noise suppression using preconditioned least-squares...
TRANSCRIPT
Noise suppression using preconditioned least-squares prestack time migration: Application to the Mississippian Limestone Shiguang Guo*, Bo Zhang, and Kurt J. Marfurt, University of Oklahoma; Alejandro Cabrales-Vargas, Pemex Exploración y Producción
Summary
Conventional Kirchhoff migration often suffers from artifacts such as aliasing and acquisition footprint, which come from sub-optimal seismic acquisition. The footprint can masks faults and fractures, while aliased noise can focus into false coherent events which affect interpretation and contaminate AVO, AVAz and elastic inversion. Preconditioned least-squares migration minimizes these artifacts.
We can implement least-squares migration by minimizing the difference between the original data and the modeled demigrated data using an iterative conjugate gradient scheme. Unpreconditioned least-squares migration better estimates the subsurface amplitude, but does not suppress aliasing. In this paper, we precondition the results by applying a structure-oriented prestack LUM filter to each common offset and common azimuth gather at each iteration. The preconditioned algorithm suppresses aliasing of both signal and noise, and improves the convergence rate.
We apply the new preconditioned least-squares migration to a survey acquired over a new resource play in the Mid-Continent, USA. Acquisition footprint in shallow targets is attenuated and the signal-to-noise ratio is enhanced. To demonstrate the impact on interpretation, we generate a suite of seismic attributes to image the Mississippian limestone, and show that karst-enhanced fractures in the Mississippian limestone can be better illuminated.
Introduction
Conventional Kirchhoff migration can be regarded as the adjoint of the seismic forward modeling operator (Claerbout, 1992). Chavent and Plessix (1996) used standard migration as the zeroth iteration, and then used a conjugate gradient scheme to compute the Hessian matrix. They then used a least-squares formulation to obtain an optimized image. Schuster (1993) added constraints to the objective function. Following Nemeth (1996), he used least-squares migration to overcome uncompensated migration artifacts due to incomplete data, which can give rise to acquisition footprint.
Least-squares migration may require many iterations to reach convergence, consuming significant computer resources. For this reason, significant effort has focused on
preconditioning the input data to decrease the number of iterations. Wei and Schuster (2009) and Aoki and Schuster (2009) preconditioned the data by using a deblurring filter, thereby reducing the number of iterations needed. Wang and Sacchi (2009) evaluated running average and prediction filter constraints to improve the convergence rate of a 2D least-squares migration algorithm. Cabrales Vargas (2011) used mean and median filters as constraints in 3D preconditioned least-squares migration in his master thesis.
Post-stacked structure-oriented filtering is commonly used in conditioning stacked volumes after migration to facilitate interpretation (Fehmers and Höecker, 2003). Luo et al. (2002) extended Kuwahara et al. (1976) algorithm to 3D seismic data as an alternative edge-preserving smoothing algorithm. Marfurt (2008) proposed a modification of Luo et al.’s (2002) technique. First, he used coherence rather than the standard deviation to choose the most homogeneous window. Then, instead of using the mean, median or the α-trimmed mean, he used a principal component (or Karhunen-Loeve) filter to that more fully uses trends in the analysis window to replace the amplitude at the analysis point. Corrao et al. (2011) showed how an LUM-based structure-oriented filter can reject outliers, yet better retain the original character of the seismic data. Kwiatkowski and Marfurt (2011) showed how such filters can be applied to prestack time-migrated common-offset-azimuth gathers. To suppress aliasing within the conjugate gradient PLSM algorithm, we apply LUM-based structure-oriented filters to the common-offset-azimuth gathers, which reduces the number of iterations needed by PLSM.
In this paper, we begin our discussion by examining the role of Kirchhoff migration as the adjoint of the seismic modeling operator and demigration as the seismic modeling operator in a PLSM algorithm. Next, we will introduce the mathematics of the PLSM algorithm, I demonstrate the value of my PLSM algorithm and workflow to one prestack data volumes from Ness Co., Ok and illustrate the effectiveness by analyzing seismic attributes computed along the top of the Gilmore City horizon.
