IEEE Signal Processing - March 2018 - 133

the conventional seismic processing technologies, we provide
possess, are valuable for geohazard avoidance and better reseran introduction to the FWI theory, the fundamental mechavoir characterization.
nism behind the cycle-skipping phenomenon, the theoretical
FWI takes into account the full waveform information of
and practical aspects of various algorithms, workflows, and
seismic data to reconstruct an earth model including not only
strategies developed to solve this issue, the essence of the
the geologic structures but also the geophysical properties.
underlying challenges and difficulties we are facing, and the
Properly taking care of various frequencies, offsets, azimuths,
implications for future directions of this research topic. This
and other factors of seismic data, FWI is expected to generoverview will serve as an accessible guide to both geophysiate the maps of geophysical properties continuously covering
cists and signal processing engineers to explore the potential
a broadband wavenumber spectrum [4]. Due to the extremely
opportunities in the FWI research for subsurface exploration.
large number of unknowns, most FWI methods employ gradient-based local optimization algorithms [5]-[9] that may converge to a local minimum when the inversion starts at high
Conventional approach and FWI
frequencies or the starting velocity model is not sufficiently
In a conventional tomography-migration-AVA workflow, the
close to the true model. In current seismic data acquisition
first step is to build a smooth velocity model honoring the
environments, reliable low-frequency components below 5 Hz
kinematic information only, as shown in Figure 1(a), which
do not practically exist in typical seismic data sets [10]. Thereis an exceptionally good model for the purpose of delivering
fore, the local minimum problem, commonthe concept. According to the wavenumly referred to as the cycle-skipping issue,
ber spectra, the tomography velocity model
From a signal processing
remains as one of the biggest challenges
substantially deviates from the true velocity
perspective, one of the
today to fully utilize the FWI capabilities.
model [Figure 1(c)] in terms of spatial resoeffective approaches to the lution, because the tomography resolution
In recent years, many research efforts have
cycle-skipping mitigation
been devoted to overcoming this challenge,
is approximately determined by the Fresnel
and some of the achievements have greatly
zone radius [13], [14], which is dependent
without acquiring lowbenefited from the advances in signal profrequency data is to retrieve not only on the wavelength, but also on the
cessing. From a signal processing perspecpropagation length. In the second step, with
the low wavenumber
tive, one of the effective approaches to the
the kinematically correct velocity model
information buried in the
cycle-skipping mitigation without acquirgenerated in the first step, the recorded
high-frequency data.
ing low-frequency data is to retrieve the
seismic data are tracked backward from the
low wavenumber information buried in the
receivers to the subsurface domain through
high-frequency data. In this context, the key component of
a migration engine to accurately position the reflectors and
FWI research on cycle-skipping suppression is how to make
the scattering points in the spatial domain, providing valuable
low wavenumber information visible through various signal
subsurface structural information at high resolution. Combinprocessing techniques.
ing the tomography velocity and the migration image, a broad
There are some surveys in the literature that give excellent
wavenumber spectrum may be recovered, but a significant
reviews of the FWI theory, algorithms, applications, and the
spectrum gap always exists, as shown in Figure 1(a) and (b).
cycle-skipping phenomenon [11], [12]. After a brief review of
On the other hand, FWI attempts to fill this gap by delivering

(m)
1,250

3,750

(m)
6,250

8,750

1,250

3,750

(m)
6,250

8,750

1,250

3,750

6,250

8,750

(m)

1,250
2,500
3,750

k
(a)

k
(b)

k
(c)

Figure 1. (a) The tomography velocity model and its wavenumber spectrum. (b) A migration image and its wavenumber spectrum. (c)The true velocity
model and its wavenumber spectrum.
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March 2018

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133
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