Imaging Passive Seismic Data

8/2/2019 Imaging Passive Seismic Data

http://slidepdf.com/reader/full/imaging-passive-seismic-data 1/11

Imaging passive seismic data

Brad Artman1

ABSTRACT

Imagingpassive seismic datais theprocess of synthesizing

the wealth of subsurface information available from reflec-tion seismic experiments by recording ambient sound using

an array of geophones distributed at the surface. Crosscorre-

lating the traces of such a passive experiment can synthesize

data that are identical to actively collected reflection seismic

data. With a correlation-based imaging condition, wave-

equation shot-profile depth migration can use raw transmis-

sion wavefields as input for producing a subsurface image.

Migration is evenmore important for passively acquireddata

than for active data because with passive data, the source

wavefields are likely to be weak compared with background

andinstrument noise — a conditionthatleads toa low signal-

to-noise ratio. Fourier analysis of correlating long field

records shows that aliasing of the wavefields from distinct

shots is unavoidable.Although thisreduces the order of com-putations for correlation by the length of the original trace,

the aliasing produces an output volume that may not be sub-

stantially more useful than the raw data because of the intro-

duction of crosstalk between multiple sources. Direct migra-

tion of raw field data still can produce an accurate image,

even when the transmission wavefields from individual

sourcesare not separated. To illustrate direct migration, I use

images from a shallow passive seismic investigation target-

ing a buried hollow pipe and the water-table reflection.These

images show a strong anomaly at the 1-m depth of the pipe

and faint events that could be the water table at a depth of

around 3 m. The images are not clear enough to be irrefut-

able. I identifydeficiencies in survey design and execution to

aid future efforts.

INTRODUCTION

Passive seismic imagingis an example of wavefield interferomet-

ric imaging. In this case, the goal is to produce subsurface structural

images by recording the ambient noise field of the earth using sur-face arrays of seismometers or geophones. The images produced

with this technique are directly analogous to those produced with

conventional reflection seismic data. In the exploration seismic

community, the words imaging andmigration often are used synon-

ymously. Likewise, this paper presents the processing of passive

seismic dataas a migration operation.

Using subsurfacesources to image the subsurface was introduced

by Claerbout 1968. That work provided a 1D proof that autocorre-

lation of time series collected on thesurfaceof the earth canproduce

the equivalent of a zero-offset time section. Subsequently, Zhang

1989 used plane-wave decomposition to prove the result in three

dimensions over a homogeneous medium. Derode et al. 2003 de-

veloped the Green’s function of a heterogeneous medium with

acoustic waves viacorrelation andvalidated thetheorywith an ultra-sonic experiment. Wapenaar et al. 2004 used one-way reciprocity

to prove that crosscorrelation of traces of the transmission response

of an arbitrary mediumsynthesizes thecomplete reflection response,

in the formof shot gathers,collected in a conventional active-source

experiment. Schuster et al. 2004 showed that the Kirchhoff migra-

tionkernel oneuses to image correlatedgathers is identical to themi-

gration kernel one uses to migrateprestack activedata when one as-

sumes that impulsive virtual sources are located at all receiver loca-

tions. In summary, it is well established that time differences calcu-

lated by correlation are informative about the medium between and

below the receivers.

Data collected using subsurface sources are called transmission

wavefields or T . The conventional reflection-seismic data volume is

referred to as R. The first section of this paper explains the basic ki-nematics of extracting R from T . Next, I introduce the use of shot-

profile wave-equation depth migration to create an image of subsur-

face structure without first correlating the traces from the transmis-

sion wavefields.

One important attribute of truly passive data is that thebulk of the

raw data is likelyto be worthless. Useful seismic energy captured in

Manuscript received by the Editor March19, 2005; revised manuscript received January 24, 2006; publishedonlineAugust 17, 2006.1Stanford University, Stanford Exploration Project, Mitchell Building, Department of Geophysics, Stanford, California 94305.E-mail: brad@sep.

stanford.edu.© 2006Societyof ExplorationGeophysicists.All rights reserved.

GEOPHYSICS,VOL. 71,NO. 4 JULY-AUGUST2006; P. SI177–SI187,14 FIGS.,2 TABLES.10.1190/1.2209748

SI177

Downloaded 28 Feb 2012 to 116.0.5.136. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/



thetransmissionwavefield mayinclude randomdistributionsof sub-

surface noise, downhole source noise, or earthquake arrivals. As-

suming thatthese noise sourcesare not happening continuously, and

not knowing when they will occur, the passive seismologist must

record continuously. Through Fourier analysis, one can explore the

ramifications of processingan entirepassivelyrecorded datavolume

rather thanindividualwavefieldsfrom separate sources.

Finally, results from a small field experiment are presented. Pas-sivedata wererecorded over severaldayson clean beachsand with a

2- 2-m array of 72 geophones.A hollow pipe was buried beneath

the array to provide an imaging target. Several data volumes from

different times of the day and various preprocessing strategies were

imaged for comparison with an active survey collected at the same

location.

FROM TRANSMISSION WAVEFIELDS

TO REFLECTION WAVEFIELDS

Figure 1, simplified for clarity, shows the basic kinematics ex-

ploited in processing transmission data. The figure includes two

recording stations capturing an approximately planar wavefrontemerging from a two-layer subsurface. Figure 1a shows a raypathas-

sociated with thedirect arrivaland a raypathreflected bothat thefree

surfaceand at a subsurfaceinterface.The second travel pathlabeled

reflection ray has the familiar kinematics of the reflection seismic

experiment with a source that is excited at receiver one. The trans-

mission wavefield is depicted in Figure 1b. Wavelet polarity is ap-

propriate for direct arrivals and for reflection. The three main fea-

tures of transmission wavefields can be appreciated here. First, the

exact timing of the arrival is unknown. Second, the phase and dura-

tion of transmitted energy are unknown and likely are complicated.

Third, if the incidentwavetrain coda is long, arrivalsin the transmis-

sion record can interfere.

