We present a high-resolution P-wave velocity model of the sedimentary cover
and the uppermost basement to
The final velocity model shows a number of geological structures that
cannot be identified in the travel-time tomography models or easily
interpreted from seismic reflection images alone. A sharp strong velocity
contrast accurately defines the geometry of the top of the basement.
Several low-velocity zones that may correspond to the abrupt velocity
change across steeply dipping normal faults are observed at the flanks of
the basin. A 200–300
Seismic methods are one of the most powerful existing geophysical tools to
extract information on the structure and properties of the Earth's
subsurface. These techniques have been, and currently continue to be, widely
used to obtain images of the sediments and crust and to map the variations in
physical properties, particularly P-wave velocity (
One example of near-vertical seismic acquisition is marine multichannel reflection seismic (MCS) systems. The set-up of MCS systems is designed to record near-vertical reflections with a high redundancy (large number of channels), but offset is limited to the streamer length. In deep-water settings, the critical distance for refracted waves is often beyond this distance. Near-vertical reflections hold indirect information on the velocity field and on the depth of the layer where they are reflected. Due to the inherent velocity–depth trade-off and to the possible errors in the identification of the reflector boundaries, we cannot expect a precise velocity model by travel-time inversion using only one or few reflectors with no lateral or vertical continuity.
Aside from the lack of long offsets or wide-aperture acquisition systems and, hence, of refracted phases and wide scattering angles needed for TTT, the
ability to solve low-wavenumber information of the subsurface is also
influenced by the low angular frequency content of the signal
A common approach to mitigate the above-mentioned issues and apply TTT–FWI to
marine MCS data in deep-water settings is by re-datuming the collected data
Our goal here is designing and testing a data processing or modelling strategy
that allows applying FWI to limited-offset MCS data in deep-water settings
starting FWI at frequencies higher than 5
Having a good initial model is essential to overcome the inherent
non-linearity of FWI for band-limited seismic data. A key ingredient to build
that model is using travel times of refracted waves, which for deep water and
short-offset settings are not visible as first arrivals. The objective of our
workflow is solving these challenges and applying FWI under these adverse
conditions. The proposed approach consists of the following steps: (1) data
re-datuming by downward continuation (DC) of the recorded data to the
seafloor, (2) joint refraction and reflection TTT of the original and
re-datumed shot gathers, (3) FWI of the original shot gathers using the model
obtained in (2) as initial reference, and (4) pre-stack depth migration of the
original shot gathers using the FWI
General scheme of the workflow. We build the
As stated in the introduction, refractions are essential to build a
macro-velocity model with the correct low-wavenumber content on it. As MCS acquisition systems have a limited offset (Fig. 2a), the first
arrivals in deep-water environments are typically dominated by the direct
wave as well as reflections, whereas refractions are hidden behind these
phases (Fig. 2b). Several methods have been proposed to recover refracted
signals by changing the plane of the acquisition geometry
The idea is eliminating the effect of the water layer by simulating a sea bottom acquisition (both sources and receivers). Without the water layer, the direct-wave signal and the seafloor reflections disappear, and the critical distance is reduced to zero offset. Thus, the virtual recordings contain early refractions visible as first arrivals (e.g. Fig. 2d).
