us closer to the estimation of the error during real-data processing, not only because we know the underlying structure exactly but also because of the possibility of investigating the influence of different approximations, experiment geometries, or noise.

At the current stage of development, we believe that GO_3D_OBS is sufficiently realistic to explore the validity of various tomographic and inversion methods on synthetic datasets with different acquisition designs. Future branches of development of this benchmark can cover different aspects including both structural components and parameterization. For instance, one of the interesting topics is extension toward anisotropy. Building such an anisotropy model consistent with geological studies of the deep crust could be challenging due to the general difficulty of precise anisotropy estimation. Nevertheless, it would significantly increase the authenticity of the corresponding seismic data. On the other hand, generating an accompanying dataset for the current models can further broaden their impact. A possible dataset could include sparse 3D and dense 2D OBS deployments, as well as corresponding streamer data. Such a dataset could be directly used for a given type of processing. In particular, generating the seismic data without and with a realistic type and level of noise would help to further evaluate the impact of noise on the accuracy of the reconstruction of the final structure.

We developed the GO_3D_OBS reference geomodel for the purpose of assessing different crustal-scale seismic imaging methods, as well as for guiding various seismic acquisition designs. The 3D model structure allows for the extraction of sub-volumes representing a different level of complexity that can be found in subduction zone environments. The viscoelastic parameterization of the medium gives the potential user the possibility to assess the impact of various physical approximations during model reconstruction. There are various components influencing the current state of the art in terms of crustal-scale imaging. Among them, methodological developments aimed at computationally efficient seismic wave modelling engines and robust inversion schemes assessed against realistic large-scale problems significantly contribute to further exciting geological discoveries. From this perspective, we believe that our model will help to further stimulate high-resolution seismic imaging of the deep lithosphere and thus will help to understand the processes that shape the earth's crust.

The current version of the model and the user manual are available from the data repository of the Institute of Geophysics, Polish Academy of Sciences:

AG and SO initiated the research and setup the overall concept of the 3D model. AG designed and implemented the workflow for building the model structure, the physical parameterization, and the stochastic components. SO validated each of the model ingredients. AG designed and performed seismic modelling simulations. AG prepared the initial version of the paper, which was further updated toward the final version with the contribution from SO.

The authors declare that they have no conflict of interest.

This study was partially funded by (i) the SEISCOPE consortium (

This research has been supported by the Polish National Science Center and the SEISCOPE consortium.

This paper was edited by Rolf Sander and reviewed by Rie Nakata and one anonymous referee.