If we choose trace r 1 as the comparison trace, Figure 1c depicts

the correlationspikesassociated withthe arrivals in the datapanel of Figure1b, where is correlation.A solid linewith linear moveout is

superimposed across the correlated traces corresponding to the di-

rect arrival recorded at each receiver location. The dashed line on

Figure1c hashyperbolicmoveout.However, no correlationpeak ex-

istson the r 1 r 1 trace under the hyperbola. Notdrawn,the second

arrival on r 2 will have a counterpart on r 1 from a ray reaching the

free surface farther to the left of the model. In fact, the correlations

produced from a single-plane wave will produce another plane

wave.

However,each planar reflection is moved to the lag time associat-

ed with a two-way trip from the surface to the reflector. Correlation

removes the wait time for the initial arrival and maintains the time

differences between the direct arrival and the reflections. Summing

the correlations from a full suite of plane waves builds hyperbolic

events through constructive and destructive interference. Analysisof seismic data in terms of plane-wave constituents is a commonly

invoked tool in seismic processing. Summing the correlations from

incident plane waves is a plane-wave superposition process that

builds hyperbolas.

Passive seismic imagingis predicatedon raypaths bouncingevery

which way from every direction. Cartoons depicting the transmis-

sion experimentalwaysleave something out,whichcauses an incon-

sistency that needs more raypaths and receivers to explain it. Unfor-

tunately, the trend continues nearly forever. Such a complication

arises withthe inclusion of a second reflector. Thetwo reflection rays

correlate positively with each other. The two travel paths share the

time through theshallow layer, so they correlate at a lag or time dif-

ference equal to the two-way traveltime through the deep layer.

Such a correlationis not a problem, however.An upcoming intrabedmultipleevent arrivesafterthe direct arriv-

al that was delayed by the two-way traveltime through the deeper

layer. This multiple eventhas a polarityopposite to that of the direct

arrival after it changes its propagation direction from upward to

downward. The multiple’s arrival at receiver r 2 is delayed, com-

pared with the timing of the direct arrival at receiver r 1 by the same

lagas that of thecorrelationbetweenthe reflectors,and it has theop-

posite sign. Therefore, the internal multiple cancels potential arti-

facts of the correlation. This shows the importance of modeling

transmission data with a two-way extrapolator. Without all possible

multiples, correlation artifacts will quickly overwhelm the earth’s

structure in the correlated output.

Crosscorrelation of each trace with every other trace resolves the

three main difficulties associated with transmission data: timing,waveform, and interference. First, the output of the correlation is in

lag units, which when multiplied by the time-samplinginterval, pro-

vide the time delays betweenlike events on differenttraces.The zero

lagof thecorrelation is thezero timefor thesynthesized shot gathers.

Second,each trace records the character and duration of the incident

energy as it is reflected at thesurface.This becomesthe sourcewave-

let analogous to a recorded vibrator sweep. Third, overlapping

wavelets are separated by correlation.

To calculate theFourier transform of the reflection response of the

subsurface, Rxr ,xs, , Wapenaar et al. 2004 proved

2R Rxr ,xs, = xs − xr

− Dm

T xr , , T *xs, , d2 ,

1

where * represents conjugation. The vector x will correspond herein

to horizontal coordinates, where subscripts r and s indicate different

station locations from a transmission wavefield. After correlation, r

and s acquire the meaning of receiver and source locations, respec-

tively, that are associated with an active survey. The right-hand side

RHS of equation 1 representssumming correlations of windows of

passive data around the occurrence of individual sources from loca-

Figure 1. aAn approximately planar arrival with rays showing im-portant propagation paths for passive imaging. b Idealized tracesfrom a transmission wavefield. c A shot gather reflection wave-field synthesized using trace r 1 as the source. Many details ex-plainedin the textare omittedhere forsimplicity.

SI178 Artman




tions . The symbol Dm represents the domain boundary that sur-

rounds thesubsurface region of interest on whichthe sourcesare lo-

cated.The transmissionwavefieldsT xr , , containthe arrivaland

reverberations fromonly one subsurfacesource. For exact synthesis

of the reflection experiment, impulsive sources should completely

surround thevolumeof thesubsurfacethat oneis trying to image.Al-

ternatively, many impulses can be substitutedby a full suite of plane

waves emerging from all angles and azimuths, as in the kinematicexplanation above.

DIRECT MIGRATION

Artman and Shragge 2003 introduced the applicability of direct

migration for transmission wavefields. Artman et al. 2004 provid-

ed the mathematical justification for zero-phase source functions.

Shragge et al. 2006 showed results for the special case of imaging

with teleseisms. Direct migration of transmission wavefields re-

quires an imaging algorithm composed of wavefield extrapolation

and a correlation-based imaging condition. Shot-profile wave-equa-

tion depth migration Claerbout, 1971 fulfillsthese requirements.

Shot-profile migration uses one-way extrapolators to indepen-

dently extrapolate upgoing energy, U , and downgoing energy, D,through the subsurface velocity model. The term U , extrapolated

acausally, is a single shot gather. The term D, extrapolated causally,

is a wavefield modeled to mimic the source used in the experiment. I

will define the causal extrapolation operator, E +, andthe acausal op-

erator, E −. These are adjoint phase-shift operators calculated Claer-

bout, 1985 by

E ± = e±ik z z , 2

where

k z = s2 − kr 2, 3

kr is the wavenumber dual variable for receiver location xr , and s is

slowness. These one-way operators cannot extrapolate evanescent

waves, but that limitation is not crippling. To avoid adding needless

complexity, I do not include the details of the more accurate phase-

shift-plus-interpolation PSPI extrapolation operators Gazdag and

Sguazzero, 1984 used for migration examples herein. Wavefields

are extrapolated to progressivelydeeper levels, z, by recursive appli-

cation of E ±:

U z+1kr ;xs, = E −U zkr ;xs, and 4

D z+1kr ;xs, = E + D zkr ;xs, . 5

Theimaging condition combines thetwo wavefields andoutputs a

subsurface image. The zero-offset imaging condition for shot-pro-

file migration is defined as the zero lag of the crosscorrelation of the

two wavefields

i zxr = xs

U zxr ;xs, D z*xr ;xs, . 6

The sum over frequency extracts the zero lag of the correlation. The

sum over shots, xs, stacks the overlapping images from all the indi-

vidual shot gathers.