Theory
We can express modeling (demigration) in matrix notation as:
, (1)
© 2012 SEG DOI http://dx.doi.org/10.1190/segam2012-1547.1SEG Las Vegas 2012 Annual Meeting Page 1
Dow
nloa
ded
01/2
9/13
to 1
29.1
5.12
7.24
5. R
edis
trib
utio
n su
bjec
t to
SEG
lice
nse
or c
opyr
ight
; see
Ter
ms
of U
se a
t http
://lib
rary
.seg
.org
/
whethesmod
W
Whepres
′ i
Stanmod
Sub
Wto mdue diag199
prec
whetermfuncsidemin
gradconsalgo
Exa
showresebarruncothe Misshalbeenregiaquithe rand
ere Lsis pdel, a
We
ere stack
is th
ndarddelin
bstitu
We m. If
to gona6).
Sch clos
cond
ere m onctiones ofnimiz
Wedientstituorith
ampl
Dicwn iervoirels onfoMe
ssissillown doionalifer reserlow
L coprestand
defi
isk), an
he mi
d mng op
uting
can f
spaal su
husteser t
dition
is tn then, anf equze th
e wit sch
utes m (S
le
ckmain Fiir, w
of ormaeramippia-sheocuml uncsystrvoi
w per
nstittack d is
ne m
s thend
igrat
migraperat
g equ
reg app
arse uch
er (1to thner F
the oe rignd Cuatiohe fu
ill shem
a Schu
an fiigure
whichoi
ably mecia
an relf cmentconftem ar, w
rmea
tutestim
the
migra
adjo
tion
ationtor
uatio
ard prox
surfthat
1997he idF to
objecght-hC is on 4 unctio
solveme, g
preuster
ield, e 1, h hail. over
an Sresercarboted formacts hich
abilit
s theme d
mod
ation
oint
appr
n .
on 1
the imatface
′
7) atdentobta
|
ctivehandthe by Lon:
e eqgivineconr, 199
locais a
as pIn rlie
Spergrvoironatto
mity sas a
h in tty G
e fordemideled
n as
′
oper
roxi
is
into
matrtes th acq ha
ttenutity main:
|
e fund sidcons
LT, I
quating rinditio97).
ated a typroduthe the gen
r in es. extesurfaa verturn ilmo
rwardigratd dat
rator
mati
the
o equ
rix he idquisas m
uatedmatr
|
nctiode ofstraiI for
ion ise toned
in Npical uced
fieMis
andDickKar
end ace. ry stis u
ore C
d motion)ta.
,
r of
ion t
e a
uatio
adentition
migra
d therix.
||
on tof theint mrm th
5 foto ad le
Northsup
d appeld, sissid Wkma
rst-ensevThe
trongunderCity
odel), m
L, (i
to th
djoin
on 2,
.
as a tity mn, ation
ese In th
||
o be e eq
matrihe n
or an iteast-
hernper mprox
Peippia
Warsan finhaneral
e Weg borlainlime
ling m is
in th
he Ea
nt o
I ob
linematr
in art
artifhis w
,
minquatiix. Morm
..
usierati-squ
n Comatuximaennsan reaw ield nced
meesterttom
n by eston
operthe
his p
arth'
of t
btain
ear fix.Uis altifac
factswork
nimizion iMult
mal eq
ing ive
uares
untyure Mately ylvaeservlimis c
d fraetersrn Inm wa
the ne.
ratore ref
aper
s ref
the
n
filterUnfor
lmoscts (
s by k, w
zed, is thtiplyquat
a cmeth
s m
y, KaMissi
1.7anianvoir esto
compacturs benterioater dlow
r (inflect
r is
flect
forw
r apprtunast nNem
mawe a
the he mying tions
onjuhod
migra
ansaissip
7 min srockne. poseres helow or Pldriveporo
n thistivity
(2)
tivity
ward
(3)
pliedately
nevermeth
akingdd a
(4)
firstmisfit
boths and
(5)
ugatethat
ation
as, asppianllion
strataks ofThe
ed ofhave
thelainse forosity
s y
)
y.
d
)
d y, r
h,
g a
)
t t h d
)
e t n
s n n a f e f e e s r y
FBinre
Fh
amthfofe3lere
varinthfore
FigurBlackndicaepre
Figurhoriz
Fmplihe loor theaturb aness neflec
Folumrrownterphree ootpetain
re 1k boxates sent
re 2:on. T
Figuritudeow she lares.
nd 3cnoisected
igurme w indpreta
iterrint
ned.
