Waveform tomography in 2.5-D to appropriately handle 3-D geometry

Abstract

In order to improve the tractability of waveform tomography when applied
to field data acquired along a crooked-line, we implement 2.5-D forward
modeling and inversion. Waveform tomography combines conventional
velocity-model building (i.e. tomography) with full-waveform inversion
to reconstruct an image of subsurface acoustic velocity. For reasons of
computational efficiency, it is desirable to use 2-D full-waveform
inversion when processing data acquired with 2-D seismic survey
geometry. However, crooked-line acquisition results in a cross-line
component of the source-receiver offset that cannot be accounted for by
2-D forward modeling. If the cross-line geometry components are
significant, full-waveform inversion may be intractable. To address the
latter difficulty, we first apply 3-D traveltime tomography to generate
a 2-D cross-sectional initial velocity model by taking a representative
average slice through the 3-D model. Then this initial model from
traveltime inversion is iteratively updated by 2.5-D full-waveform
inversion using a frequency-domain viscoacoustic implementation. The
2.5-D method generates waveform data by combining the solutions of
multiple 2-D wave equation components. Each wavefield represents the
solution of a modified wave equation in which the cross-line wavenumber
takes a value between zero and ~ω/c. The results are combined by
inverse Fourier transform in the cross-line coordinate. This produces a
synthetic wavefield that is a solution to the 3-D viscoacoustic wave
equation in a 2-D velocity model. Consequently, the 2.5-D synthetic
wavefield better approximates seismic field data (including crooked-line
geometry), when compared to a 2-D synthetic result. Cross-line
source-receiver offsets can be accounted for by reconstructing the
wavefield out-of-plane with respect to the source. The amplitude and
phase of the wavefield are consistent with a 3-D solution in a model
that is homogeneous in one direction. The 2-D model is ideally aligned
along the seismic survey line to minimize cross-line offsets, since this
method does not incorporate cross-line model variation. A synthetic
result highlights the benefits of this method of full-waveform
inversion. A real-data comparison is presented to contrast this result
with an approach using a static correction for geometry followed by the
more usual 2-D full-waveform inversion. When 3-D geometry is present on
the seismic acquisition line, this newly developed 2.5-D method yields
improved results over 2-D full-waveform inversion. In addition, the
2.5-D method is substantially less expensive computationally than full
3-D full-waveform inversion applied to 2-D crooked-line acquisition.

Full text

Waveform tomography of field vibroseis data using an approximate
2D geometry leads to improved velocity models
Brendan R. Smithyman1and Ronald M. Clowes1
ABSTRACT
Waveform tomography, a combination of traveltime tomogra-
phy (or inversion) and waveform inversion, is applied to vibro-
seis first-arrival data to generate an interpretable model of
P-wave velocity for a site in the Nechako Basin, south-central
British Columbia, Canada. We use constrained 3D traveltime
inversion followed by 2D full-waveform inversion to process
long-offset (14.4 km) first-arrival refraction waveforms, result-
ing in a velocity model of significantly higher detail than a con-
ventional refraction-statics model generated for a processing
workflow. The crooked-line acquisition of the data set makes
2D full-waveform inversion difficult. Thus, a procedure that im-
proves the tractability of waveform tomography processing of
vibroseis data recorded on crooked roads is developed to gen-
erate a near-surface (< 2km) velocity model for the study area.
The data waveforms are first static corrected using a time shift
determined by 3D raytracing, which accounts for the crossline
offsets produced by the crooked-line acquisition. The velocity
model generated from waveform tomography exhibits substan-
tial improvement when compared with a conventional refrac-
tion-statics model. It also shows improved resolution of sharp
discontinuities and low-velocity regions when compared to the
model from traveltime tomography alone, especially in regions
where the geometry errors are moderate. Interpretation of the
near-surface velocity model indicates possible subbasins in
the Nechako Basin and delineates the Eocene volcanic rocks
of the study area. This approach limits the ability of the full-
waveform inversion to fit some propagation modes; however,
the tractability of the inversion in the near-surface region is im-
proved. This new development is especially useful in studies
that do not warrant 3D seismic acquisition and processing.
INTRODUCTION
Vibroseis multichannel seismic acquisition is typically designed
to produce high-quality near-offset reflection-data with the goal of
imaging reflectors at depth. The interrogation of the shallowest
layers of a study region is a secondary goal in many seismic sur-
veys. The application of refraction-statics, which typically involve a
form of traveltime inversion, is normally used to account for near-
surface heterogeneities when processing later arrivals. To a lesser
extent, it is sometimes used to produce velocity models that can
be useful for near-surface geological interpretation. Due to the dif-
ficulty of picking first-arrival traveltimes at longer offsets, the full
lateral extent of the geophone spread is not always used. In contrast,
our traveltime and full-waveform inversion efforts are designed pri-
marily to produce high-quality velocity models from vibroseis first-
arrival data to aid in near-surface interpretation. To date, many
successful applications of waveform tomography have been
shown in synthetic data studies (e.g., Brenders and Pratt, 2007;
Ben-Hadj-Ali et al., 2008;Krebs et al., 2009;Shah et al., 2010)
and field projects in crosshole (Pratt and Goulty, 1991;Pratt
et al., 2005) and offshore settings (Dessa et al., 2004;Kamei
and Pratt, 2010). Onshore applications have been shown using ex-
plosive sources (e.g., Operto et al., 2004;Malinowski and Operto,
2008;Jaiswal et al., 2009), but typically include low-frequency in-
formation that is not available in conventional vibroseis acquisition.
An excellent overview is presented by Virieux and Operto (2009).
