Annual Report 2008.pdf - SAMSI

The extraordinary challenge that the oil industry must face for hydrocarbon exploration requires
the development of leading edge technologies to reconstitute the three-dimensional structure of
the Earth. The use of seismic reflections is one of these essential and strategic methods. The
industry has seen a fantastic leap in the ability to process seismic data and to build an
increasingly accurate image of the Earth’s structure. The pre-stack depth migration technique
(PSDM) is currently the most common method employed for seismic depth imaging. PSDM
methods fall into one of two families, depending on how the solution to the wave equation is
approximated: the asymptotic (infinite frequency) approximation leads to what is known as the
Kirchhoff implementation; finite-frequency techniques are known as Wave Equation methods.
Wave equation migration is a rapidly growing tool for complex structure imaging Compared
with the Kirchhoff migration method the wave-equation migration methods can often produce
more accurate images provided that the velocity field is well defined. Most widely-used wave
equation methods are based on solving the one-way acoustic wave equation. There are many
different methods to numerically solve the one-way wave equation. These methods can be
grouped into three classes: Fourier methods solved in the wave number domain; finite difference
methods (FD) and mixed methods that are a linear combination of spectral and finite-difference
methods. One Way wave Equation Migration can be formulated into two separate methods:
Sinking survey or Double Square (DSR) PSDM and Shot Profile PSDM (SP). The first is
generally written in the mid-point offset domain, the second in the shot domain. Accurate wideangle
extrapolation is essential for prestack depth migration because at least one of the paths
connecting the imaging point to the source or receiver is likely to be at a wide angle, especially
when data are acquired with long offsets.
In TOTAL E&P we have implemented both Common Azimuth Migration (CAM based on
common azimuth approximation of the full DSR) and Shot Profile Migration. Compared to the
reverse time Migration (RTM) , One Way implementation are very fast and very well design for
processing very large surface. But they can have some limitation when imaging very steep dip
reflector or in presence of turning waves.
In this paper we show that reformulating the DSR (CAM) in source-receiver domain and using
optimized Fourier Finite Difference (FFD) of the wide angle extrapolation term of the one Way
propagator both in CAM and SP implementation can improve the final migrated image.
Margaret Cheney
Rensselaer Polytechnic Institute
cheney@rpi.edu
“Waveform Design for Radar Detection and Imaging”
This talk discusses the question of what radar waveforms are best for forming images. A number
of different formulations of the question are considered. One formulation leads to a close
connection with iterative time-reversal algorithms; another formulation involves a statistical
treatment of imaging.
Josselin Garnier
Universite de Paris VI