Observation and analysis of frequency-dependent anisotropy

www.elsevier.com/locate/jappgeo

Journal of Applied Geophysics 54 (2003) 319–333

Observation and analysis of frequency-dependent anisotropy from

a multicomponent VSP at Bluebell-Altamont Field, Utah$

E. Liua,*, J.H. Queenb, X.Y. Lia, M. Chapmana, S. Maultzscha,H.B. Lynnc, E.M. Chesnokovd

aBritish Geological Survey, Murchison House, West Mains Road, Edinburgh EH9 3LA, UKbConocoPhillips Inc., Houston, TX, USA

cLynn Inc., 14732 F Perthshire, Houston, TX 77079, USAdUniversity of Oklahoma, Norman, OK 73019, USA

Received 23 April 2002; received in revised form 12 November 2002; accepted 20 January 2003

Abstract

In this paper, we present results from the analysis of a multicomponent VSP from a fractured gas reservoir in the Bluebell-

Altamont Field, Utah. Our analysis is focused on frequency-dependent anisotropy. The four-component shear-wave data are

first band-pass filtered into different frequency bands and then rotated to the natural coordinates so that the fast and slow shear-

waves are effectively separated. We find that the polarisations of the fast shear-waves are almost constant over the whole depth

interval, and show no apparent variation with frequency. In contrast, the time delays between the split shear-waves decrease as

the frequency increases. A linear regression is then applied to fit the time-delay variations in the target and we find that the

gradients of linear fits to time delays show a decrease as frequency increases. Finally, we apply a time-frequency analysis

method based on the wavelet transform with a Morlet wavelet to the data. The variation of shear-wave time delays with

frequency is highlighted in the time-delay and frequency spectra. We also discuss two mechanisms giving rise to dispersion and

frequency-dependent anisotropy, which are likely to explain the observation. These are scattering of seismic waves by

preferentially aligned inhomogeneneities, such as fractures or fine layers, and fluid flow in porous rocks with micro-cracks and

macro-fractures.

D 2003 Elsevier B.V. All rights reserved.

Keywords: Anisotropy; Fracture characterisation; Velocity dispersion; Frequency-dependent anisotropy; Multicomponent seismic

0926-9851/$ - see front matter D 2003 Elsevier B.V. All rights reserved.

doi:10.1016/j.jappgeo.2003.01.004

$ Presented at the 10th International Workshop on Seismic

Anisotropy, Tulzing, Germany, 14–19, April 2002. Revised version

submitted to Journal of Applied Geophysics (Proceedings of

10IWSA) on 4 Oct. 2002.

* Corresponding author. Tel.: +44-131-650-0362; fax: +44-131-

667-1877.

E-mail addresses: [email protected] (E. Liu),

[email protected] (J.H. Queen),

[email protected] (H.B. Lynn),

[email protected] (E.M. Chesnokov).

1. Introduction

The presence of micro-scale (grain) cracks and

macro-scale (formation) fractures is considered to be

one of the dominant causes of observed anisotropy in

hydrocarbon reservoirs. One commonly used method

to examine fracture-induced azimuthal anisotropy is

shear-wave splitting. The two basic parameters are the

polarisation direction of fast shear-waves, interpreted

E. Liu et al. / Journal of Applied Geophysics 54 (2003) 319–333320

as the strike of aligned vertical fractures and the time-

delay between the fast and slow shear-waves, giving

the degree of anisotropy (i.e. fracture density). Re-

cently, observational evidence suggests that the mea-

sured seismic anisotropy as inferred from time delays

of split shear-waves does actually depend on frequen-

cy (Marson-Pidgeon and Savage, 1997; Chesnokov et

al., 2001; Liu et al., 2001), which we believe has an

important implication in our understanding of the

causes of seismic anisotropy.

The interpretation of anisotropic measurements

made from seismic data requires theoretical models

that relate measurable seismic parameters (such as

polarisation and time delays of split shear-waves) to

macroscopically determined rock properties (e.g. frac-

ture density and orientations). Based on the assump-

tion that the scale-lengths associated with the cracks

and fractures are considerably smaller than the seismic

wavelength, a description of the average properties of

a medium will be sufficient, i.e. an equivalent (or

effective) medium description. Various equivalent me-

dium theories have been proposed (e.g. Thomsen,

1995; Hudson et al., 1996, 2001; Hudson, 1981;

Bayuk and Chesnokov, 1998; Chesnokov et al.,

1998; Liu et al., 2000; Pointer et al., 2000). These

theories have provided the foundation of anisotropy

analysis, but most theories fail to provide an adequate

explanation of velocity dispersion at ‘low’ or seismic

frequency and hence variation of anisotropy with

frequency is not predicted. It is also not possible to

determine the size of fractures (thus fracture volume or

storability) from seismic data based on conventional

equivalent medium theories. In those theories, veloc-

ities are given in terms of crack density, a single

parameter that depends on both the crack radius and

the number density of the cracks.