: Mx ou
thet oil p
TimThe
re 3e alosignayerAftec, the coener
re 4aafterdicatationrationis al
Map outlinee loprod
me-stwhi
3a ong al-tos, aner twe sig
ontamrgy f
a shor cotes fn of ns olmos
of thes Nocatiducti
tructte bl
showpro
o-noind r
wo angnal-minafrom
ows onvefootpsubt
of PLst eli
2
he MNess ion ion.
ture lock
ws ofilesise r
randond th-to-nation
m con
a timentioprinttle gLSMimin
2km
MissCouof (Aft
mapk arro
verts AAratioom nhree noisen, wnven
me sonal t, itsgeolo
M in nated
m
sissipunty,
Dicter N
p of tows
ticalA’ oo caunoisiterae rat
whichntion
slice mig
s conogicFig
d and
ppia and
ckmaNisse
the tindi
l sliof cousesse mationtio ish intnal m
at tgratintamcal fegure d the
A
A
an sud thean Fen et
top oicate
ices onve the
masksns ofs enhterfe
migra
t=0.4ion.
minatfeatur
4b e stru
A’
A
ubcre whiFieldt al.,
of the coll
threntioe poos subf PLhanceres ation
406sThe
tion res. and uctu
rop ite bd. B200
he Gilaps
rougonal or ilbtle SM
ced awith
n.
s of te winteAfteFigu
ural f
in KblockBlack09).
ilmoe fea
gh smig
llumgeoin F
and th th
the swhiteerfereer twure featu
Kansk arrk d
ore Cature
seismgrati
minatologiFigurtheree m
stack bloes wwo a4c,
ures
sas. row dots
City es.
mic ion, tion ical rers e is
main
ked ock
with and the are
© 2012 SEG DOI http://dx.doi.org/10.1190/segam2012-1547.1SEG Las Vegas 2012 Annual Meeting Page 2
Dow
nloa
ded
01/2
9/13
to 1
29.1
5.12
7.24
5. R
edis
trib
utio
n su
bjec
t to
SEG
lice
nse
or c
opyr
ight
; see
Ter
ms
of U
se a
t http
://lib
rary
.seg
.org
/
(
(c
(a
1
FiguprofmigPLSThe
(a)
(b)
c)
a)
000f
ure 3files
gratioSM. e red
A
A
A
ft
3: VeAA
on, aThe bloc
A
A
A
erticA’ as and a
whick ar
cal slshow
afterite brrow
lice twn ir (b) lock
ws in
throin Fitwo
k arrondica
ugh igure
o, andows ate G
seise 2: d (c)indi
Gilm
smic(a) u) threicate
more
ampusingee ite colCity
plitug conteratillapsy hor
ude anvenion ose ferizon
alongntionof ature
n.
g nal
es.
A
A
A
A’
A’
A’
(
(c
(
Fvanin
cococooPsufe
b)
c)
a)
Figurolumnd (n (a)
oheronveollapn th
PLSMuppreatur
re 4:mes (c) th) and
Figurenceentiopse fe co
M inresseres c
Timafterhreed (b)
ure e vonal featu
oheren Figed. clear
me slr (a) iterindi
5a volumig
uresence gure The
rly in
lice ) conratioicate
showumesgratio. Noattr5b
e redn for
at t=nvenns oe foo
ws cs alon. T
ote thributand d brm o
=0.4ntionof CLotpri
cohelongThe he ce. AFigulock
of co
06s nal mLSMint.