Extrapolation in the Fourier domain, across a depth interval, is a

diagonal matrix whose values are phase shifts for each frequency-

wavenumber component in the wavefield. Correlationof two equal-

length signals in the Fourier domain has one signal along the diago-

nal of a square matrix multiplied by the second signal vector. As

such, the two diagonal-square operations are commutable. This

means that the correlation required to calculate the earth’s reflection

response from transmission wavefields can be performed after ex-

trapolation as well as at the acquisitionsurface, if the velocitymodel

is accurate.

Table 1 demonstrates pictorially how direct migration of trans-

mission wavefields fits into the framework of shot-profile migrationto produce the 0th and 1st depth levels of the zero-offset image. The

correlationin the imagingconditiontakes the place of preprocessing

the transmission wavefield. The summationsover shot locations and

frequency in equation 6 are omitted to reduce complexity. Note,

however, that the sum over shot locations in equation 6 takes the

place of the integral over source locations in equation 1. Also, after

the first extrapolation step, using the twodifferent phase-shift opera-

tors, the two transmission wavefields are no longer identical and can

be redefined as U and D. This is noted with superscripts on the T

wavefields at depth.

Transmission wavefields from 225 impulsive sources across the

bottom of the velocitymodel in Figure 2c were modeled with a two-

way time-domain extrapolation program. The time sampling rate

was 0.004 s, and the source functions were Ricker wavelets with a

dominant frequency of 25 Hz. Figure 2a is theimage created by cor-

relating each transmission wavefield implementing equation 1 and

migrating the shot gathersby the algorithm described on the leftside

of Table 1. Figure 2b was produced by migrating each transmission

wavefield directly and summing the images as described by the right

column of Table1. Theyare identical to machineprecision.

The term T is the superposition of U and D. Extrapolating the

transmission wavefield with a causal phase-shift operator propa-

gatesthe energy reflected downward from the free surfacethat is the

source functionfor later reflections. Thisallowsthe use of T in place

of D in shot-profile migration. Extrapolating the transmission wave-

field with an acausal phase-shift operator, reverse-propagates the

upcoming events reflected from subsurface structure. This allows

the use of T in placeof U in shot-profile migration.

In effect, the extrapolations redatum the experiment to succes-

sively deeper levels in the subsurface. At those deeper levels, the

wavefields are correlated in accordance with the general theory of

equation 1. The physics captured in the formulation of shot-profile

migration remainsthe same, regardlessof thetemporal or areal char-

acteristicsof initialconditionsin the wavefields.

Extraction ofonlythe zero lag ofthe correlation for the image dis-

cards energy in the two wavefields that is not collocated. This in-

Table 1. The equivalence of shot-profile migration of reflec-tion data and direct migration of transmission wavefields.

2

Shot-profile migration Transmission imaging

U z=0xr ;xs, D z=0xr ;xs, = T z=0xr ; , T z=0xr ; ,

E − E + E − E +

↓ ↓ ↓ ↓

U z=1xr ;xs, D z=1xr ;xs, = T z=1− xr ; , T z=1

+ xr ; ,

2T xr , ,t are the wavefields of equation 1. The term xs has a

meaningsimilar to . The sums xs, and produce the image i zxr

for both methods. Only the first and second levels of the recursiveprocess are depicted.

Imaging passive seismic data SI179




cludes energy that has been extrapolated in the wrong direction be-

cause the same data are used initially for both U and D wavefields.

Conveniently, the only modification needed to make a conventional

shot-profile migration program into a transmission-imaging pro-

gramis touseT as D insteadof using a modeledwavefield.

Very important among the motivations for migrating transmission

wavefields,is theneed to increasethe signal-to-noise ratio of theout-

put. If the experiment records only a small amount of energy, thesynthesized gathers from correlation may be completely uninter-

pretable. The synthesized shot gather in Figure 3a was produced us-

ing the same 225 transmission wavefields used in Figure 2, although

here each wasconvolvedwith a random source function. Thewave-

fields were individuallycorrelatedand summed.A fewevents canbe

seen centeredaround4000 m, butthe gather is dominated by noise.

Figure 3b shows an image produced by direct migration of the

transmission wavefields, followed by stacking the 225 images. An

identical image, not shown, was produced by correlating and then

migrating the synthesized gathers. Combining the weak redundant

signal within each shot gather with all of the others through migra-

tion produces a very good result, despite the low quality of the shot

gather produced withthe same data.

TRULY PASSIVE DATA

I differentiate passive seismic data from transmission wavefields

when the timings of individual sources are unknowable and may

overlap. For passively collected transmission wavefields, the time

axis and the shot axis are combined naturally. The parameterization

of field data, T f ,isintermsof xr and time rather than xr , ,t , which

is the parameterization of equation 1. Within , many individual

sources, and the reflections that occur t seconds afterward, are dis-

tributedrandomlyacrossthe total recording time. Both t and repre-

sent the realtime axisand therefore share the sampling ratet = .

However, I will parameterize wavefields with the understanding that

maxt is the two-way time to the deepest reflector of interest, and

is the time axis from the beginning to the end of the total recording

time.The difficulty in separatingthe datainto constituentwavefieldsfrom a single source, parameterizing as function of , comes from

not knowing the time separation between events and from the possi-

bility that the sources mayoverlap in time andspace.

If it is impossible to separate fielddata intoindividualwavefields,

transforming the long data to the frequency domain has important

Figure 2. Images created by a shot-profile migration of correlatedshot gathers and b summing of images from direct migration of in-dividual transmission wavefields. c The velocity model used formodeling and migration.

Figure 3. a A synthesized shot gather implementing equation 1,with a source trace from x = 4000 m from a passive data set mod-eled with the velocity model in Figure 2c and random source func-tions. b A zero-offset image produced by direct migration of themodeled data usedto create the shot gather in a.

