[Show abstract][Hide abstract] ABSTRACT: We apply Laplace-Fourier 2D and 2.5D waveform tomography to a challenging wide-angle land data set from a geologically complex region in Japan. The survey line is crooked (up to 500 m deviation from the 2D line over the 16 km line length), and the area contains significant topographic relief (up to 400 m) and near-surface weathering layers. The lack of reflections previously prevented conventional reflection processing. We demonstrate that 2D acoustic waveform tomography is capable of extracting a reliable velocity model from refractions and wide-angle reflections with carefully designed data-preconditioning and inversion strategies. Sources and receivers are projected onto a 2D plane without preserving offsets: we eliminate traces where errors in offsets are large. We restrict the inversion to phase information at lowest frequencies, and discretize the model with a fine grid, in order to minimize the effects of the crooked line and the topography. We use balanced data amplitudes (using surface-consistent static deconvolution) to conduct the source estimation. We extensively validate the obtained velocity model by comparisons with a well log and observed waveforms, through scrutiny of the resulting reverse-time-migration image. An additional test with 2.5D waveform tomography demonstrates that 2D waveform inversion is adequate for these data.
[Show abstract][Hide abstract] ABSTRACT: In seismic waveform inversion, non-linearity and non-uniqueness require appropriate strategies. We formulate four types of L2 normed misfit functionals for Laplace-Fourier domain waveform inversion: i) subtraction of complex-valued observed data from complex-valued predicted data (the ‘conventional phase-amplitude’ residual), ii) a ‘conventional phase-only’ residual in which amplitude variations are normalized, iii) a ‘logarithmic phase-amplitude’ residual and finally iv) a ‘logarithmic phase-only’ residual in which the only imaginary part of the logarithmic residual is used. We evaluate these misfit functionals by using a wide-angle field Ocean Bottom Seismograph (OBS) data set with a maximum offset of 55 km. The conventional phase-amplitude approach is restricted in illumination and delineates only shallow velocity structures. In contrast, the other three misfit functionals retrieve detailed velocity structures with clear lithological boundaries down to the deeper part of the model. We also test the performance of additional phase-amplitude inversions starting from the logarithmic phase-only inversion result. The resulting velocity updates are prominent only in the high-wavenumber components, sharpening the lithological boundaries. We argue that the discrepancies in the behaviours of the misfit functionals are primarily caused by the sensitivities of the model gradient to strong amplitude variations in the data. As the observed data amplitudes are dominated by the near-offset traces, the conventional phase-amplitude inversion primarily updates the shallow structures as a result. In contrast, the other three misfit functionals eliminate the strong dependence on amplitude variation naturally and enhance the depth of illumination. We further suggest that the phase-only inversions are sufficient to obtain robust and reliable velocity structures and the amplitude information is of secondary importance in constraining subsurface velocity models.
[Show abstract][Hide abstract] ABSTRACT: We use the pore pressure distribution predicted from a waveform tomography (WT) velocity model to interpret the evolution of the mega-splay fault system in the Nankai Trough off Kumano, Japan. To map pore pressure around the mega-splay fault and plate boundary décollement, we integrate the high-resolution WT velocities with laboratory data and borehole well log data using rock physics theory. The predicted pore pressure distribution shows that high pore pressures (close to lithostatic pressure) along the footwall of the mega-splay fault extend seaward to the trough region, and the normalized pore pressure ratio is nearly constant over that extent. This continuity of the overpressured zone indicates that a coseismic rupture can potentially propagate nearly to the trough axis. We interpret a high-pressure belt within an accretionary wedge on the landward side of the present mega-splay fault as evidence of the ancient mega-splay fault. Because the ancient mega-splay fault soles into the active mega-splay fault, the active mega-splay fault may function as a basal detachment fault and is directly connected to the seaward plate boundary décollement.