To the best of our knowledge, results from waveform tomography
processing of band-limited on-shore vibroseis data acquired on a
crooked-line have not previously been published.
In this study, we use the extended offset data available from the
2008 Geoscience BC Nechako Basin vibroseis seismic survey
(Calvert et al., 2009) to demonstrate the efficacy of our approach.
We develop a method that accounts for several of the limiting
Manuscript received by the Editor 21 February 2011; revised manuscript received 23 August 2011; published online 3 February 2012.
1University of British Columbia, Department of Earth and Ocean Sciences, Vancouver, Canada. E-mail: bsmithyman@eos.ubc.ca; rclowes@eos.ubc.ca.
© 2012 Society of Exploration Geophysicists. All rights reserved.
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GEOPHYSICS. VOL. 77, NO. 1 (JANUARY-FEBRUARY 2012); P. R33–R43, 7 FIGS.
10.1190/GEO2011-0076.1
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factors that might otherwise make waveform tomography of vibro-
seis data intractable. The use of data from offsets up to 14.4 km in
the traveltime inversion process provides velocity models with
depths of investigation on the order of 2–3 km (dependent on local
geology). Full-waveform inversion improves on the resolution and
fidelity of the traveltime inversion velocity models by fitting the
waveform amplitude and phase.
The waveform tomography algorithm that we applied is based
on a 2D implementation (Pratt, 1999) that could be used effectively
with limited computational resources. However, the vibroseis data
were acquired on existing (crooked) roads and were not necessarily
conducive to 2D analyses. The combination of time shifts due to
out-of-plane geometry and data that are band-limited due to the vi-
broseis source provided challenges in taking advantage of the full
14.4 km horizontal offsets of the data. Because of the crooked-line
acquisition geometry used in the Nechako Basin survey, we found it
necessary to carry out geometry corrections to make the waveform
inversion problem tractable for the 2D implementation.
Improved velocity models from our studies (and the methods that
produced them) have relevance in seismic interpretation and proces-
sing workflows for two main reasons: (1) interpretation can provide
valuable information about the near-surface region that is not well
parameterized by reflection methods; and (2) additional near-sur-
face velocity information may be used to improve stacking and mi-
gration results in seismic-reflection workflows. Information from
(1) can be helpful in identifying differing rock types and their re-
levance for further exploration or geological understanding. This is
the example that is used in our study. By carrying out waveform
inversion on first-arrival data, improved resolution may be achieved
in the near-surface, i.e., the shallowest 2–3 km (for 14 km offsets)
that are normally mainly interrogated by refracted waves rather than
reflected ones. Improved velocity models also may enable better
images of the subsurface when prestack depth migration or other
specialized processing procedures are carried out.
TECHNICAL BACKGROUND
We apply a technique known as waveform tomography, in which
high-quality traveltime data are processed by traveltime (tomo-
graphic) inversion (Zelt and Barton, 1998) followed by frequency-
domain, 2D acoustic full-waveform inversion of preconditioned
waveform data (Pratt and Worthington, 1990;Song et al., 1995;
Pratt, 1999;Brenders and Pratt, 2007). This technique takes advan-
tage of the reduced nonlinearity of the traveltime inversion objective
function compared to the objective function found in full-waveform
inversion. Ideally the velocity model resulting from traveltime in-
version is similar to a low-wavenumber model using wave-equation
methods. By careful use of traveltime-inversion techniques, a start-
ing model can be designed that is close to the global minimum of
the eventual solution.
Tarantola (1984) and Mora (1987) discuss full-waveform inver-
sion of acoustic data by time-domain finite differences, whereas
Pratt and Worthington (1990) and Liao and McMechan (1996) use
frequency-domain finite-difference implementations. Vigh and
Starr (2008) discuss some of the benefits of each. The chief advan-
tages to a frequency-domain approach are: (1) improved modeling
and inversion efficiency in 2D through factorization of the
impedance matrix; and (2) access to multiscale inversion benefits
by inverting low frequencies first. Because of its low computational
cost, we employ 2D frequency-domain full-waveform inversion.
The density model is derived from an empirical relation using the
P-wave velocity model (after e.g., Brenders and Pratt, 2007). Other
workers are exploring 3D full-waveform inversion and/or waveform
tomography (Plessix, 2009;Mika et al., 2010;Virieux et al., 2010;
Warner et al., 2010), as well as elastic wave-equation implementa-
tions (Brossier et al., 2009;Kamei and Pratt, 2010;Singh
et al., 2010).
The application of full-waveform inversion requires that the
characteristics of the survey be reproduced accurately when gener-
ating synthetic data (forward modeling). This is the simplest in
cases where geometry and survey characteristics are regular or ea-
sily controlled; examples include synthetic studies, marine acquisi-
tion and crosshole experiments. Land acquisition in general, and
vibroseis acquisition in particular, is more difficult to simulate in
a 2D full-waveform modeling code because topographic features
and land-use concerns often control the placement of source points
and receiver groups. The incorporation of offline (y-direction) sta-
tion offsets is often unavoidable, and the irregular geometries pro-
duce effects in the data that cannot be modeled correctly with a 2D
processing workflow. The exact constraints quantifying how much
deviation from 2D is acceptable will vary greatly depending on the
processing methods used. For 2D full-waveform inversion, the
traveltime errors due to incorrect encoding of offsets should be
much less than one half cycle at the frequency of interest, or equiva-
lently the path-length difference should be much less than one half
wavelength. We have designed a method that makes the problem
tractable when these errors are small. In the absence of computa-
tional limitations, however, the application of a 3D method (Plessix,
2009;Mika et al., 2010;Virieux et al., 2010;Warner et al., 2010)
should always provide superior results.