SI180 Artman




ramifications on further processing. The definition of the discrete

Fourier transform DFT foran arbitrary signal f canbe evaluated

for a particular frequency,, as

F = DFT f =

1

n

n=0

n

−1

f n e−in , 7

where n

is the number of samples in f . The frequency-domain dual

variable of is , and I will use for the frequency domain dual

variable of t . Ifthe longfunction f is broken into N sections, gnt ,

of length n / N , the amplitude of any frequency = also can be

calculated as

F =1

N n=1

N

DFTgnt =1

N DFT

n=1

N

gnt

8

by simply changing the order of summation for convenience and

scaling the result. Therefore, F calculated with equation 8 is an

N -times-subsampled versionof F calculated withequation 7.

The center equality of equation 8 the sum of short transforms

shows that frequency components common to the two transforms

are identical after a simple amplitude scaling. The right equality the

sum of time windows shows that the long transform stacks thecon-

stituent windows at commonfrequencies.The twoalternatives inter-

preted together show that subsampling thelong transform aliasesthe

time domain. This relationship between sampling and aliasing in a

signal’s representation in twodomains is the Fourier dualto subsam-

pling a timesignal to reduce itsNyquist frequency at therisk of alias-

ing high frequencies.

Passive seismicfield data,T f , take the role ofthe general signal

f , and the gnt are T xr , ,t =n as well as background noise be-

tween sources. Equation 8 states that T f

xr ,

is a subset from

T f xr , and that

T f xr ,t =

T xr , , t . 9

Therefore, implementing a single correlation of passive field data

does notproduce R, butinsteadsome unknown quantity R̃ :

R˜ xr ,xs, =1

N T f xr , T f

*xs, , 10

where N isthe number of time windows of length max t intowhich

the totalrecording time can be divided and whereT f can be calculat-

ed with equation 9. The relationship is undefined at frequencies

.

Figure 4a shows a processing flow of a simple 1D time-domain

signal,and a zoomed-inviewof each traceappears in Figure 4b. The

top trace is the input signal T f with 4096 samples. It represents a

long field recording, including three transmissionwavefields explor-

inga subsurfacewith a singlelayer. Themiddletrace is itsautocorre-

lation calculated with all frequencies, R̃ = DFT−1T f T f *.

The bottom autocorrelation was calculated by first summing eight

constituent windows of T f before discrete Fourier transformation

DFT,sothat

T f =1

8DFT

n=1

8

gnt , 11

where thenumber of samplesin each gnt was512.An identicalre-

sult can be produced by subsampling T f by 8. To facilitate plot-

ting, the trace was padded with zeros, although the function actually

is undefined at times greater thanthe last visibleenergy.

Both versions of the output — the middle and bottom traces —

have latecorrelation lagsthat do notcorrespond to physical raypaths

found in R. Mostefficiently, they arewindowed away inthe time do-

main before further processing. From the bottom trace, notice that

increasing the decimation factor to 16 would alias the symmetric,

acausal lags into the reflection response. To avoid this problem, the

short time windows, gnt , must be more than twice as long as the

time to thedeepest reflection of interest. In this example, thefirst two

correlations of R˜ are R. Producing the bottom trace involves O10fewer computations thanproducingthe middle trace.

Wavefield summation

Unfortunately, the beginning of R̃ is not always R. The stacking of

wavefields implicit in processing field data can be explored by con-sidering field data composed of transmission wavefields axr ,t and

bxr ,t from individual sources. As is the case for the input trace of

Figure4, thetransmissionwavefieldsare placed on thefield record at

unknown times a and b so that

T f = a * t − a + b * t − b. 12

Correlationin the Fourier domain to implement equation 10 yields

T f T f * = AA* + BB* + AB*e−i a− b + BA*e−i b− a .

13

The sum ofthe firsttwoterms isthe resultdictated byequation 1.The

last twotermsare crosstalk.If b − a maxt , one term isacaus-

al,and the other is at late lags that canbe windowed away in thetimedomain. That was the case in the middle trace of Figure 4. If b

− a maxt , the cross terms are included in the correlated gath-

ers. In light of the previous section, the last scenario will be the pre-

dominant situation if the source delays a and b are truly random.

For this reason, Figure 4 is not a fair representation of field data be-

cause values for a,bwere selectedvery carefully.

Figure 4. The top row is a trace representing three identical subsur-face sources in a model with a single reflector. The middle row is anautocorrelation of top trace. The bottom row is an autocorrelation of the top trace, performed with every eighth frequency and paddedwith zeros to facilitate plotting. Direct arrivals and reflections fromeach source do not interfere. Column b is the first 1.0 s of columna forall rows.





Next, we redefine A and B as the impulse response of theearth, I e,

convolved with source functions, F , which now contain their phase

delays.As such, the cross terms of equation13 are

AB* = F a I eF b I e* = F aF b

* I e

2 = F c I e2. 14

Asdo the first twoterms in equation 13, the cross terms here contain

the desired information about the earth. However, the source func-

tion f c included is not zero phase. These terms may be the “other-

terms”or virtualmultiples mentioned in Schuster et al. 2004.Ifthe

source functions are random series,terms with residual phase F c I e2within the gathers will decorrelate and diminish in strength as the

length of f and the number of cross terms increases. Although we

hope to collect many sources, it probably is unreasonable to expect

very many of them to be random series of great length. That is not

probable if thenoise sourceshave similarsourcemechanisms.

Inclusion of these cross terms in the correlation explains why R̃

produced with equation 10 is not equivalent to R from equation 1.

Virtual multiple events resulting fromns sourceslikely will be more

problematicthan conventional multiples becauseevery reflector can

be repeated ns ! / ns − 2! times. The ratio of desirable zero-phaseterms, I e, to cross terms, F j I e

2, decreases as 1/ ns − 1 if the source

terms containthe same wavelet.

Figure 5 shows the effect of the cross terms when one is calculat-

ing correlations. The figure is directly analogous to Figure 4, al-

though with a more realistic input trace. First, there are overlapping

source-reflection pairs: The second source arrives at the receiverbe-

fore the reflection from the first source arrives.Second, the direct ar-

rivals are spaced randomly along the time axis, in contrast to Figure

4, in which the direct arrivals were placed at samples 1, 513, and

2049. That contrivance allowed the summing of constituent time

windows 256 or 512 samples long without introducing residual

phase functions as described in equation 14.