Two mechanisms which can introduce velocity

dispersion and thus frequency-dependent anisotropy

are the scattering of seismic waves in media with

preferentially aligned heterogeneities, such as fractures

or fine layers, and fluid flow in fractured porous rock.

The former has been investigated by Werner and

Shapiro (1999); and Chesnokov et al. (2001), while

the latter has been the subject of Magnitsky and

Chesnokov (1986); Bayuk and Chesnokov (1998);

Parra (2000); Tod and Liu (2002). Chesnokov et al.

(2001) have attempted to model the observed varia-

tions of shear-wave anisotropy with frequency using a

multiple scattering correlation approximation, aiming

at estimating the size of the scatterers (fractures).

Bayuk and Chesnokov (1998), Chapman et al.

(2002); and Tod and Liu (2002) have presented theo-

retical models to allow vertically aligned meso-scale

fractures inserted in porous rock to include multi-scale

fluid flow. Their models predict velocity dispersion at

‘low’ or seismic frequencies and can explain the

observed frequency-dependent seismic anisotropy.

In this study, we analyse multicomponent VSP data

acquired from a fractured tight gas reservoir in the

Bluebell-Altamont Field in the Uinta Basin, Utah. Our

work may be regarded as a continuous and comple-

mentary study of early work by Lynn et al. (1995,

1996, 1999) who have used P- and S-wave azimuthal

anisotropy to characterise fractured reservoirs. How-

ever, we focus our analysis on frequency dependent

anisotropy. In Section 2, we use a conventional

technique to process the four-component shear-wave

data, that is, rotating the four-component data into the

natural coordinate system to separate the fast and slow

shear-waves. The rotation is performed after a series

of band-pass filters have been applied so that aniso-

tropic parameters can be extracted for each of the

frequency bands. Our results show that the polar-

isations of the fast shear-waves are almost constant,

and show no apparent variation with frequency (ex-

cept at very low frequency). However, the time delays

between split shear-waves decrease as the frequency

increases. We apply a linear regression to fit the time-

delay variations in the target formation and find that

the gradients of the linear fits show a decrease as

frequency increases, indicating that anisotropy

decreases as frequency increases. In Section 3, we

apply a time-frequency analysis method based on the

wavelet transform to the data in order to highlight the

variation of shear-wave time delays with frequency.

Finally, in Section 4, we discuss two possible causes

of observed variation of anisotropy with frequency:

seismic scattering and multi-scale fluid flow in frac-

tured porous rock.

2. Data and multicomponent shear-wave analysis

for anisotropy

The geological setting of the Bluebell-Altamont

field, Uinta Basin in northeastern Utah, has been

E. Liu et al. / Journal of Applied Geophysics 54 (2003) 319–333 321

described in detail by Lynn et al. (1995, 1996, 1999).

A brief summary of their description is given below.

Gas in the Bluebell-Altamont field is produced from a

tight sand/shale reservoir in the Tertiary upper Green

River Formation at depths of approximately 6500 ft

(1981 m) to 8500 ft (2590 m). Individual lenticular

sands are encased in tight shales and carbonates and

vary from 5 to 20 ft (2 to 6 m), but they often stack

vertically to thicknesses over 80 ft (24 m). The local

structure is subhorizontal sediments with no faulting

observed at target intervals, and it has a very gentle

anticlinal closure that is less than 50 ft (15 m). Matrix

porosity and permeability in the reservoir rocks are

generally low (porosity is less than 8% and perme-

ability is less than 1 mD), and fracturing yields

substantially higher production rates. Consequently,

seismic detection of fracturing is potentially an im-

portant aid to field development. Two joint and

fracture sets were identified in surface mapping, one

striking N22jW to N32jWand one striking N60jE to

N77jE. Maximum horizontal stress was estimated as

N40jW to N45jW from borehole elongation ob-

served in four-arm calliper logs in two adjacent wells

and from the N40jW orientation of recent, nearby,

gilsonite dikes. These are seen as a natural hydro-

fracturing event, when over-pressured fluids fractured

the overlying rocks upon expulsion from the lower

Green River formation.

Lynn et al. (1995, 1996, 1999) have analysed

extensive datasets as part of a US Department of

Energy funded project. They have used both surface

and borehole P-waves and shear-wave 3D-3C data to

characterize fractured reservoirs in the Bluebell-Alta-

mont field. The P-wave response is an azimuthal

variation of AVO signature, which depends on

source-receiver azimuths relative to fracture strike.