In 2-D, the recorded wave field can be expressed as
Here the inverse extrapolation follows the boundary value migration (BVM)
scheme of
The inserted wave field is propagated back in time following the acoustic wave
equation solved by the forward extrapolation scheme
Unlike re-datuming approaches that use the Kirchhoff implementation
In the inverse extrapolation process, complex-frequency-shifted perfectly
matched layers (CFS-PML)
In summary, the main steps of the DC approach are the following: first, we
back-propagate the shot gathers through the water layer from the receiver
positions to a virtual surface located at the seafloor. Then, we sort the
resulting virtual seismograms into common receiver gathers. After that, we
back-propagate the receiver gathers through the water layer, this time from
the virtual surface to the source positions, in the opposite direction to its
true trajectory. Finally, we re-sort the resultant wave field in the original
shot gather domain (Fig. 2d). The rearrangement of the data is possible
because of the reciprocity principle, so that if source and receiver have
identical directional characteristics, then interchanging the positions of
sources and receivers yields the identical seismic trace
The final virtually recorded wave field with sources and receivers located at
the seafloor can be expressed as
The accuracy of the resulting wave field also depends on the precision of the
forward solver. The numerical algorithm
Another effect that can affect the result is the presence of artefacts such
as diffraction tails located at the edges of the array and therefore where
the observed wavefronts are truncated. These artefacts are due to the finite
aperture of the recording system. Their effects are larger for small aperture
set-ups, where they can interfere with the energy focusing in the new datum
surface and mask the true arrivals. Moreover, the finite aperture of the
acquisition array causes a non-uniform illumination of the wavefronts, which
results in energy mitigation near the recording limits. Finally, the
resulting extrapolated wave field is also influenced by numerical dispersion,
which attenuates high frequencies as it travels backwards in time through the
medium. Thus, the spectrum of the frequency bandwidth of the data is reduced
due to the Earth effect that acts as a filter
The goal of this step is to obtain a reference
We use a version of the TOMO2D code
The partial derivatives of travel-time residuals with respect to velocity
(for first arrivals and reflections) and reflector depth (only for
reflections) are introduced in the Fréchet matrix with additional
regularization constraints (smoothing, damping). Thus, this interface depth
model is inverted simultaneously with the
The last inversion step of the proposed approach is using the
For the forward problem, we consider the 2-D acoustic wave equation in the
time domain expressed in the form that appears at Eq. (
The goal of the inversion is to find the parameters
The acoustic 2-D forward modelling code compensates for the actual 3-D amplitude
decay of the field data multiplying the field data by
The following step consists of updating the model in the direction where the
misfit decreases. For this purpose, we calculate the gradient of the misfit
following the adjoint-state method proposed by
The gradient of the objective function with respect to the model,
We use the steepest descendent (SD) approach in the optimization problem
because it has particularly low sensitivity to noise. The step used to find
the direction in the model space where the misfit function locally decreases,
is just the opposite of the gradient in the SD approach,
A multi-scale approach where frequency bands are inverted sequentially, from
low to high frequencies
We apply a 2-D Kirchhoff depth migration to image the subsurface structures
directly at depth by using the
The field data used to test the described approach correspond to an
experiment conducted in the Alboran Sea, a complex basin located in the
westernmost Mediterranean (Fig. 3)
Relief map of the study area
The seismic records used in this study were collected in 2011 on board
Spanish R/V
Decimated example of the field data set; only 10 traces in each
kilometre are plotted (so 0.2 of the total) for clarity. From
Here we show the results after applying each step of the modelling strategy
described in the previous sections (see Fig. 1). We work under the premise
that we have no a priori information on the structure and properties of the
subsurface, so the goal is to recover all the possible information on the
Seismic data obtained after the first DC step of the streamer shots
recorded in the TOPOMED cruise. The wave fields are displayed for every fifth
trace (so 10 traces each kilometre, 0.2 of the total). From
We compute the data re-datuming by wave equation DC of the streamer
recordings to the seafloor surface. Figure 5 shows the result after the first
step of the DC for three shot gathers derived using the full wave field of each
shot and a heterogeneous water layer model built as explained in the
Methodology section. The grid size in both the
In the second step, we re-sort the virtual OBS-type wave field in receiver gathers, and then, the data from all shot gathers are combined to construct the final virtual shot gather. Figure 6 shows the final result for the three shot gathers also shown in Fig. 5. The DC has collapsed the seafloor reflection towards a single point, so refractions from shallow subsurface can now be identified and tracked as first arrivals from zero offset. First arrivals are more difficult to identify at long offsets because of amplitude attenuation and the appearance of diffraction tails. Lower panels (d–f) in Fig. 6 show the first arrivals used as input for the TTT (blue dots).