The characteristics of the vibroseis acquisition provide
advantages and disadvantages for full-waveform inversion. Vibro-
seis commonly allows for high signal-to-noise ratios through high-
fold surveys and stacking of shots. The spatial sampling of vibration
points is also typically much finer than that found with explosive
shots. This is beneficial, especially with horizontally traveling
waves, because the station spacing controls the maximum fre-
quency that can be inverted without spatial aliasing. However, vi-
broseis seismic data are band-limited by the vibroseis sweep. The
low-frequency signals (i.e., below 8 Hz in our case study) that are
very beneficial in full-waveform inversion are typically not included
in the vibroseis source.
METHOD
We develop a method for application of 2D waveform tomogra-
phy to vibroseis data acquired along crooked roads. This approach
incorporates approximations that are not necessary or desirable in a
3D full-waveform inversion workflow. Our goal is not to improve
upon existing 3D workflows; rather, we aim to overcome obstacles
that limit the effectiveness of 2D waveform tomography in cases
that may not justify 3D processing.
We make use of the traveltime inversion package FAST (First-
Arrival Seismic Tomography; Zelt and Barton, 1998) to develop
3D velocity models that are constrained to be smooth in one
dimension. Although we constrain the model updates to be homo-
geneous in one direction, the raytracing methods applied are still
dependent on the eikonal equation in a 3D model; the smoothness
in the y-direction comes from model regularization constraints.
This allows us to develop the initial model in the context of accurate
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source and receiver locations in three dimensions, but to prepare for
later processing to be carried out in 2D. We apply smoothing reg-
ularization to favor horizontal features with an anisotropic Gaussian
filter. We also implement a maximum filter on the 3D model up-
dates in the y-direction (i.e., perpendicular to the 2D plane of inter-
est) to reflect the sensitivity of the eikonal equation to the maximum
local velocity. This reduces the tendency of the traveltime inversion
to develop narrowly supported unrealistic high-velocity features
in 3D and improves the stability and convergence rate. The step
length of each model update is controlled by iteratively reweighted
Tikhonov regularization.
To partially account for the 3D acquisition geometry, we apply a
static correction to the waveform data before beginning full-
waveform inversion. This is derived from the difference between
the synthetic traveltime data using the 3D acquisition geometry
and the desired 2D projected geometry.
Full-waveform inversion is carried out for velocity using the pro-
gram fullwv (Pratt, 1999). We begin inversion by using successive
groups of frequencies from the low-frequency part of the data
domain. The source signature is inverted based on the initial model
(i.e., from traveltime inversion), and updated at several points
through the procedure (a linear best-fit source signature estimate
from the current model). The amplitude versus offset characteristics
of the data are normalized in a log-linear fashion to fit the synthetic
data (heuristically; this partially accounts for irregularities in apply-
ing 2D wave-equation backpropagation to field seismic data). The
velocity model updates are regularized via iterative Tikhonov reg-
ularization to be close to the initial model from traveltime inversion
(i.e., the initial model is also the reference model). During the pro-
cess, the reference model is updated on the basis of the earlier stages
of inversion, before incorporating additional data frequencies. The
velocity model updates are computed by a conjugate gradient algo-
rithm and preconditioned by 2D low-pass filtering in wavenumber,
which limits the perturbation sharpness to the theoretical resolution
supported by the maximum inversion frequency at each stage. The
smoothing filter is mildly anisotropic (2∶1) to favor horizontal
features (appropriate given the acquisition geometry and basin
environment of the test case).
CASE STUDY: NECHAKO BASIN
The motivation and test case for our method comes from the
Nechako Basin seismic exploration work undertaken by CGG
Veritas on behalf of Geoscience BC in July 2008. We carried out
waveform tomography inversion of vibroseis data collected along
line 10 of the Nechako Basin seismic survey; refer to Calvert et al.
(2009) for details on data collection. We used a subset of the full
line comprising 699 source points, each with 960 active receiver
groups arranged in a split-spread configuration (720 to the west,
240 to the east). The source point spacing was 40 m and receiver
group interval was 20 m. The data were correlated vibroseis records
from diversity stacking of four sweeps, each using four vibrators.
The nominal source-group width was 60 m along-line. The vibro-
seis signal was a linear sweep from 8 to 64 Hz over 28 s (i.e.,
2Hz∕s), including 0.9 s tapers. This line is located along the north-
ern boundary of the most prospective (south-eastern) region of the
Nechako Basin, approximately 100 km west of Quesnel, south-
central British Columbia (Figures 1and 2).
Geological background
The Nechako Basin is a sedimentary basin in the Intermontane
Belt of the western Canadian Cordillera (Figure 1). This area has
been characterized as prospective for hydrocarbon development.
Hayes et al. (2003) identified the south-eastern portion of the basin
as having the highest prospectivity.
Figure 2shows the study area in detail, highlighting the geometry
of the seismic acquisition line and the surface geological units.
Figure 3presents a simplified depositional/emplacement history
for the study area. The structural geology of the site is generally
not known sufficiently well to produce an authoritative stratigraphic
section; the closest well control comes from two wells each about
50 km from seismic line 10, which differ greatly. Basaltic andesite
and volcaniclastic rocks of the Hazelton Group (part of the Stikine
Terrane) were deposited in the Early to Middle Jurassic. These were
followed by mixed sedimentary rocks of the Bowser Lake Group,
but these are not observed in our area of study.