Aseismologistusing passive seismicdata to producea zero-offset

trace from R, thebottomtracein Figure 4,cannotdo soby autocorre-

lating the top trace in Figure 5. The middle trace is the autocorrela-

tion with input T . The bottom autocorrelation was computed af-

terfirst stacking eight constituentwindows. In contrast to the twoau-

tocorrelations in Figure 4, here not even the early lags are the same.

The presence of more aphysical correlations in the middle trace for

this example has caused the symmetric peaks at late lags to be

aliased into theearly lags of the bottom result at this level of decima-

tion. Both methods produce the wrong result at almost all times.

However, theyare correctand identical at zerolag.

This analysis shows that without invoking long, purely random

source functions, a single correlation of passive data will not model

shot gathers from a reflection survey. In the next section, I use 2D

synthetic data to show the extentof theproblemand theabilityof di-

rect migration to produce a correct subsurface image, despite thesummation of wavefields.

Examples with synthetic data

To demonstrate theeffects of wavefieldsummation, I usetwo syn-

thetic acoustic passive-data sets. Transmission wavefields from 225

impulsive sources across the bottom of the velocity models were

propagated with a two-way extrapolation program, as before. To

then simulate a passive recording campaign, I convolved a unique

source function with each wavefield before summing all of them to-

gether. Thetotal length of the source-function trace mimicsthe dura-

tionof the recording campaign. The shape, time location, and length

of the waveletused within the source-function trace, otherwise zero,embodies my assumptions on the nature of the ambient subsurface

noisefield. The source functions incorporate many of the features of

the toy examplein Figures4 and 5.

Figure 6 shows synthetic data from a model containing two dif-

fractors in a constant-velocity medium. Figure 6a is a transmission

wavefield from a subsurface source below the far left of the model,

whereas the source in Figure 6b was below x = 5000 m. Source

wavelets were 50 ms long, with a dominant frequency of 25 Hz,and

were placed on the time axisto align their direct arrivals.This exper-

iment is the 2D analog to Figure 4. Figure 6c is the sum of all 225

similar wavefields from shots below the entire width of the surface

array. The coherent summation of the direct arrivals makes a strong

plane wave at t 0.6 s, and the diffractors are captured well bymeans of constructive interference. Crosstalk between the wave-

fields hasbeen canceledusingdestructive interference. The summed

wavefield below the strong plane wave is the same as would be col-

lected from a zero-offset reflection experiment. Correlation of the

traces in Figure 6c does not produce shot gathers. Instead, each xs

plane from R̃ contains a series of plane waves that completely mask

the diffractors. However, the slice from the correlated volume xs= xr is interpretable.The autocorrelation produces a result similarto

Figure 6c, in which the plane wave is moved from t 0.6 s to zero

lag.

In contrast, Figure 7 shows synthetic data from the same model,

with the addition here of random phase delays for the source func-

tions throughout the experiment. Figure 7a–c correspond to its re-

spective panels in Figure 6. Note that theminimum traveltime of thedirect arrivals in Figure 6a and b is thesamewhereasthose in Figure

7a and b are not the same. The strong plane-wave and coherent dif-

fractors from Figure 6c have beenreplaced by an uninterpretablesu-

perposition. Correlating traces from this wavefield returns R̃ that is

completely unusable, rather than the reflection wavefield R. This is

the 2Dequivalentto Figure5.

Data alsowere synthesized using a model that contained two syn-

clines. Source functions were identical to those used for the diffrac-

tor exercise above. Figure 8a shows summed wavefields with cor-

rection for the onset time of the 225 subsurface sources, and Figure

Figure 5. The top row is a trace representing three identical subsur-face sources as in Figure 4. The middle row is an autocorrelation of the top trace. The bottom row is an autocorrelation of the top trace,performed with every eighth frequency and paddedwithzeros tofa-cilitate plotting. Thedirect arrival of the second source is before thereflection resulting from the first source.Column b is thefirst1.0 sof column a forall rows.

SI182 Artman




8b shows the wavefields without correction. Again, correlating the

superposition of wavefields, from either panel, returns an unusable

data volumerather thanshot gathersof R.

DIRECT MIGRATION OF PASSIVE DATA

If we use equation 10 to correlate field data because we are un-

able to collect T as a function of individual source functions, wecannot processthe result of the correlation by using conventional re-

flection data tools. Without separating the wavefields from each

source for independent processing, we cannot eliminate all time de-

lays completely, as shown in equation 13. However, the superposi-

tion of wavefields inherent in the Fourier transform of passive field

data, equation 8, has a direct counterpart to migration of active

sourcedata.

Shot-profile depth migration produces the correct image if the

sourcewavefield, D, is correctfor thedata wavefield,U . Shot-profile

migration becomes plane-wave migration if all shot gathers are

summed forthe upcoming wavefield xsU , andif a horizontal planar

sourceis used forthe downgoing energy, xs D. The wavefield inFig-

ure 6c couldbe imaged successfullywith a horizontal planewave at

t = 0.6 s modeledfor D.

This shot-profile migration method can introduce crosstalk be-

tween the individual experimentswhilewe areattemptingto process

them all together. Such crosstalk will be avoided in two cases. First,

Figure 6. Representative transmission wavefields with sources abelow x = 1200 m and b below x = 5000 m. c The sum of 225transmission wavefields from sources evenly distributed across thebottom of the model. Minimum traveltime of the direct arrival ineachwavefield is the same.

Figure 7. Representative transmission wavefields with sources abelow x = 1200 m and b below x = 5000 m. c The sum of 225transmission wavefields from sources evenly distributed across thebottom of the model. In contrast to Figure 6c, the minimum travel-time of thedirect arrival in eachwavefield here is random.





sourcesthat are separated areally will not interfere, such as whenwe

are migrating the first and last shots of a sail line, and those shots do

not investigate the same subsurface volume. Second, an approxi-

mately contiguous distribution of sources will cancel the crosstalk

by means of destructive interference and will synthesize a zero-off-

set data acquisition. The modeled data used herein have sources be-

neath the entire surface array and thus fulfill the latter requirement.