[Show abstract][Hide abstract] ABSTRACT: We successfully apply the acoustic Laplace-Fourier waveform tomography
method to delineate P-wave velocity structures of the mega-splay fault
system in the central part of the seismogenic Nankai subduction zone
offshore Japan, using densely sampled wide-angle ocean bottom
seismograph (OBS) data originally acquired in 2004. Our success is due
to new and carefully designed data preconditioning and inversion
strategies to mitigate (i) the well-known non-linearity of waveform
inversion, (ii) the challenges arising from crustal-scale survey designs
(e.g. undersampling of the OBSs), and (iii) modelling errors due to the
use of the acoustic assumption.
We identify a sixfold set of key components that together lead to the
success of the high-resolution waveform tomography image: (i)
Availability of low-frequency components (starting at 2.25 Hz) reducing
the non-linearity, and access to large offset data (up to 55 km)
increasing the depth of illumination and the recovery of low wavenumber
components. (ii) A highly accurate traveltime tomography result (with an
rms error of approximately 60 ms) that further mitigates the
non-linearity. (iii) A hierarchical inversion approach in which phase
spectra are inverted first to reduce artefacts from the acoustic
assumption, and amplitude information is only incorporated in the final
stages. (iv) A Laplace-Fourier domain approach that facilitates a
multiscale approach to mitigate non-linearity by restricting the
inversion to the low frequency components and early arrivals first, and
sequentially including higher frequencies and later arrivals. (v) A
pre-conditioning strategy for eliminating undesirable high wavenumber
components from the the gradient. (vi) A strategy for source estimation
that reduce the influence of the instrumental design.
In the OBS case study used for illustration purposes, Laplace-Fourier
waveform tomography retrieves velocity anomalies as small as 700 m
(horizontally) and 350 m (vertically) above the top of the Philippine
Sea Plate. The resulting velocity structures include low-velocity zones
and thrust structures which have not been previously identified clearly.
The velocity models are validated by scrutiny of synthetic and observed
waveforms, by evaluating the coherency of source estimates, and by
comparison with 3-D pre-stack migrated (PreSDM) images. Chequerboard
tests and point-scatter tests demonstrate both the reliability and the
limitations of the acoustic implementation.
Geophysical Journal International 08/2013; 194(2):1250-1280. · 2.85 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Visco-acoustic waveform inversion can potentially yield quantitative
images of the distribution of both velocity and the attenuation
parameters from seismic data. Intrinsic P-wave attenuation has been of
particular interest, but has also proven challenging. Frequency-domain
inversion allows attenuation and velocity relations to be easily
incorporated, and allows a natural multiscale approach. The
Laplace-Fourier approach extends this to allow the natural damping of
waveforms to enhance early arrivals. Nevertheless, simultaneous
inversion of velocity and attenuation leads to significant `cross-talk'
between the resulting images, reflecting a lack of parameter resolution
and indicating the need for pre-conditioning and regularization of the
We analyse the cross-talk issue by partitioning the inversion parameters
into two classes; the velocity parameter class, and the attenuation
parameter class. Both parameters are defined at a reference frequency,
and a dispersion relation is assumed that describes these parameters at
any other frequency. We formulate the model gradients at a forward
modelling frequency, and convert them to the reference frequency by
employing the Jacobian of the coordinate change represented by the
dispersion relation. We show that at a given modelling frequency, the
Fréchet derivatives corresponding to these two parameter classes
differ only by a 90° phase shift, meaning that the magnitudes of
resulting model updates will be unscaled, and will not reflect the
expected magnitudes in realistic (Q-1 ≪ 1) media. Due to
the lack of scaling, cross-talk will be enhanced by poor subsurface
illumination, by errors in kinematics, and by data noise. To solve these
issues, we introduce an attenuation scaling term (the inverse of a
penalty term) that is used to pre-condition the gradient by controlling
the magnitudes of the updates to the attenuation parameters.