Seismic data obtained from the DC of the streamer shots recorded in
the TOPOMED cruise. Only 10 traces each kilometre are plotted (so 0.2 of
the total) for clarity. From left to right, shot locations are at 171.1,
138.7, and 112.5
Relevant inversion parameters used in the TTT.
The inversion parameters used in the TTT are shown in Table 1. We do not use
the entire data set to reduce computational burden, but all receivers are used
to ensure data redundancy. The selected reflection corresponds to the top of
the basement (TOB), which is a clear event (e.g. see Fig. 9). Reflection
travel times are picked from MCS common midpoint gathers where it is a
bright continuous reflection, which is also interpreted at the same time in a
fully processed stacked image (Fig. S1 in the Supplement). The source and
receiver positions were projected to a straight line defined between first
and last shots, preserving their offset distance. Correlation lengths for the
velocity model are set at the top and bottom nodes of the grid and are
linearly interpolated for the intermediate nodes. The velocity gradient is
stronger in the vertical direction, so the vertical correlation lengths are
selected to be shorter than the ones defined in the horizontal direction. Our
inversion process follows the layer-stripping strategy as described in
The final macro-velocity model is presented in Fig. 7d. The joint refraction
and reflection TTT allows recovering the long-wavelength geometry of the
sharp sediment–basement boundary. The ray coverage of the model inversion is
quantified by the derivative weight sum (DWS)
Histogram of travel-time residuals. Panel
Figure 8 shows histograms of travel-time residuals for three data groups
after the first and last iterations of the two inversion steps of the
layer-stripping strategy. The distributions of data misfit with the initial
model (red lines) are asymmetric and wide for both refractions and
reflections. After the first inversion step (orange lines), the distributions
are symmetric and narrower with the highest pick around zero. At the initial
stage of the second inversion step of the layer stripping (green lines), an
increase in positive travel-time residuals is shown with respect to the
distribution after the first step (orange lines) due to the insertion of
higher velocities below the TOB to recover the sharp velocity contrast. Thus,
the distributions (green lines) are slightly asymmetric and wider than after
the first step of the layer stripping (orange lines). The final distributions
of travel-time residuals (blue lines) are narrower than the previous ones and
approach to a Gaussian centred at zero with the largest counts. This fact
evidences the improvement of the velocity model, and therefore the
corresponding travel-time fitting during the inversion. Lower panels (d–f)
in Fig. 6 show the first arrivals for three DC shot gathers used as input for the
TTT (blue dots) and the first arrivals recovered after TTT (red squares). The
final velocity model in Fig. 7d shows a good convergence with root mean
square (rms) residual travel times of
Two-way time-transformed
Moreover, to assess the reliability of the inversion results, we convert the
velocity and TOB models to two-way time and superimpose the results on top of
the time-migrated image (TMI) (Fig. 9). The figure shows that the TTT
After TTT, we perform FWI of the original streamer shot gathers starting from
a smoothed version of the TTT
We apply a data preconditioning to emphasize reflections between the first
arrival, typically the seafloor reflection, and its first multiple, using data windowing. We define a time window centred at the seafloor reflection.
We identify this phase by using a maximum kurtosis and k statistics criterion
We start the multi-scale FWI at 6
Final velocity model after the FWI using Fig. 7d as initial model.
Figure 10 displays the final FWI velocity model. This model has higher
resolution than the TTT one (Fig. 7d), showing velocity contrasts of
intermediate and short wavelength and a number of geologically meaningful
structures that cannot be identified in the TTT model. The improvement due to
the higher inverted frequencies is clearer in the shallow part of the model.
The velocity contour of
A basin from 95 to 137
Streamer synthetic seismograms, which are computed using the
initial
To show the model improvement in the data domain, in Fig. 11 we compare a
recorded shot gather (Fig. 11c) and a synthetic one generated with the FD
solver
Misfit decrease plotted on a log axis along the iterations. Panel
The misfit reduction for three steps of the multi-scale strategy is shown in Fig. 12. Normalized least-squared misfit is reduced after the whole inversion, and the final residual tends to zero typically after five iterations.