The information lost in this sum is the redundancy across the offsetaxis. Forsimple structuralimaging, thezero-offset image is satisfac-

tory. For more complicated mediums or further processing, a full

plane-wave migration can be implemented Sun et al., 2001; Liu et

al., 2002.

Table 2 demonstrates pictorially how direct migration of passive

field datafits intothe frameworkof plane-wavemigration analogous

to Table 1. Summation of shot gathers from an activedata set before

migration is represented on theleft. The toprow of theright column

recognizesthe sumover thesourceaxis inherentin the Fourier trans-

formof passive field data shown in equation 8.Regardless ofthe ini-

tial conditions of U , D, or T , they are extrapolated correctly to the

next subsurfacelevel,if the velocitymodel is accurate.Figure 9a and b shows zero-offset images produced by direct mi-

gration ofthe data shown in Figure 8a andb, respectively. The quali-

ty of Figure 9a is equivalent to a zero-offset reflection migration.

Dipping reflectors and sharp changes in slope produce migration

tails. Figure 9b is a remarkably clean image, given the appearance of

the input data, although it is not as high quality as its counterpart.A

faint virtual multiple that mimicks the first event can be seen at z

= 350 m. The physical multiplefromthe first reflector at z = 485 m

is very dim which actually highlights the second reflector that gets

masked in Figure 9a. The summed wavefields shown in Figure 8a

and used asthe data for the image in Figure 9aalso could be imaged

with a source function modeled as a horizontal plane wave at t

= 0.6 s. However,the summed data shown in Figure 8b andusedfor

the image in Figure 9b require a complicated source function withtemporal topography that would be impossible to extract from the

data.

The lengths of the source functions used to synthesize the data

were equal to themodeling time of thetransmissionwavefield.Thus,

summing the wavefields as dictated by equation 9 does not accom-

modate the requirement that the wavefields be at least twice as long

as maxt to avoid aliasing the symmetric acausal lags. The short

time axis also allows late time events to wrap around the time axis

when one is applying the random phase delays. For these reasons,

the image in Figure 9b represents a worst-case scenario of careless

data preparation.

FIELD EXPERIMENTCrosscorrelating seismic traces of passively collected wavefields

has a richhistory inthe studyof thesunDuvall et al.,1993. Howev-

er, only two dedicated field campaigns that test the practicality of

passive seismic imaging on earth can be found in the current litera-

ture: Baskir and Weller 1975 and Cole 1995. Neither experiment

produced convincingresults.Hopingthat hardware limitationsor lo-

cality could explain their lack of success, I conducted a shallow,

meters-scale, passive-seismic experiment in the summer of 2002.

Seventy-two 40-Hz geophones were deployed on a 25-cm grid on

the beach of Monterey Bay, California, and were

linked to a Geometrics seismograph. The experi-

ment was combined with an active investigation

of the same site using the same recording equip-

ment and a small hammer Bachrach and Muker-

ji, 2002. A short length of 15-cm-diameter plas-

tic pipe was buried a bit less than 1 m below the

surface. The array was approximately 100 m

from the water’s edge. The water table was ap-

proximately 3 m deep. The velocity of the sand,

derived from the active survey, was a simple gra-

dient of 180 to 290 m /s from the surface to the

water table, below which it was1500 m/s.

Figure 10 shows the time-migrated active-

source image, which has a clear anomaly associ-

Table 2. The equivalence between direct migration of passive field data andsimultaneous migration of all shots in a reflection survey. 3

Plane-wave migration Wavefront imaging

xsU z=0xr ;xs, x

s D z=0xr ;xs, = T z=0xr , T z=0xr ,

E − E + E − E +

↓ ↓ ↓ ↓

U z=1xr , D z=1xr , = T z=1− xr , T z=1

+ xr ,

3Only the first and second levels of the iterative process are depicted. produces theimage i z forboth methods.

Figure8. Summedtransmissionwavefieldsfrom 225sources evenlydistributed across the bottom of the syncline model in Figure 2c. aMinimum traveltime of the direct arrival in each wavefield is thesame i.e., is analogous to Figure 6c. bMinimumtraveltime of thedirectarrival in eachwavefieldis randomi.e.,is analogous to Figure7c.

SI184 Artman




ated with the hollow pipe andthe watertable.A simple rms gradient

velocity to thewater table was used for imaging. Thewater-table re-

flection at 26 ms in the section carries a wavelet approximately

2.5 ms in duration, which gives it a dominant frequency of 400 Hz.

The high quality of thebeach sand resultedin recording useful ener-

gyas high as1000 Hz Bachrachand Mukerji, 2002.

Passive data were collected at several sampling rates over the

course of 2 days, 2 weeks after the active survey. Because of limita-tionsof the recording equipment, only 1 hour of data exists from the

campaign. The seismograph was only able to buffer 1 s of data in

memorybeforewriting to a file. Thetime required to write,reset,and

retrigger was at least five times greater than the length of data cap-

tured, depending on sampling rates. By continuously triggering the

seismograph, the system wrote subsequent records as soon as the

buffer/write cycle was complete. Then the individual records were

splicedtogether along the time axis to producelong traces.The gaps

in the traces do not invalidate the assumptions of the experiment, as

long as the individual recordings were at least as long as the longest

two-way traveltime to the deepestreflector.

Because the array was only eight-by-nine stations, shot gathers

produced by correlation, even when resampled as a function of radi-

al distance from thecenter trace, had toofew traces to findconsistentevents. Migrating the data provides both signal-to-noise enhance-

ment, as described above, as well as interpolation. In this case, five

empty traces were inserted between the geophone locations for mi-

gration, as shown in Figure 11. During extrapolation, the energy on

the live traces moves laterally across to fill the empty traces. After

the distance propagated is approximately equal to the separation be-

tween live traces, wavefronts have coalesced into close approxima-

tions to their expressionif thedata were interpolated first.

