Waveform inversion using a logarithmic wavefield

Cited 170 time in Web of Science Cited 289 time in Scopus

Shin, Changsoo; Min, Dong-Joo

Issue Date
Society of Exploration Geophysicists (SEG)
Geophysics, 71, R31-R42
Waveform inversionlogarithmic wavefieldWavefiledInversion
Although waveform inversion has been studied extensively
since its beginning 20 years ago, applications to seismic field
data have been limited, and most of those applications have
been for global-seismology- or engineering-seismology-scale
problems, not for exploration-scale data. As an alternative to
classical waveform inversion, we propose the use of a new, objective
function constructed by taking the logarithm of wavefields,
allowing consideration of three types of objective function,
namely, amplitude only, phase only, or both. In our waveform
inversion, we estimate the source signature as well as the
velocity structure by including functions of amplitudes and
phases of the source signature in the objective function. We
compute the steepest-descent directions by using a matrix formalism
derived from a frequency-domain, finite-element/finite-
difference modeling technique. Our numerical algorithms
are similar to those of reverse-time migration and waveform inversion
based on the adjoint state of the wave equation. In order
to demonstrate the practical applicability of our algorithm,
we use a synthetic data set from the Marmousi model and seismic
data collected from the Korean continental shelf. For noisefree
synthetic data, the velocity structure produced by our inversion
algorithm is closer to the true velocity structure than
that obtained with conventional waveform inversion. When
random noise is added, the inverted velocity model is also close
to the true Marmousi model, but when frequencies below 5 Hz
are removed from the data, the velocity structure is not as good
as those for the noise-free and noisy data. For field data, we
compare the time-domain synthetic seismograms generated for
the velocity model inverted by our algorithm with real seismograms
and find that the results show that our inversion algorithm
reveals short-period features of the subsurface. Although
we use wrapped phases in our examples, we still obtain reasonable
results. We expect that if we were to use correctly unwrapped
phases in the inversion algorithm, we would obtain
better results.
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