Figure 1. Relevant geological terranes in central British Columbia,
showing the location of the study area. The Nechako Basin is sub-
divided into two main regions; this study encompasses the northern
edge of the south-eastern region, roughly at the boundary between
rocks of the Stikine Terrane and those of the basin proper (Massey
et al., 2005).
Waveform tomography of vibroseis data R35
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A variety of terrigenous clastic sequences were deposited in the
Cretaceous, exemplified by the Middle Cretaceous Skeena Group
rocks and the overlying Late Cretaceous sediments of the Sustut
Group. Sedimentary units are seen to be in excess of 2500 m thick
in some parts of the basin (Hannigan et al., 1994), but appear to be
significantly thinner in our study area. Ootsa Lake rocks including
mixed sediments and rhyolite were deposited before and contem-
poraneously with Endako Group mixed volcanic rocks; the volcanic
sequences were likely erupted in conjunction with Eocene exten-
sional tectonics. The Chilcotin Group rocks are flood basalts typi-
cally ~50 m thick (Calvert, 2009) erupted in the Neogene. These are
covered locally by mixed Quaternary sediments that are quite vari-
able over the study area. The prospective units for oil and gas ex-
ploration in the Nechako Basin are Middle Cretaceous clastic
sedimentary rocks, mainly the Skeena Group, that overlie the
Stikine Terrane (Hannigan et al., 1994). They contain anticlinal
structural traps formed by compression through the mid-Jurassic
to mid-Eocene and normal fault traps from subsequent extension.
The overlying Late Cretaceous sedimentary rocks are classified as
nonprospective based on the absence of oil and gas shows, despite
the existence of structures similar to those in the Skeena Group
rocks (Hannigan et al., 1994). They do not outcrop in the region
of our study. The Hazelton Group, part of the Stikine Terrane, out-
crops near the seismic line as shown in Figure 2(Massey et al.,
2005). The near-surface is dominated by Eocene volcanic rocks
of the Ootsa Lake and Endako groups, and by the younger Neogene
Chilcotin basalt. These volcanic units also dominate the near-
surface seismic response. Based on rock-physics results, the Chil-
cotin basalt was originally expected to show a higher bulk P-wave
velocity than the Ootsa Lake and Endako units. However, recent
work by Calvert et al. (2011) indicates that brecciation may cause
the Chilcotin basalt to possess lower P-wave velocities throughout
much of the region. Quaternary deposits of differing types and vary-
ing thicknesses overlie the older rocks (Figures 2and 3). Recent
work by others has increasingly found that the Nechako Basin is
more appropriately thought of as a collection of related subbasins
(J. Riddell, personal communication, 2011).
Traveltime inversion
Velocity models of the shallow subsurface are typically devel-
oped as part of the reflection-seismology workflow to facilitate
common depth point (CDP) stacking and migration; however, these
models are often coarse and of limited use for interpretation. When
applying waveform tomography, it is important to produce detailed
velocity models at the traveltime inversion stage; this, in turn,
requires precise traveltime picks. Without a sufficiently accurate
starting model, waveform inversion methods cannot succeed. We
picked first-arrivals over the full (14.4 km) offset range of 699 shot
gathers; the bandwidth present in the early arriving waveforms was
approximately 8–16 Hz. We picked a particular phase in the band-
limited data, hence the traveltime picking error is likely on the order
of 20–30 ms. The picking error was controlled by the dominant data
frequency in the first-arrivals, which remained relatively consistent
over the offset range of interest. The assigned error for the picks was
chosen to be uniform across the data set; however, low-confidence
picks were manually removed before inversion. Traces with large
traveltime data residuals were excluded from subsequent processing
of the data waveforms. We found that very careful consideration
was necessary due to significant shingling in the first-arrival wave-
forms. This was due in part to the attenuation of high-frequency
Figure 2. Geometry of seismic line 10 in relation to lithology and several other seismic lines from the 2008 Geoscience BC Nechako Basin
vibroseis survey; map area as indicated in Figure 1. The map is projected to UTM coordinates (NAD 27). The surface of the central portion of
line 10 is dominated by the Ootsa Lake group, including rhyolite and other volcanic rocks erupted in the Eocene. Both flanks are overprinted by
the Chilcotin basalt (Massey et al., 2005), characterized by variable observed seismic velocities most likely due to variable vesicularity and
brecciation. To the north, the Hazelton Group volcanic rocks of the Stikine Terrane appear to plunge beneath line 10 toward the south. The 2D
geometry for the model profile used in waveform inversion is shown by the red line. The receiver array for this study spans the model line; the
part covered by the active source array is shown in blue.
R36 Smithyman and Clowes
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parts of the data waveforms and the (nominally) zero-phase source
imposed by the vibroseis correlation.
We initially processed these picks using FAST (Zelt and Barton,
1998) and GLI3D (a well-known commercial package; Hampson
and Russell, 1984). Both codes were able to fit the first-
arrival picks in 3D with an rms traveltime misfit of 20–25 ms.
Because of the need for manual control over the traveltime-
inversion process, we primarily used FAST (an academic code).
To find the smoothest model that fit the traveltime data within the
expected misfit range, the velocity model was regularized by an
anisotropic 3D Gaussian filter at each iteration. The filter was
chosen to enforce smoothness in the crossline direction and to
encourage a smooth model in the 2D plane of interest. A 5∶1
horizontal to vertical smoothing ratio was chosen to reflect the ex-
pected dominance of horizontal geological features and the re-
fracted arrivals used in our procedure. The size of the smoothing
filter was chosen empirically to guide the model toward an rms data
misfit in the target range. Operating in constrained 3D (i.e., 3D geo-
metry and 2D velocity model), FAST was able to fit the first-arrival
data within an rms misfit of 27 ms. Giventhat dominant frequencies
of the first-arrival data were 8–16 Hz, the resulting velocity model
was appropriate as a low-wavenumber starting model for full-
waveform inversion.
