Full waveform inversion
improves subsurface models
Full waveform inversion is providing the E&P industry with ever-more detailed images and models of the subsurface that can make exploration, develop- ment, and production more effcient
and reduce drilling risk.
One of oil and gas exploration’s greatest
challenges is to image reservoirs with suffcient accuracy to pinpoint oil and gas deposits
and to reduce drilling risk. Surface seismic
surveys measure the two-way travel time of
acoustic waves to subsurface refectors. To
convert travel time to depth requires knowledge of the velocity of sound, and its travel
path, through all the layers above and around
a particular refector. While converting time-domain information into a reliable depth model of the Earth remains an inexact science,
advances in data processing technology are
delivering continuous improvement.
Technological advances have delivered success in the exploration of complex structures
such as deepwater subsalt reservoirs in the
Gulf of Mexico, South America, and West Africa. However, despite signifcant progress in
recent years, there remain many challenges to
earth model building and imaging in the most
complex geological environments. Increased
complexity in imaging challenges, combined
with ever-increasing computing capacity and
cost-effciency, has driven a change from traditional ray-based methods to waveform methods for model building and imaging.
The seismic industry has moved to using
two-way wave equation imaging algorithms
commonly known as reverse-time migration
(RTM), especially in areas of complex geology. It has become increasingly obvious that
to obtain full benefts from these advanced
imaging algorithms requires development
of an accurate velocity model. Inversion is
a mathematical process by which an earth
model is generated that is consistent with
the measured surface seismic data and other
available controls such as well log and vertical seismic profle (VSP) data. The model includes the depth and thickness of subsurface
layers and their acoustic velocities, optionally
including azimuthal anisotropy.
Full waveform inversion (FWI) has long
been considered the next logical step in deriving detailed velocity models. The availability of long offset datasets with high signal-to-noise ratio and broad bandwidth, particularly
including low frequencies, now allows FWI to
FWI methodology General workflow deployed on FWI projects.
Starting velocity model
Updated velocity model
Velocity Gradient & ∆V
build high-defnition velocity models that can
enable more detailed imaging of reservoirs.
An accurate earth model is essential to any
successful depth imaging project. FWI is an
advanced velocity model building process
that uses the full two-way wave equation and
overcomes the limitations of existing methods that use a ray-tracing approach to distribute velocity errors within the model.
Full waveform inversion
FWI, based on the fnite-difference approach, was introduced in the time-space domain around 1984. Inversion can also be implemented in the frequency domain. Within
the last fve years, 3D FWI has been applied
to several datasets from both offshore and
onshore. These projects demonstrate that
FWI can be used for velocity updates if the
acquired data have enough low frequencies
and long offsets. In particular, the shallow
part of the model can be enhanced signifcantly with FWI, which can result in an improved depth image at reservoir level(s).
One diffculty with FWI is convergence to
the local minima. To avoid converging to a local minima requires a starting velocity model
that bridges the gap between the low frequencies and long offsets acquired in the data.
Generally the starting model is a smoothed
version of a tomography-derived legacy model
calibrated with well logs, VSPs, gravity, mag-netotelluric, and other available measurements. Such tomography-derived models are
not immune from convergence to local minima, hence the need to smooth such models.
Successful results from FWI frst require
a feasibility study to ensure that an optimum
combination of acquisition parameters,
starting velocity model, and data with appropriate preprocessing are available. Modern
acquisition designs that deliver low ( 2-3 Hz)
frequencies, long ( 12-20 km/7. 45-12. 47 mi)
offsets, and data from a full range of source-receiver azimuths can relax the requirements of the starting velocity model. Starting with a simple smooth velocity model
without local minima is desirable; however,
older acquisition designs lacking in low frequencies, long offsets, and azimuths require
adding detail to the starting model, usually
with several iterations of tomography.
Starting data ideally are minimally processed, typically with noise attenuation only,
as it is easier to match modeled data with
the acquired data if the original waveform of
the acquired data is preserved. Early arrival
data, rich in refractions and diving wave energy, should be preserved to allow for the
low-frequency update of the velocity model.
Care must be taken to not mute out these
early arrivals – not only for FWI but also for
imaging with R TM.
A 3D time-domain TTI anisotropic acoustic
version of full waveform inversion has been
implemented using the two-way wave equation with an elastic correction factor to model
seismic data using an initial best guess of the
earth model. This can be a depth model from
a previous processing effort and/or calibrated
to well logs and any other seismic or non-seis-mic measurements. Seismic waveform inver-