Joint Designature of data with a diversity of Sources
Shuki Ronen*, Thibaut Allemand, Stéphane Laroche, and Philippe Herrmann, (Sercel); Hamish Macintyre,
Maksym Kryvohuz, and Guido Baetan (Shell)
Summary
Designature is deterministic deconvolution and is often
called the art of dividing by zero. The zeros may be not only
outside the spectral band but also in troughs and notches
within the band. Pneumatic sources such as airguns, have
deep bubble peaks and troughs. Arrays have shallower
troughs. Conventionally, arrays are formed in acquisition.
In this paper we present a method to form arrays in
processing. The advantage of forming arrays in processing
is that we want sources with different voices to have their
practical shot intervals and optimal depths. We call forming
arrays in processing Joint Designature. This idea is
demonstrated on real data using two different sources.
Introduction
The need for low frequency seismic data is well recognized
(Ten Kroode et al, 2013). The requirement is coming from
imaging targets under complex overburden such as salt or
basalt (Ziolkowski et al, 2003), from the ability of low
frequency signal to mitigate the challenge of local minima in
Full Waveform Inversion (FWI), for deep target Imaging
and long offsets acquisitions, for improved resolution by
reducing the interference of side lobes and from the need for
low frequencies for building blocky reservoir models.
To acquire low frequency signal, we need sources that
produce and receivers sensitive to low frequency waves.
While great progress has been made with receivers such as
ocean bottom nodes (OBN), micro-electromechanical
systems (MEMS), solid streamers, slanted streamers, and
multi-sensor streamers, low frequency sources are only now
becoming available.
One such low frequency source is the Tuned Pulse Source
(Chelminski et al, 2020; Chelminski et al, 2021; Tellier et al,
2021). The TPS was tested in a recent survey together with
Airguns. Near Field Hydrophones recorded all shots. NFH
provide accurate designature by better characterization of
individual shots and accounting directionality effects of
source signatures. Technically speaking, both of these
effects can be accounted for in the joint designature, thus
making NFH data for joint designature as useful as for
conventional designature. In this work, however, for the
purpose of illustration, we consider a simpler case of
constant 1D wavelets for both sources, which were yet
inferred from the NFH data.
Processing the data from this survey with a diversity of
sources, provides us with both challenges and opportunities.
One opportunity is testing a joint designature method that
takes advantage of the source diversity.
Conventional designature has one input data, one input
signature, and one output data. In this paper we present joint
designature with two input data, two input signatures, and
one output data.
The Method of Joint Designature
Designature can be done either in the time or in the
frequency domain. In the frequency domain it may be
defined,
() =
()̅()
|()|
ଶ
+
where r is the (offset dependent-) reflectivity, d is the data,
s is the source signature, and is the pre-whitening factor to
avoid division by 0. is typically a constant value, or
frequency dependent with () = |()|
ଶ
: n is the
average ambient + instrument noise and a constant factor.
The upper bare (
-
) for complex conjugate is a reminder that
we are in the frequency domain. If we have two sources,
then joint designature is,
() =
ଵ
()̅
ଵ
() +
ଶ
()̅
ଶ
()
|
ଵ
()|
ଶ
+ |
ଶ
()|
ଶ
+
with two input data;
ଵ
and
ଶ
, and two source signatures
ଵ
and
ଶ
. The scheme can, of course, be extended to more than
any number of sources.
For the above method to work we assume that the source
signatures
ଵ,ଶ
are stable and that we know them exactly, that
the data
ଵ,ଶ
are deblended and interpolated to have the
same locations, and if sources are at different depths, then
the data are deghosted before or during joint designature.
With joint designature, the denominator has the sum
|
1
()|
ଶ
+ |
2
()|
ଶ
. The source diversity dictates that the
zeros in |
1
()| are at different frequencies to the zeros in
|
2
()|, and as a result the problem of divide-by-zero is
diminished, and the choice of the pre-whitening factor
becomes less important.
A similar expression can be derived in the image domain
with a joint designature imaging between
ଵ,ଶ
the time
10.1190/image2022-3746507.1
Page 31
Second International Meeting for Applied Geoscience & Energy
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DOI:10.1190/image2022-3746507.1