Data were collected to correspond to distinct environmental con-

ditions throughout the course of the experiment. Afternoon data

were collected during high levels of cultural activity and wind ac-

tion. Night data had neither of these features, whereas morning data

had no appreciable wind noise. In all cases, the pounding of the surf

remained mostly consistent. By processing data within various timewindows,I hoped thatimages of thewater table could be produced at

different depths. However, given the 2-m maximum offset of the ar-

ray, ray parameters less than17° from the vertical would be required

to imagea 3-mtable reflectorat the very center of thearray. Very lit-

tle energy was captured at such steep incidence angles. Had we not

been carefulto avoid walkingaround thearray duringrecording,this

mightnot have beenthe case.

Figures 12–14 show the images produced during the different

times of the day. Approximately 5 minutes of

0.001 s/sample data were used to produce each

image by direct migration. Usable energy past

450 Hz is contained in all the data collected.

Abiding by the one-quarter-wavelength rule, and

using 200 m/s with 400 Hz, the data should re-solve targets to 12.5 cm. Other data volumes

corresponding to various faster and slower sam-

pling rates were processed, although these results

are the most pleasing. All output images contain

an appreciableanomalyat the locationof thebur-

iedpipe.

In most cases, preprocessing consisted of a

low-cut filter that removed energy below 150 Hz

to eliminate electrical grid harmonics. Also, the

higher octaves carry the only useful signal con-

sidering thelow velocity ofthe beachsandand thesmall areal extent

of the array. Figure 12 is the image produced at midday. Figure 12a

and b are the x and y sections corresponding to the center of the bur-

ied pipe.

Figure 13 was produced withdata from around midnight. The im-

age planes are the same as for the previous figure. One-dimensional

spectral whitening alsowas tried, althoughthe simpleapplicationre-

mained stable onlyduring night acquisition.Figure 14 was produced with the whitened version of the data

used for the previous figure. Notice the instability at shallow depths

before the wavefront healing has interpolated across the empty trac-

es. Data collected in the morning did not yield images sufficiently

different fromthe night datato warrant inclusion.

Figure 9. a A zero-offset image produced by direct migration of Figure 8a. b A zero-offset image produced by direct migration of Figure 8b.

Figure 10.An inline, x, and crossline, y, time-migrated active-seismicimage. The hollowpipe causes an overmigrated anomaly at x = 12 m, t = 12 ms. A strong water-table re-flection is imaged at 28 ms.After Bachrachand Mukerji2002.





In the whitened-night-data image and the bandpassed-day-data

image, there is a hint of a reflector at a depth that could be the water

table. High tide on that day was at 4:30 in theafternoon,and lowtide

was atabout 9:30 P. M., sothe relative change ofthishintof a reflector

is consistent. However, because of the limitations of the array, dis-

cussed above, and the lack of strength and continuity along the

crossline direction, I do not consider this a very reliable interpreta-

tion.

DISCUSSION

Draganov et al. 2004 systematically explored the quality of a

passive seismic processingeffort as a function of the number of sub-

surface sources, the length of assumed source functions, and migra-

tion. Rickett and Claerbout 1996 identified increasing the signal-

to-noise ratio by the familiar 1/ n factor, where n can be time sam-

plesin the source function, or the number of subsurfacesources cap-

tured in the records.

If the natural rate of seismicity within a field area is constant, ac-

cumulation of sufficient signal dictates how long to record. When

one is interpreting the increase in signal by the factor 1 / t , with ap-plication to short subsurface sources, t represents the mean length of

the source functions rather than the total recording time. Assuming

some rate of seismicity associated with each field site, the total re-

cordingtimewill control thequality of theoutput by 1/ ns, where nsis the number of sourcescaptured.

Another method for increasing the quality of the experiment is to

field more instruments and thereby to migrate more traces. Migra-

tion facilitates the constructive summation of information reflected

from a subsurface reflection point and captured by each receiver in

the survey. Therefore, the use of more receivers sampling the ambi-

entnoise field resultsin more-constructivesummationto eachimage

location in the migrated image. In this manner, migration increases

the signal-to-noise ratio of a subsurface reflection by the ratio 1 /

r ,where r is the numberof receivers thatcontain the reflection.This al-

lows theproductionof veryinterpretable images,despite raw data or

correlated gathersthat show little promise.

Definitive parametersfor the numbersof geophones required, and

sufficient length of time to assure high-quality results for a passive

seismic experiment, are ongoing research topics because few field

experiments have yet been analyzed. However, it is clear that a very

complete sampling of the surficial wavefield will be required and

that thelength of time requiredwill be dictated on theactivityof the

local ambientnoise field. Considering the layout of equipment,very

complete sampling means that more receivers are better and that ar-

eal arrays are much better than linear ones. The limitations of linear

arrayscan be seenby consideringa plane wave propagating along an

azimuth other than that of a linear array. After the direct arrival iscaptured, the subsequent reflection path pierces the earth’s surface

again in the crossline direction awayfrom the array. Thisacquisition

limitationrequires a 2.5D approximation. The apparent-rayparame-

ter of the arrival will suffice, given an areally consistent and planar

source wave and a limited velocity contrast perpendicular to the re-

ceiver line. Because the true direct arrival associated with a reflec-

Figure 11. A small time window of inline and crossline sections of araw passive-transmission wavefield inserted on a five-times-finergrid formigration.

Figure 12. A migrated image from passive data collected during thewindy afternoon.This inline andcrosslinedepth sectionwas extract-edat the coordinates ofthe buried pipe.

Figure 13. A migrated image from passive data collected during thenight.This inline and crossline depth section wasextracted at the co-ordinates of the buried pipe.

Figure 14. A migrated image from passive data collected during thenight. One-dimensional spectral whitening was applied before mi-gration to the same raw data used in Figure 13. This inline andcrossline depth section wasextracted at the coordinates of the buriedpipe.

SI186 Artman




tion travel pathis not recorded, erroneous phase delays and wavelets

mayoccur, and theymay distortthe result.