erencg th
red conta
After ure
k arollaps
thromigraM. T
ce hhe bloc
amintwo5c,
rrowse ch
oughation
The w
horizGilm
ck anatioo andconts hhara
h stacn andwhite
zon mor
arrowon ofd thrtamiighli
acter
ckedd afte blo
slice C
w def ranree itinatinight .
d amter (bock
es tCityenotendomteratng n
the
mplitub) twarro
throuy afes kam notionsnoisee ka
ude wo, ows
ugh fter arst oise s of e is arst
© 2012 SEG DOI http://dx.doi.org/10.1190/segam2012-1547.1SEG Las Vegas 2012 Annual Meeting Page 3
Dow
nloa
ded
01/2
9/13
to 1
29.1
5.12
7.24
5. R
edis
trib
utio
n su
bjec
t to
SEG
lice
nse
or c
opyr
ight
; see
Ter
ms
of U
se a
t http
://lib
rary
.seg
.org
/
(
(
b)
c)
(a)
Figucoheusiniteracoll
Figupressamcont
)
ure 5eren
ng coationapse
ure stack
me etinua
5: Hnce vonvens oe fea
6a k gateventation
Horizvolumentiof PL
ature
shothersts inn and
zon mes onal LSMs.
ws s fron Fd les
slicecommig
M. R
the om cigurss no
es amputgrati
Red b
comonve
re 6oise
alongted fion, block
mmoentio
6c acont
g thefromandk ar
on ronal
and tami
e Gim seid (b)rrow
reflemigFigu
inati
ilmoismi) two
ws in
ectiogratioure on.
ore Cc amo, a
ndica
on pon. A6d
City mplitand (ate t
pointAftesho
throtude(c) tthe k
t (Cer CSw m
oughe: (a)threekarst
CPR)SLMmore
h ) e t
) M, e
FgPw
C
Aa gnmqrathwwan
A
WPfi
(b
(c
Figurathe
PLSMwhite
Conc
Applirap
athenoisemigraqualitandohe su
we awill naly
Ackn
We aProceinan
b)
)
re 6ers (aM. Te blo
clusi
icatipid ers ane, wationty oom nubsuantici
resuysis.
nowl
also essincial
: A a) af
The wock a
ions
ion oimpnd s
whichn. PLf subnoiseurfacipateult i
ledg
thanng supp
reprfter mwhitarrow
of PLprovesignih imLSM
ubseqe ance gee thain im
geme
nk thand port.
resemutite blws in
LSMemenificanmpedM proquennd coeologat pmpro
ents
he sIn
.
ntatiing,lock n (b)
M to nt ont atdesovid
nt seohergy o
precooved
ponsnterp
ive (b)
k arro) and
the of sttenuinte
des sismient n pr
onditd pr
sors pretat
convtwo,ow id (c)
Gilmignauatioerpresigniic atnois
restationeresta
of tion
vent, andin (aindi
moreal-toon ofetatioificanttribuse thck ged lack
the C
tionad (c)a) inicate
e Cit-noif fooon fnt imutes.
hat isgatheeast-inve
OU onso
ally ) thrndicae noi
ty limse rotprifrommpro. PLs incers. F-squersio
Attortiu
migree itates ise a
mestratioint a
m coovem
LSMconsFor t
uareson a
tribuum
grateteratnois
atten
toneo foand ronvement
elimsistenthis s miand
ute-Aand
d Ctionsse. T
nuate
e shor Crandentiot in minant wreas
igratAV
Assisd th
CRP s of The ed.
ows CRP dom onal
the ates with son, tion
VAz
sted heir
© 2012 SEG DOI http://dx.doi.org/10.1190/segam2012-1547.1SEG Las Vegas 2012 Annual Meeting Page 4
Dow
nloa
ded
01/2
9/13
to 1
29.1
5.12
7.24
5. R
edis
trib
utio
n su
bjec
t to
SEG
lice
nse
or c
opyr
ight
; see
Ter
ms
of U
se a
t http
://lib
rary
.seg
.org
/
http://dx.doi.org/10.1190/segam2012-1547.1 EDITED REFERENCES Note: This reference list is a copy-edited version of the reference list submitted by the author. Reference lists for the 2012 SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web. REFERENCES
Aoki, N., and G. Schuster, 2009, Fast least-squares migration with a deblurring filter: Geophysics, 74, no. 6, WCA83–WCA93.