Figure 4a shows real and synthetic first-arrival data and residuals
resulting from forward modeling in the constrained 3D FAST
model. The resulting velocity model is shown in Figure 5a. The data
residuals are approximately normally distributed, with an rms
misfit of 27 ms, i.e., comparable to the picking error. The true
3D geometry of the survey cannot be represented correctly in
the 2D full-waveform inversion process. Figure 4b shows synthetic
traveltime data calculated in the 3D geometry (as in Figure 4a) and a
best-fit 2D projected geometry. The corresponding residuals
represent the traveltime error resulting from the 2D geometry
approximation (under the infinite-frequency approximation and
in the velocity model of Figure 5a). The magnitude of these errors
corresponds closely with the locations along the acquisition line in
which the offset error is high (from the 2D projection; compare with
the line geometry visible in Figure 2). We used the traveltime re-
siduals presented in Figure 4b to static correct the data waveforms
before carrying out full-waveform inversion.
Full-waveform inversion
The velocity model in Figure 5a was the input (starting) velocity
model for full-waveform inversion. The goal of the full-waveform
inversion process is to improve on the velocity model provided by
traveltime inversion in two main ways:
•Finer spatial resolution can be expected because of the
migration-like generation of the model updates.
•Ability to resolve low-velocity zones is possible due to the
incorporation of multiple phases and amplitude information.
Figure 4. Traveltime and residual plots are shown for (a) real and
3D synthetic data, and (b) 2D and 3D synthetic data. The horizontal
axis represents source-receiver midpoint along the line for each re-
sidual. The 3D synthetic data (generated in a 2D model) predict the
true data within an rms misfit of approximately 27 ms, and the re-
siduals are well distributed about zero mean. The 2D synthetic data
differ from the 3D synthetic data due to the projection of the geo-
metry onto a plane (striking approximately 106°).
200
145
130
97
65
23
52
45
2.6
GD
GD
GD
GD
Hazelton
group
Skeena
group
Sustut
group
Ootsa lake
group
Endako
group
Chilcotin
group
Q
D
Jurassic Cretaceous Eocene NeogeneP
ε
O
G
0
D
(Ma)
166
Figure 3. Figure 3. A schematic stratigraphic column for the region
of study, outlining the depositional/emplacement sequences
relevant to line 10 of the Nechako Basin seismic survey. D—diorite
plutons; GD—granodiorite plutons; OG—Oligocene; Pε—
Paleocene; Q—Quaternary.
Waveform tomography of vibroseis data R37
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The aforementioned static corrections were effective at improv-
ing the quality of the initial waveform fit. To test this, initial syn-
thetic waveforms (also used in inversion) were calculated using a
delta function. The initial correspondence between the phase of the
real data and synthetic data was high in the eastern portion of line 10
but lower toward the west. This is likely due to the large offline
displacements of sources and receivers (relative to the ideal 2D line)
at the western end. Smaller displacements were well accounted for
by the time-shifting method.
We carried out full-waveform inversion between 8 and 11 Hz,
using an approach in which we iteratively increased the frequency
content of the inversion by fractions of a hertz. The upper end of the
inverted frequency range was limited by the ability to fit the real
data waveforms (discussed below). The initial stages used 8.0,
8.5 and 9.0 Hz frequencies; subsequent stages incorporated data
up to 11 Hz at 0.5 Hz intervals. At early stages, a delta function
source was used to approximate the response of the ideal broadband
vibroseis source. Once frequencies above 9 Hz were incorporated,
the inversion proceeded with a synthetic source signature derived
directly from the data. The resulting updated velocity model is pre-
sented in Figure 5b.
Corrugation testing was carried out to aid in judging the spatial
resolution in different parts of the velocity model. This was per-
formed by multiplicatively perturbing the waveform tomography
velocity model (Figure 5b)byþ∕−5% in an alternating checker-
board pattern. The maximum perturbation was 344 m∕s, and each
cell of the checkerboard was 1000 m wide by 500 m high. Synthetic
data were modeled using the perturbed velocity model. Figure 5d
shows the recovered perturbations after inversion with the model
from Figure 5b. The spatial resolution of the method is finer in
the near-surface where the angular coverage is the greatest and
the propagation velocities are the lowest. The wavepaths are predo-
minantly horizontal at depth, which limits the maximum achievable
horizontal resolution and depth of penetration with inversion of data
from transmitted wave energy. Vertical resolution remains reason-
able at a depth of 1–2 km, but horizontal resolution is most likely
coarser than 1 km. In regions where the acquisition line is straight,
fitting of reflection arrivals is expected to improve the depth of pe-
netration. However, fitting reflections is less valid in parts of the
model where the array contains large crossline offsets and conse-
quently the focusing at depth is less effective.
a)
b)
c)
d)
Figure 5. Velocity models from traveltime inversion (a) and subsequent full-waveform inversion (b). The difference (c) is shown to help
identify features that are changed in the full-waveform inversion. The result of a corrugation testing procedure (d) is provided to help judge
the expected resolution. The waveform data-fit from traveltime inversion was excellent in the eastern portion of the model, leading to very
small perturbations from full-waveform inversion.
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Figure 6shows a comparison of real and synthetic data from two
representative shot gathers in the data set. This acts as a quality
control on the success of the method, and in particular provides
valuable information about which features in the model are robust.