Initial results from a suite of synthetic cross-hole tests using a
three-layer randomly heterogenous model with both intrinsic and
extrinsic (scattering) attenuation demonstrate that cross-talk is a
significant problem in attenuation inversion. Using the same model, we
further show that cross-talk can be suppressed by varying the
attenuation scaling term in our pre-conditioning operator. This strategy
is effective for simultaneous inversion of velocity and attenuation, and
for sequential inversion (a two-stage approach in which only the
velocity models are recovered in the first stage). Further
regularization using a smoothing term applied to the attenuation
parameters is also effective in reducing cross-talk, which is often
highly oscillatory. The sequential inversion approach restricts the
search space for attenuation parameters, and appears to be important in
retrieving a reliable attenuation model when strong time-damping is
applied. In a final test with our synthetic model, we successfully carry
out visco-acoustic inversions of noise-contaminated data.
Geophysical Journal International 08/2013; 194(2):859-884. · 2.85 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We apply Frequency-domain Waveform Tomography to form quantitative, high-resolution P-wave velocity images of a megasplay fault system within the central Nankai subduction zone offshore of southwest Japan, using controlled source Ocean Bottom Seismometer (OBS) data originally acquired in 2004. The Waveform Tomography method exploits recorded seismic waveforms beyond their first arrivals, and thus achieves a much higher resolution (of the order of a wavelength) than that of conventional Traveltime Tomography methods. Frequency-domain Waveform Tomography facilitates a multi-scale approach to stabilize the inversion, in which initial Traveltime Tomography results are sequentially improved on by first fitting low frequency components of the seismic records (starting at 2.25 Hz); higher frequency components (up to 8.5 Hz) are then introduced progressively.Our final Waveform Tomography image allows velocity anomalies as small as 700 m (horizontally) and 350 m (vertically) to be discerned and interpreted, as confirmed by checkerboard modeling tests. The improved explanatory power of the final images is verified by observing that synthetic waveforms calculated from the final results yield much better fit to the observed waveforms than those estimated from the original Traveltime Tomography image. Apparent lithological boundaries from Waveform Tomography agree well with corresponding reflections on seismic migration images, providing further confidence in the validity of the results.The megasplay fault is evident on the final Waveform Tomography image as a sharp velocity discontinuity, delineating the upper surface of a velocity reduction of nearly 1 km/s with respect to the regional 1D velocity trend. The megasplay fault can be traced continuously throughout the entire image, from a nearly horizontal section at the landward extent, moving seaward through to a steeper angle penetrating the old accretionary prisms, with several additional splays appearing to branch in the shallow subsurface. The location of the low-velocity zones imaged by our waveform tomography method coincides with two-previously-identified low velocity zones. The image reveals a low velocity zone that is continuous from deeper to shallower portions of the subsurface, suggesting that pore-fluids may be transported from the inner wedge, to the transition zone, and to the surface, through fluid conduits associated with the megasplay fault system.
Earth and Planetary Science Letters 02/2012; s 317–318:343–353. · 4.72 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We apply Frequency-domain Waveform Tomography to form quantitative,
high-resolution P-wave velocity images of a megasplay fault system
within the central Nankai subduction zone offshore of southwest Japan
using controlled source Ocean Bottom Seismometer (OBS) data originally
acquired in 2004. Waveform Tomography attempts to fit recorded waveforms
rather than just first arrivals, and thus generates a high-resolution
velocity structure in a scale of a wavelength, while the conventional
Traveltime Tomogrpahy is limited to the scale of the Fresnel zone. The
frequency-domain implementation facilitates a multi-scale approach, in
which initial results are matlabgenerated using low frequencies
(starting at 2.25 Hz), and higher frequencies (up to 8.5 Hz) are
introduced progressively. These results also yield significant
improvements in the data fit to the OBS data, in comparison with those
obtained from Traveltime Tomography conducted by Nakanishi et al., 2008.
A remarkable agreement of apparent lithological boundaries from Waveform
Tomography with corresponding reflections on seismic migration images
(Moore et al., 2009, Park et al., 2010) provides further confidence in
the validity of the results. The megasplay fault is evident on the final
image as a sharp velocity discontinuity, delineating the upper surface
of a velocity reduction of nearly 1 km/s with respect to the regional 1D
velocity trend. The megasplay fault can be traced continuously
throughout the entire system, from a nearly horizontal section at the
landward extent, moving seaward through to a steeper angle penetrating
the old accretionary prisms, with several additional splays appearing to
branch in the shallow subsurface. The Waveform Tomography images further
confirms a connection zone 1.5 km thick between two potentially
over-pressured low velocity zones in the system, suggesting that
pore-fluids may be transported from the inner wedge, to the transition
zone and to the surface through fluid conduits associated with the
megasplay fault system.