Two-way time-transformed
As in the case of the TTT model, we have converted the FWI
The seismic data used for the PSDM are not the same as for FWI but data that have been processed to attenuate coherent and incoherent noise. Streamer field data were processed using a Wiener filter and a surface-consistent deconvolution to increase the vertical resolution attenuating the ringing of the source. Data were sorted in the CDP (common depth point) domain. An amplitude balance (quality factor of 100) was applied to recover the energy lost by geometrical spreading.
We interpolate the FWI result to a 3.125
Finally, we repeat the PSDM but using the final FWI
A good fit is obtained between the shape of the geological features and the isovelocity contours in Fig. 15c. The volcano-like structure and dipping faults, coincide with well-defined velocity anomalies. Furthermore, a high-velocity layer, which was not visible with TTT in Fig. 14b, is also clearly imaged within the sediment package. The combined interpretation helps us to better define the geological structures and to obtain a proper characterization of the nature of the features.
Information on the structure and properties of the subsurface in the Alboran
margin is retrieved by applying a combination of TTT and FWI, particularly
the
Using the TTT information alone, a coarse
While some studies use waveform modelling in downward continued data
Panels
The data re-datuming allows recovering and identifying the refracted phases
as first arrivals, but not all the energy collapses at its corresponding
point, making the first arrival picking even more difficult (see Fig. 6). To
check the first arrival travel-time errors introduced by the DC procedure we
have reproduced the re-datuming processing but using synthetic shot gathers
simulated with the streamer acquisition geometry and the final FWI
The target of applying FWI is to obtain a high-resolution model of the
properties of the subsurface. However, due to the non-linear behaviour
typical FWI applications use data with low-frequency content or good
kinematical starting models from a priori information
In both TTT and FWI
To assess the match of the velocity model to the seismic boundaries obtained
with more traditional processing and imaging, the
The seismic line was collected to image the structure of the eastern Alboran
Basin in a region where basement is interpreted to be made up of magmatic arc
rocks
The basement top under the basin and also along the southern ridge displays several small-scale highs with steep flanks and a triangular shape with fairly symmetric flanks that do not support tectonic rotation and may indicate small-scale volcanoes, so that the image supports the basement formation by the interplay between magmatic and extensional processes as expected in a magmatic arc.
The sediment cover displays several units bound by unconformities and cut by
small sub-vertical, currently active faults. Based on regional geology, we
infer that most of the sediment sequence is possibly Pliocene but the oldest
layers may be late Miocene, although no drill hole in the vicinity provides a
calibration. The seismic velocity distribution in the basin infill may
provide some further clues regarding the age and nature of the sediment. The
We show that the proposed workflow, including DC of MCS data to the seafloor,
joint refraction, and reflection TTT and FWI, allows obtaining a detailed,
geologically meaningful
The data are not publicly accessible.
The supplement related to this article is available online at:
CG performed the DC, modelled the seismic data, and led the writing of the text. DD performed the FWI code and helped with the assessment of the inversion parameters, together with CEJT. AM helped with the assessment of the TTT inversion parameters. CEJT and AM also contributed to the writing and structure of the text. VS participated in the writing of the text and the guidelines of the research together with CRR, who also led the geological interpretation.
The authors declare that they have no conflict of interest.
This article is part of the special issue “Advances in seismic imaging across the scales”. It is a result of the EGU General Assembly 2018, Vienna, Austria, 8–13 April 2018, and of the 18th International Symposium on Deep Seismic Profiling of the Continents and their Margins, Cracow, Poland, 17–22 June 2018.
We would like to thank everyone involved in the TOPOMED survey. Special thanks to the officers and crew of the R/V
The TOPOMED survey was funded by the Spanish Ministerio de Ciencia e Innovación (grant no. CGL2008-03474-E). The work has been partially financed by REPSOL (CODOS project).
This paper was edited by Michal Malinowski and reviewed by Milena Marjanovic and one anonymous referee.