The data were windowed in time for use in the full-waveform-
inversion process, and therefore we are particularly interested in
the data fit within specific regions. Analysis of the frequency con-
tent of the early arrivals suggests that these data may support addi-
tional higher frequencies (up to ∼16 Hz) in some parts of the model
(e.g., the well-characterized region near shot 475). The maximum
supported frequency from the source array spacing is approximately
24 Hz, based upon a dominant near-surface velocity no less than
1500 m∕s. However, the early arriving data have very low ampli-
tudes above 16 Hz, which limits significantly the benefits of addi-
tional high-frequency processing.
The quality of the data fit in the eastern regions of the model was
relatively high from the initial model, resulting in small perturba-
tions, on the order of þ∕−50 m∕s, to the velocity model. However,
much stronger perturbations, which dominate the difference image
in Figure 5c, were produced on the western end of the model. The
numerical resolution of the inversion algorithm in the western por-
tion of the model was lower due to reduced data fold west of the
12 km point on the projected line, which is reflected in Figure 5d.
The high-amplitude model perturbations in the western part of the
line can most likely be traced to problems in the initial data fit from
the traveltime tomography model, which in turn are due to unre-
solved geometry errors. The geometry correction incompletely ac-
counts for approximation errors in the full-waveform inversion
stage, which are significant toward the western end of the line (see
geometry in Figure 2). The static correction improves the full-
waveform inversion fidelity in the very near-surface (less than about
1 km depth) across most of the seismic line, but substantial model
artifacts remain from the seismic traces with the largest crossline
source-receiver offsets. In the shallowest regions, low-velocity
zones are resolved that were not identifiable in the model from
tomography alone. These are highlighted well in Figure 5c —
for example, the small high-velocity anomaly visible at 17 km is
resolved sharply in the waveform tomography model and the region
surrounding it exhibits lower velocity; the square-sided feature at
22 km exhibits sharper edges than in the model from tomography,
with corresponding low-velocity features to either side.
To apply advanced processing techniques using the velocity
model we have created, additional steps would be necessary. Since
the tomographic arrivals we invert interrogate only the shallowest
2–3 km of the site, additional velocity analysis would be necessary
to establish an interval velocity model throughout the depth-range
of interest. An examination of the anisotropy characteristics of the
site would also be necessary if applying the model from waveform
tomography to a problem such as prestack depth migration of
reflected waves. Full-waveform inversion in 2.5D or 3D would pre-
serve the ability to invert reflection-data as well as the tomographic
arrivals (though without necessarily accounting for anisotropy), and
increase the useful depth of investigation of the method; however,
these methods come with additional computational cost and are not
part of the current study.
Interpretation
The velocity models derived through traveltime tomography and
full-waveform inversion can be directly interpreted to assist in
developing a geological model of the region. Because this repre-
sents a location where the structural geology is poorly understood,
we compare our results with those from other workers, who used
different data-processing methodologies and geophysical methods.
The region of highest confidence in our work is the eastern portion
of the line, due to the relatively low line-curvature. Figure 2presents
Shot 225 Shot 475
3
2
1
0
Traveltime (s)
14.4 E 4.8 W0.0
Source-receiver offset (km)
3
2
1
0
Traveltime (s)
14.4 E 4.8 W0.0
Source-receiver offset (km)
3
2
1
0
Traveltime (s)
14.4 E 4.8 W0.0
Source-receiver offset (km)
3
2
1
0
Traveltime (s)
14.4 E 4.8 W0.0
Source-receiver offset (km)
Line noise
Time shift
from geometry
Shallow
reflections
Time shift
difficult to model
Reflections
High amplitude
and velocity
Modeled
accurately Secondary arrivals
reproduced
High-amplitude
first arrival
Time shifted
first arrivals
Synthetic Real
Figure 6. Real (top) and synthetic (bottom) data are shown for two shot gathers; locations shown in Figure 2. Shot 225 (left) is representative of
the poorer data fit seen in the western portion of the model, due primarily to problems in approximating the geometry. Shot 475 (right) is
representative of the high-quality data fit found in the eastern portions of the model. Annotations highlight some of the relevant data features.
Waveform tomography of vibroseis data R39
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a)
b)
c)
Figure 7. (a) The velocity model from Figure 5b is shown annotated with features of interest (described in main text). Color legend is identified by the right-angle arrow. (b) A portion of
the poststack time-migration image overlain with resistivity values (colors), based on resistivity values from magnetotelluric studies; labels (H, J, L) have been inserted (modified from
Calvert et al., 2011). The horizontal and vertical resolution are variable between the two methods. These models share some complementary features, especially with regard to the
identification of subbasins. However, the time stretch present in the result from CGG Veritas processing (Calvert et al, 2011) makes direct comparison of features challenging. Color
legend is identified by the horizontal arrow. (c) Upper: velocity model (upper 5 km only) from prestack depth-migration processing by WesternGeco (2010) for comparison with our
velocity models. This velocity model is shown for completeness, but a direct comparison with the result in (a) is inappropriate, given the different intended uses of the two models. Lower:
Prestack depth-migrated reflectivity image from WesternGeco (2010). Letters are added to facilitate discussion (see text). Dashed lines identify several interfaces interpreted by us from the
velocity and reflectivity images.
R40 Smithyman and Clowes
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the surface geological features and Figure 3provides a simplified
stratigraphic sequence. Figure 5shows the velocity model derived
for interpretive purposes and any subsequent reflection-data repro-
cessing (to be done by others). For interpretation, we refer to labels
in Figure 7; the velocity model in Figure 5b is reproduced in
Figure 7a and 7b. Several of the features in (7b) the time-migration
image are deemphasized by the processing and/or depth conversion;
however, common features can be identified on (7a) the velocity
model from waveform tomography and the PreSDM reflectiv-
ity image.