[Show abstract][Hide abstract] ABSTRACT: Waveform tomography can generate velocity models with significantly higher resolution than travel time tomography. While this has been demonstrated for synthetic data sets, there are only a few successfull applications for real data. In 1998 the land-based SIMBA (Seismic Investigations of the Messum and Brandberg Areas) experiment was carried out in Namibia to study the deep structure of the Messum intrusive complex. As the geometry of this experiment (roll-along) was designed for near-vertical incidence reflection processing, the data are exceptional in comparison with oher data sets used for waveform tomography. Messum is a composite ring intrusion, with a central pipe of syenites surrounded by concentric gabbroic and granite layers, which cannot resolved in detail with travel time tomography. The aim of this work is to resolve these thin (tens to hundreds of m) gabbro and granite structures using waveform tomography. First, a theoretical velocity model was created based on geological interpretations of the present sub-volcanic exposure of the ring complex. A synthetic data set with 22500 traces was then generated based on the source and receiver geometry of the SIMBA project. Travel time picking and inversion provided the starting model for the waveform tomography in the frequency domain. For the inversion several parameters and the influence of noise were tested to choose the optimal parameters. With nearly the same parameters the inversion of the real data has been carried out to resolve more details of the internal structure of the complex. Furthermore we tested the influence of different approaches to consider crooked line geometry in the straight line inversion. The models derived by waveform tomography reveal detailed shallow features within the Messum Complex which are not resolved by travel time tomography.
[Show abstract][Hide abstract] ABSTRACT: Seismic waveforms contain the information not only about velocity, but also various parameters, such as attenuation (or Q factor), density, and anisotropic parameters. The Q values can provide the useful information about rheology, pore fluid, and fluid flow information. Attenuation has conventionally been imaged from the first arrival waveforms (amplitudes and/or spectra) using with ray theoretical methods. Although these methods are simple and fast, the method does not use the full record of observed waves, and the resolution is limited. By using a greater portion of the waveforms, frequency domain full waveform inversion has resulted in the improved velocity and attenuation images (Hicks and Pratt, 2001). Challenges remain regarding attenuation imaging, including the estimation of source signatures, source and receiver coupling effects, geometrical spreading, etc. Our previous work with synthetic data showed that it is critical to obtain accurate velocity images prior to attenuation imaging, in order to enhance parameter resolution (Kamei and Pratt, 2008). Inaccurate velocity structures lead to instable attenuation imaging. However the work focused on parameter separation between attenuation and velocity, and the results were limited to noise-free synthetic data. In this study we first investigate the tradeoff between the amplitudes of estimated source signatures, and attenuation models. There is inverse proportionality between Q values and source amplitudes.. Apparently waveform inversion provides relative attenuation images, and some other information is required to obtain absolute Q values. We also compare two objective function; the standard and the logarithmic L2 objective function proposed by Shin and Min (2006). The logarithmic L2 objective function enabled to recover higher wavenumber components of the attenuation model, than the standar L2 objective function, since the logarithmic function enhanced the contribution from small-valued data. Then, the waveform inversion technique is applied to the synthetic data contaminated with Gaussian noise. The attenuation imaging is severely affected by inadequate amplitude information at low and middle frequencies, although the standard L2 function showed more robustness. The noise test revealed that it is essential to use a group of frequencies to stabilize the inversion.