Shear-wave multicomponent seismic data are used to

obtain fracture orientations and fracture intensity in

the reservoirs using the concept of shear-wave split-

ting (Crampin, 1985). Our interest here is mainly in

the understanding of the variation of seismic anisot-

ropy with frequency, and for this purpose, we re-

analyse the multicomponent shear-wave VSP data.

Four vertical (P-wave) vibrators and four horizontal

(shear-wave) vibrators were used for the VSP acqui-

sition. The S-wave vibrators were Amoco S-vibrators

with rotatable baseplate. We analyse only the 550 ft

(168 m) offset VSP shear-wave data, and the receiver

depths are between 2800 ft (853 m) and 8650 ft (2636

m). A total of 118 receiver positions with an interval

of 50 ft (15 m) of VSP data were acquired. Direct

evidence of vertical fractures from cores, and fractures

mapped on outcrop, were used to orient the nine-

component seismic lines.

Fig. 1 displays the horizontal four-component data

matrix that has been rotated to the acquisition coor-

dinate, i.e. in-line (X) and cross-line (Y) directions.

The top rows marked with XX and XY are from in-

line sources, and the bottom rows marked with YX

and YY are from cross-line sources. The first letter

denotes the source orientation, and the second the

receiver orientation. The data are displayed with true

relative amplitudes so that a direct comparison be-

tween different components can be made. We can

immediately see that there is strongly coupled energy

in the cross-components, i.e. energy from the in-line

source is recorded in the cross-line receiver (XY) and

energy from the cross-line source is recorded in the in-

line receiver (YX). This feature is usually a direct

indication of the presence of azimuthal or fracture-

induced anisotropy (Crampin, 1985; Liu et al., 1993;

Queen and Rizer, 1990). Conventional analysis of

multicomponent shear-wave data involves rotation

of horizontal four-component shear-wave data into

the natural coordinate system through the use of

standard methods such as Alford rotation (Alford,

1986), or the linear transform (Li and Crampin,

1993) with the aim of separating the two split shear-

waves by minimising the off-diagonal energy. The

rotated four-component data are displayed in Fig. 2,

which shows clearly that the off-diagonal energy has

been significantly reduced. Once the shear-wave data

are rotated into their natural coordinate system, the

fast and slow shear-waves are separated. The rotation

angle then represents the polarisation angle of the fast

split shear-wave, which is commonly interpreted as

the fracture orientation. A cross-correlation can be

applied to the fast and slow components to obtain the

time-delays between the two split shear-waves. Note

that the sample rate is 2 ms, and the data have been re-

sampled to 0.5 ms using a sinc interpolation function.

Fig. 3 (top) shows the polarisation angles obtained

through successive rotations after the data were band-

pass filtered into five frequency bands. The band pass

filter that we use is a zero-phased, since-squired tapered

filter (‘sufilter’ in the Seismic Unix package of the

Fig. 1. Original four-component shear-wave data that have been rotated to the acquisition coordinates, i.e. in-line (X) and cross-line (Y)

directions. The top rows with XX and XYare from in-line sources, the bottom rows with YX and YYare from cross-line sources. The first letter

denotes the source orientation, and the second the receiver orientation.


Fig. 2. Four-component shear-wave data that have been rotated to the natural coordinates through the use of a standard method (Alford

rotation), i.e., by minimising the off-diagonal energy in the original data matrix. XX section is for fast shear-waves, and YY section is for slow

shear-waves.


Fig. 3. Variation of polarisation of fast split shear-waves (top) and time-delays of split shear-waves (bottom) with depth after the data have been

band-pass filtered into five frequency bands. The angles are relative to the in-line component.


Fig. 4. Top: Same as Fig. 3 (bottom), but the only the time delays for the target formation between the depths of 6800 ft (2072 m) and 8650 ft

(2636 m) are displayed. The straight lines in each plot are from the linear regression algorithm to fit the variation of time delays for each

frequency. Bottom: Variation of anisotropy (in percentage) estimated from the gradient in Fig. 4a with frequency in the target interval between

the depth of 6800 ft (2072 m) and 8650 ft (2636 m). The error bars represent the uncertainty to the fit of time delays.



Colorado School of Mines). Except for the very low

frequency band between 0 and 10 Hz, the polarisations

are generally constant over the whole depth interval at

40j to 45j from the in-line direction, which agrees with

the direction of predominant fracture orientations of

N43jW in the study area (Lynn et al., 1999), and there

is no apparent dependence of polarisation on frequen-

cy. Fig. 3 (bottom) shows the variations of time delays

between fast and slow shear-waves. We can identify

three distinct intervals: In Interval I (from 2800 ft (853

m) to about 4000 ft (1219 m)), as receiver depth

increases, time delays linearly increases, indicating this

interval is seismically anisotropic. In Interval II be-

tween the depth of 4000 ft (1219 m) and 6800 ft (2072

m), the time delays remain almost constant, implying

this interval is isotropic for the propagating waves as

there is no further shear-wave splitting in this interval.