The presence of the Chilcotin basalt in the eastern portion of the
survey region may be responsible for a local high-velocity anomaly
(A). This corresponds with rock-physics information suggesting
that the Chilcotin basalt is distinguishable by high seismic velocities
relative to the nearby Ootsa Lake and Endako groups. However,
recent work (Hayward and Calvert, 2009;Calvert et al., 2011) has
found that the velocity of the Chilcotin basalt in situ is typically
somewhat lower than that of the nearby Eocene volcanic rocks.
Thus, the high-velocity feature may be due to a different unit. Note
that this is at the far eastern extent of our model, and may not be as
well resolved. Immediately west of this, there is an apparent
increase in the recovered heterogeneity in the near-surface (B). This
is most likely due to volcanic rocks underlying the Quaternary cov-
er; however, the variability in velocity likely occurs at a finer scale
than we are able to distinguish. This feature appears to correlate
well with the distribution of recent surface sediments, extending
for about 10 km over the middle-eastern portion of the line. Alter-
natively, the apparent heterogeneity may be due to near-surface or
coupling effects that are too shallow for our model to resolve.
Seismic high-velocity features at Care interpreted to be due to the
Hazelton Group volcanic and volcaniclastic rocks, which outcrop
immediately north of line 10. This unit most likely plunges south-
ward beneath the Eocene volcanic rocks that dominate the near-
surface. This interpretation corresponds to the knowledge that
the basin is deeper toward the south (Hannigan et al., 1994), but
it does not preclude the possibility that Hazelton Group outcrops
toward the north could be responsible for the high-velocity
response. Because of the presence of this feature, we have not
attempted to interpret subbasin structures in this part of the model.
A deepening of the low-velocity region (∼3000 3500 m∕s)to
approximately 700 m (D) is interpreted as a subbasin. This appears,
from interpretation of velocities, to be infilled by Ootsa Lake rhyo-
lite, suggesting that the formation of the basin structure is at least
Eocene in age. The ambiguity of the velocity information (because
of overlapping velocity ranges in different rock types) makes it dif-
ficult to determine the deeper basin rock types from seismic results
alone. A sharply defined high-velocity feature at Ecould be a
volcanic plug. Another subbasin structure is seen farther west at F.
However, the confidence of the full-waveform inversion is lower in
this region, due to the poorer performance of the 2D geometry
approximation (Figure 2). An 8–10 km wide synformal structure
at Gwas initially interpreted to be an artifact of the ray tracing used
in the initial model but subsequent comparisons with other studies
have modified this view (see below).
Calvert et al. (2011) presented a preliminary interpretation of the
vibroseis seismic-reflection sections collected on behalf of
Geoscience BC (see Calvert et al., 2009; modified in our Figure 7b),
combined with magnetotelluric information (Spratt and Craven,
2010). The time-migrated reflection-data primarily represent deeper
structures than we might expect to see from the first-arrival refrac-
tion data alone, but there is a region of overlap where results of the
two methods can be directly compared. Additionally, interpretations
of rock types from magnetotelluric results complement seismic
interpretations. Calvert et al. (2011) interpret Eocene and younger
extension in the seismic-reflection section through the middle-
western portion of line 10 (∼327kmon the scale of Figure 7).
They identify highly resistive Hazelton Group basement rocks from
magnetotelluric studies in a location that corresponds well with the
high-velocity features identified above (C). Furthermore, a full-
graben structure is interpreted between 16 and 25 km (H), and a
half-graben east of 3 km (J; distances relative to Figure 7). They
find evidence for post-Eocene extension in the Chilcotin basalt near
the surface in the western portion of line 10 (Figure 2), leading to
folding and brecciation. Additionally, recent reinterpretation of
older seismic results (Hayward and Calvert, 2011) indicates strike-
slip faulting perpendicular to the seismic line in question. This may
explain regions of local variability and localized low-velocity zones.
Considering results from Calvert et al. (2011), several additional
features of interest may be identified. We see a reasonable corre-
spondence between the graben structure they interpreted at Hand
a deepening of the bedrock interface in our results (D,F; Figure 7).
The geological unit at depth here is not well constrained, but we
presume the presence of Cretaceous sediments between the younger
volcanic rocks and Stikinia. The implication is that the graben
structure was infilled by Eocene volcanic rocks after or contempora-
neous with Eocene extension. However, we identify a high-velocity
feature between Dand Fthat we assume to bound the two subba-
sins. Additionally, the subbasin we identify from velocity informa-
tion at Dis significantly shallower than the graben structure
identified by Calvert et al. (2011). The feature we interpret at E
is in a region possessing variable resistivity (Figure 7), but it is
not identified in the seismic-reflection interpretation.
Our results show high-velocity near-surface features and hetero-
geneities (compare the near-surface in subbasins Fand D) that are
spatially correlated with the brecciated Chilcotin basalt interpreted
by Calvert et al. (2011). However, the full-waveform inversion
responsible for producing this heterogeneity in the model was
negatively affected by geometry errors in this region, and the exact
placement and extent of the heterogeneity is not well constrained.
Likewise, we see a high-velocity region at Fthat cannot be well
constrained, although the heterogeneity present corresponds to
an interpreted fault from the reflection-seismic and magnetotelluric
work. The high-velocity feature at Kseems to have the same or-
ientation and location as a highly reflective folded package (L)
in the results of Calvert et al. (2011). Resolution and reliability
of our model west of the 10 km point (near K, Figure 7) is very
degraded, due to the omission of back-shots beyond this point; how-
ever, we have included it for comparison with Calvert et al. (2011)
and future work.