Cabrales Vargas, A., 2011, Suppression of aliasing artifacts on 3D land data via constrained least-squares migration: M.S. thesis, University of Oklahoma.
Chavent, G., and R.-E. Plessix, 1996, A time-domain derivation of optimal and suboptimal Kirchhoff quantitative migrations via a least-squares approach: National Institute for Research in Computer Science and Control Report RR-2967.
Claerbout, J. F., 1992, Earth soundings analysis: Processing versus inversion: Blackwell Scientific, 144–145.
Corrao, A., M. Fervari, and M. Galbiati, 2011, Hewett plattendolomite: Reservoir characterization by resolution enhanced seismic data: Proceedings of the GCSSEPM Foundation Annual Bob. F. Perkins Research conference, 66–99.
Falconer, S., and K. J. Marfurt, 2008, Attribute-driven footprint suppression: 78th Annual International Meeting, SEG, Expanded Abstracts, 2667–2671.
Fehmers, G., and F. W. Höecker, 2003, Fast structural interpretation with structure-oriented filtering: Geophysics, 68, 1286–1293.
Kuwahara, M., K. Hachimura, S. Eiho, and M. Kinoshita, 1976, Processing of RI-angiocardiographic images, in K. Preston and M. Onoe, eds., Digital processing of biomedical images: Plenum Press, 187–202
Kwiatkowski, J. T., and K. J. Marfurt, 2011, Data conditioning of legacy pre-stack time migrated gathers from the Mid-Continent: AAPG Mid-Continent Section Meeting, 90133.
Luo, Y., S. al-Dossary, and M. Marhoon, 2002, Edge-preserving smoothing and applications: The Leading Edge, 21, 136–158.
Nemeth, T., 1996, Imaging and filtering by least-squares migration: Ph.D. dissertation, University of Utah.
Nissen, S. E., T. R. Carr, K. J. Marfurt, and E. C. Sullivan, 2009, Using 3-D seismic volumetric curvature attributes to identify fracture trends in a depleted Mississippian carbonate reservoir: Implications for assessing candidates for CO2 sequestration: AAPG Studies in Geology, 59, 297–319.
Schuster, G. T., 1993, Least-squares cross-well migration: 63rd Annual International Meeting, SEG, Expanded Abstracts, 110–113.
Schuster, G. T., 1997, Acquisition footprint removal by least-squares migration: Utah Tomography and Modeling/Migration (UTAM) Research Report, 73–99.
Wang, J., and M. Sacchi, 2009, Structure constrained least-squares migration: 79th Annual International Meeting, SEG, Expanded Abstracts, 2763–2767.
© 2012 SEG DOI http://dx.doi.org/10.1190/segam2012-1547.1SEG Las Vegas 2012 Annual Meeting Page 5
Dow
nloa
ded
01/2
9/13
to 1
29.1
5.12
7.24
5. R
edis
trib
utio
n su
bjec
t to
SEG
lice
nse
or c
opyr
ight
; see
Ter
ms
of U
se a
t http
://lib
rary
.seg
.org
/
Wei, D., and G. T. Schuster, 2011, Least-squares migration of multisource data with a deblurring filter: Geophysics, 76, no. 5, R135–R146.
© 2012 SEG DOI http://dx.doi.org/10.1190/segam2012-1547.1SEG Las Vegas 2012 Annual Meeting Page 6
Dow
nloa
ded
01/2
9/13
to 1
29.1
5.12
7.24
5. R
edis
trib
utio
n su
bjec
t to
SEG
lice
nse
or c
opyr
ight
; see
Ter
ms
of U
se a
t http
://lib
rary
.seg
.org
/