CONCLUSIONS

To avoid crosstalk, previous literature discussing passive seismic

imaging assumes thatonly individualsourcewavefieldsare correlat-

ed or that the source functions are random series. Direct migration,however, is not constrained by this assumption. In its place, sources

need to be either roughly contiguous or widely distributed. Direct

migrationcan be performed with onlya minor adjustmentto conven-

tional reflection-seismic migration algorithms that use extrapolation

and a correlation-based imaging condition. Direct migration of all

the sources simultaneously also saves substantial computational

cost becauseonlyOn traces must be migrated rather thantheOn2traces associated with synthesized shot gathers.

Migration moves the correlation into the subsurface to the reflec-

tor position. Casting the processingof transmission wavefields as an

imaging problem allows direct comparison of the process to phase-

encoding and reverse-time migration strategies and introduces the

possibility for more advanced imaging conditions such as deconvo-

lution.Also, converted mode imaging strategies may provide a con-venientframework within which to explore multicomponentdata.

Migrating all sources at the same time removes redundant infor-

mation from a reflector as a function of incidence angle.Thismakes

velocity updating after migration impossible. At this early stage, I

contendthat passive surveyswill be conducted onlyin activelystud-

ied regions where very good velocity models are already available.

If thisbecomes a severe limitation, incorporation of plane-wave mi-

grationstrategiescan fillthe offset dimension of the image.

The field experiments on the beach at Monterey Bay indicate that

passive seismic experiments can work in practice. A significant

anomaly is present at the location of the hollow pipe target. Howev-

er, the target was small and localized in all dimensions, which does

not remove the possibility of an anomalous focusing of energy with-

in the aperture of the array. The probability of such an occurrence atexactly the location of the pipe is minimal, however. Because of a

multifaceted field program, two weeks passed between burial of the

pipe and the passive survey. Because the ends of the pipe were not

sealed, sand may have filled the pipe and reduced its linear dimen-

sion. Future surveys should be executed to avoid this problem and

should include burial of a target withan unnatural shape.

ACKNOWLEDGMENTS

Thanks go to my colleagues and advisers at Stanford University

for insightful discussions and development of the infrastructure to

perform these experiments. I thank Deyan Draganov of Delft Uni-

versityfor successful collaboration andfor hismodeling efforts. Ran

Bachrach provided the Michigan State shallow-seismic-acquisition

equipmentfor thebeach experimentas wellas hisimagefrom theac-

tive seismic experiment. Emily Chetwin and Daniel Rosales helped

collect data on the beach. Partial funding for this research was en-

joyed from Petroleum Research Fund grant ACSPRF# 37141-AC 2,

the Stanford Exploration Project, and National Science Foundation

grant number 0106693 to S. L. Klemperer and J. Claerbout. Manythanks go to my patient reviewers, whose constructive comments

greatlyimproved the quality of thismanuscript.

REFERENCES

Artman, B., and J. C. Shragge, 2003, Passive seismic imaging: EOS, Trans-actions, American Geophysical Union, 84, AGU Fall Meeting, AbstractS11E–0334.

Artman, B.,D. Draganov,C. P.A. Wapenaar, and B. Biondi,2004, Direct mi-gration of passive seismic data: 66th Conference and Exhibition, EAGE,Extendedabstracts, P075.

Bachrach,R., andT. Mukerji,2002,The physics of seismic reflections withinunconsolidated sedi-ments:Technologyfor nearsurface3D imaging usingdense receiver array: EOS, Transactions, American Geophysical Union,83,AGU FallMeeting,AbstractT22B–1141.

Baskir, C. J., and C. E. Weller, 1975, Sourceless reflection seismic explora-

tion: Geophysics, 40, 158.Claerbout, J. F., 1968,Synthesis of a layered mediumfromits acoustic trans-

mission response: Geophysics, 33, 264–269.——–, 1971, Toward a unified theory of reflector mapping: Geophysics, 36,

467–481.——–, 1985, Imaging the earth’s interior. Blackwell Scientific Publications,

Inc..Cole, S. P., 1995, Passive seismic and drill-bit experiments using 2-D arrays:

Ph.D. thesis, Stanford University.Derode, A.,E. Larose, M. Campillo,and M. Fink, 2003, Howto estimate the

Green’s function of a heterogeneous medium between two passive sen-sors? Application to acoustic waves: Applied Physics Letters, 83, 3054–3056.

Draganov, D., C. P. A. Wapenaar, and J. Thorbecke, 2004, Passive seismicimaging in the presence of white noise sources: The Leading Edge, 23,889–892.

Duvall, T. L., S. M. Jefferies, J. W. Harvey, and M. A. Pomerantz, 1993,Time-distance helioseismology: Nature, 362, 430–432.

Gazdag, J.,and P. Sguazzero, 1984,Migration of seismic data by phase-shift

plus interpolation: Geophysics, 49, 124–131.Liu, F., R. Stolt, D. Hanson, and R. Day, 2002, Plane wave source composi-

tion:An accurate phase encodingscheme forprestackmigration:72ndAn-nualInternational Meeting, SEG,ExpandedAbstracts, 1156–1159.

Rickett,J., and J. F. Claerbout, 1996, Passive seismic imaging applied to syn-thetic data:Stanford ExplorationProject,Annual Report, 92, 83–90.

Schuster,G. T., J. Yu, J. Sheng, andJ. Rickett,2004, Interferometric/daylightseismic imaging: Geophysics Journal International, 157, 838–852.

Shragge, J. C., B. Artman, and C. Wilson, 2006, Teleseismic shot-profile mi-gration:Geophysics,this issue.

Sun, P.,S. Zhang,andJ. Zhao,2001,An improved planewave prestack depthmigration method: 71stAnnual InternationalMeeting,SEG ExpandedAb-stracts, 1005–1008.

Wapenaar, C. P. A., J. Thorbecke,and D. Draganov,2004, Relationsbetweenreflection and transmission responses of three-dimensional inhomoge-neous media: Geophysical Journal International, 156, 179–194.

Zhang, L., 1989, Reflectivity estimation from passive seismic data:StanfordExplorationProject, Annual Report, 60, 85–96.


Imaging Passive Seismic Data

Documents

Transcript of Imaging Passive Seismic Data