Recent prestack depth migration (PreSDM) processing of the
Geoscience BC line 10 data set by WesternGeco (2010) provides
information about reflectivity in a geometry compatible with our
velocity model. Velocity and density models used for PreSDM were
determined by WesternGeco (2010) from joint inversion of magne-
totelluric, gravity and seismic information; the upper part of their
velocity model is reproduced for reference purposes in Figure 7c.
Their near-surface velocity structure is similar to the traveltime
tomography and waveform tomography models in this paper
Waveform tomography of vibroseis data R41
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(Figure 5), but is significantly smoother. Information in the near-
surface was developed primarily from maximum-amplitude travel-
time inversion and gravity data inversion, whereas the deeper model
was constrained mostly by iterated migration velocity analysis and
magnetotelluric data inversion. To date, these results have not been
interpreted by other researchers, and we attempt to form a joint
interpretation alongside our result. It is inappropriate to compare
directly the velocity model from waveform tomography (Figure 7a)
and the velocity model used in migration (Figure 7c, upper), be-
cause the intended applications of these results are very different.
A direct comparison between the resulting migrated image and
our waveform tomography velocity model (Figure 7c, lower and
Figure 7a, respectively) is more appropriate. This comparison
shows strong reflection events at several features we previously
identified.
A region of strong reflectivity is present in the shallow near-
surface at M(Figure 7c) that coincides spatially with a heteroge-
neous region identified at Bin the waveform tomography velocity
result. This is also coincident with the presence of Quaternary cover
on the interpreted surficial geology (overlaid on Figure 7a). High
reflectivity is also visible at the same lateral location in the time-
domain reflectivity section from Calvert et al. (2011), and likely
represents a reflection off of the top boundary of Stikine Terrane
basement rocks of the Hazelton group (i.e., C). Strong reflectivity
is also present at N, which appears to delineate a continuous basin
reflector encompassing the same extent as features Dand Fin
Figure 7a. Little indication is present of a feature corresponding
to the local high-velocity anomaly at E; however, the occurrence
of moderately strong near-surface reflectivity near Ocorresponds
spatially with velocity heterogeneities observed in the waveform
tomography velocity model (Figure 7a). Additionally, a reflection
feature below Oresembles the local shallowing of the velocity inter-
face at Fand may be a feature that is distinguishable from the inter-
face continuing from N. A second subbasin is interpreted at P,
which agrees with a feature seen in our velocity model (G) and
the half-graben (J) interpreted by Calvert et al. (2011); however,
the western extent of this feature is not resolved well. Local high
reflectivity at Qand the presence of a high-velocity anomaly at K
are interpreted as a shallowing of the flanking subbasins. However,
this feature could be due to heterogeneities in the Chilcotin basalt at
surface or a plutonic feature. A deeper reflector (at a depth of
∼3km) is observed at Rand the presence of linear features suggests
that this may be a continuation of the interface interpreted at N. This
may indicate volcanic in-filling of a deeper basin, which would ex-
plain observations of shallower high-velocity features (Figure 7a)
and high conductivity (Figure 7b).
CONCLUSIONS
We present results of waveform tomography applied to multi-
channel seismic data from the Geoscience BC Nechako Basin
seismic survey. To successfully process these data, we tested
several techniques to overcome the limitations of the 2D full-
waveform inversion techniques we applied. Careful initial model
building and static corrections can make this problem tractable.
However, we found that geometry effects that might usually be
ignored in MCS reflection processing can cause significant pro-
blems for full-waveform inversion (especially in the near-surface).
Modeling and inverting data acquired in a 3D geometry using 2D
techniques requires careful and time-intensive correction of the
waveform data, and the assumptions used to make these corrections
affect the result significantly. We built the initial model using 3D
first-arrival traveltime inversion, which enabled static corrections to
be applied to the waveform data; one result is that the ability to
incorporate nontomographic waveform data is hampered. Conse-
quently, this technique is mostly useful for incorporating amplitude
information from waveforms that interrogate a similar subsurface
region to the tomographic arrivals modeled by ray-theory methods.
In general, 3D full-waveform inversion techniques do not suffer
from the geometry approximation errors that limited this workflow,
and are therefore expected to produce a better result. In problems
similar to our test case, in which offline offsets are not large, a
2.5D full-waveform inversion may present the best compromise be-
tween 2D and full 3D methods. This has the benefit of properly
accounting for 3D geometry and geometric spreading effects, but
with much of the simplicity of a 2D approach.
The detailed velocity information available from waveform
tomography processing of seismic data is valuable in making inter-
pretations about features in complex near-surface geology. This is
especially true when rock-physics information is able to constrain
the range of velocities expected for each rock type. However, the
relative difficulty of interpreting velocity information alone means
that joint interpretation along with other geophysical information
(e.g., high-resolution PreSDM images and other physical property
measurements) is necessary to present a complete geological model.
ACKNOWLEDGMENTS
We appreciate the support received from Geoscience BC in
carrying out this research. Thanks also to the Natural Sciences
and Engineering Research Council of Canada (NSERC) for funding
this and ongoing research through a scholarship to BRS from the
Canadian Graduate Scholarships program and a Discovery
Research grant to RMC. We deeply appreciate discussions and tech-
nical support from A. Calvert and his associates at Simon Fraser
University, and R. G. Pratt’s group at the University of Western
Ontario.
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