[Show abstract][Hide abstract] ABSTRACT: Waveform Tomography, when implemented in the frequency-domain, potentially yields images of the intrinsic attenuation from seismic waveform data (Pratt et al., 1998). The attenuation (or its inverse, the seismic Q value) is strongly related to rheology, fluid flow, pore fluid content and fractures. Since phase and amplitude anomalies are also caused by velocity structure (due to geometrical and scattering effects), it is critical to assess inversion strategies as to their ability to resolve these effects. We compared two sets of strategies: first, velocity and attenuation models were updated jointly at each iteration ("simultaneous inversio"). In a second test, ("sequential inversion"), a velocity model alone was first inverted, followed by simultaneous inversion. While the predicted waveforms from both strategies agreed with the observed data, only the sequential inversion strategy imaged attenuation structure well in the presence of small-scale velocity heterogeneities. This highlights the strong dependence of attenuation imaging on the quality of the velocity model. We then tested the approach using a shallow seismic dataset collected on an engineered clay embankment at Seven Sisters Falls, Manitoba. The test embankment contained three targets composed of granitic rip- rap; these corresponded to higher velocities and higher scattering potential than the surrounding in-situ clays. Waveform Tomography was applied to long-offset refraction data collected over the embankment using 70 weight-drop shots and 48 geophones. The starting model was developed with traveltime tomography on the hand-picked first arrivals. The data were inverted between 20 Hz and 150 Hz, corresponding to wavelengths between approximately 100 m and 13 m. We were able to resolve sub- wavelength targets on the order of 3-4 m in cross-section using the final velocity model. Interpretation of the seismic-Q images along with the velocity allowed us to define the target positions. In order to assess the quality of our model fit, we compared synthetic results with the real data. A very good fit between model and observed data was achieved, indicating the reliability of the results.
[Show abstract][Hide abstract] ABSTRACT: Crosshole seismic experiments were conducted to study the in-situ properties of gas hydrate bearing sediments (GHBS) in the Mackenzie Delta (NW Canada). Seismic tomography provided images of P velocity, anisotropy, and attenuation. Self-organizing maps (SOM) are powerful neural network techniques to classify and interpret multi-attribute data sets. The coincident tomographic images are translated to a set of data vectors in order to train a Kohonen layer. The total gradient of the model vectors is determined for the trained SOM and a watershed segmentation algorithm is used to visualize and map the lithological clusters with well-defined seismic signatures. Application to the Mallik data reveals four major litho-types: (1) GHBS, (2) sands, (3) shale/coal interlayering, and (4) silt. The signature of seismic P wave characteristics distinguished for the GHBS (high velocities, strong anisotropy and attenuation) is new and can be used for new exploration strategies to map and quantify gas hydrates.
Geophysical Research Letters 01/2008; 35(19). · 3.98 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Seismic inversion is a multiparameter problem: the observed waveforms contain information not only on velocity structure, but also on various other parameters, including attenuation and density (and the possibility of anisotropy). Among these parameters, the attenuation (or its inverse, the seismic Q value) is strongly related to useful geological variables such as rheology, fluid flow, pore fluid content and fractures. In this work, we investigate methodologies for obtaining velocity and attenuation images simultaneously. In contrast to ray-based inversions of first arrival times and/or amplitudes, Full Waveform Inversion incorporates scattered, refracted and reflected waves, and consequently improves image resolution and accuracy. In frequency domain implementations, instead of inverting Q values directly, complex valued velocities are estimated using steepest descent algorithms. The real and imaginary parts of the velocity fields, (vr, vi), have differing sensitivities, making the simultaneous inversion of (vr, vi) with steepest descent methods difficult. Although Newton methods may enable a true simultaneous inversion, these are computationally expensive, and the instability of the Hessian matrix remains problematic. A possible solution to the simultaneous inverse problem is the subspace method (a Newton method in a chosen subspace), in which we search for an optimal update direction in a 2D subspace spanned by each of the two model type steepest descent vectors: P-wave velocity and Q values. The proposed 2D subspace method requires only one additional forward modelling over the steepest descent method, and inverting the 2 × 2 projected Hessian is trivial. The off-diagonal terms of the projected Hessian matrix indicate the coupling of data sensitivities to the two model parameter types. In this study, we implemented the subspace method into frequency-domain full waveform inversion, and compared the results to the standard steepest descent method. Because the model parameterization may influence robustness and resolution of the inversion procedure, we also examined several model parameterizations, including (vr, vi), (vr, Q), and their respective inverses.