Below a depth of about 6800 ft (2072 m), the time

delays begin to increase abruptly. This interval (Inter-

val III), which is also the target of the reservoir in the

Bluebell-Altamont field, thus, shows strong anisotropy

(about 3% to 4%), which is attributed to the presence of

intense fracturing in the reservoir. Note that a layer-

stripping procedure is not necessary as there is no

Fig. 5. Examples of spectral plots for all 4-component shear-w

obvious change of the polarisation with depth, imply-

ing there is no change of fracture orientation with depth

in at least the interval between 2800 ft (853 m) and

8650 ft (2636 m). In particular, we see the variation of

time delays with frequency shown in Fig. 3 (bottom).

The variation of shear-wave time delays with frequency

was noticed by one of the authors of this paper (Heloise

Lynn, Lynn) and the results were included in a report to

the US Department of Energy in 2000.

The shear-wave anisotropy is interpreted as due to

the presence of open and aligned vertical fractures,

striking northwest in the Upper Green River Forma-

tion. If we assume that the magnitude of shear-wave

anisotropy (time delays between split shear-waves) is

proportional to the fracture density, then the highest

density of open, gas-filled fractures is interpreted to be

in the interval between 6800 ft (2072 m) and 8650 ft

(2636 m). In Fig. 4 (top), we plot the time delays at

the target interval between 6800 ft (2072 m) and 8650

ft (2636 m) estimated for five different frequency

bands. In general, time-delays show linear an increase

with depth, and a decrease as frequency increases. A

linear regression is applied to fit the time delay

variations with depth for each frequency band. Except

aves recorded at the receiver depth of 6800 ft (2072 m).


for the lowest frequency band (0–10 Hz), at which the

amplitudes are small (Fig. 5), we see a slight decrease

in the gradient of time delays, and this can be clearly

seen in Fig. 4 (bottom). Note that in Fig. 4 (bottom),

we have omitted the first point (0–10 Hz). However,

Tod and Liu (2002) have presented an alternative

model that predicts an increase of anisotropy with

frequency before it begins to decrease with frequency,

and the low anisotropy at 0–10 Hz supports their

theoretical prediction.

Fig. 5 shows the examples of spectral plots for all

four-component shear-waves recorded at the receiver

depth of 6800 ft (2072 m). The data have a frequency

band between 10 and 35 Hz. One may say that the

band-pass filtering technique used in Figs. 3 and 4

might be one of the factors of the observed variation

of anisotropy with frequency. According to the un-

certainty principle, we cannot have optimal resolution

in time and frequency at the same time. This restricts

to what we can do with our data using the band pass

filtering technique. However, we have performed a

series of tests on synthetic data generated using

Fig. 6. Variation of time-delays of split shear-waves with depth from a synth

filtered into five frequency bands. The synthetic data were computed usi

anisotropy.

frequency-independent elastic constants, and the syn-

thetic data are band-pass filtered in exactly the same

way as the real data, no frequency-dependent time-

delays are observed. An example of such test is given

in Fig. 6, demonstrating that the band-pass filtering

technique does not introduce frequency-dependency.

3. Time-frequency analysis

In this section, we shall present a technique to

process multicomponent shear-wave data based on a

continuous time-frequency analysis. One of the

advantages of such analysis is that frequency content

from multiple arrivals, such as the scattered waves and

split shear-waves, can be identified. In our analysis,

the continuous wavelet transform with a Morlet wave-

let used (Niitsuma et al., 1993).

Our analysis procedure is described below. Firstly,

the four-component data are rotated into the natural

coordinate system, i.e., fast and slow shear-waves are

separated into different components as discussed in

etic multicomponent VSP dataset after the data have been band-pass

ng Hudson’s (1981) model which predicts no frequency-dependent

Fig. 7. Time-frequency spectra of the fast and slow shear-waves recorded at the receiver depth of 6800 ft (2072 m). Top plot is for the fast shear-

wave and bottom plot is for the slow shear-wave at this depth.


Time-frequency analysis

Time-frequency analysis

Depth (m)

dt (ms)50

45

30

25

20

15

10

5

0

35

40

dt (ms)50

45

30

25

20

15

10

5

0

35

40

Fre

quen

cy (

Hz)

0

5

10

15

20

25

30

351000 1200 1400 1600 1800 2000 2200 2400 2600

Depth (m)

Fre

quen

cy (

Hz)

0

5

10

15

20

25

30

352000 2100 2200 2300 2400 2500 2600

Fig. 8. Time-frequency analysis of shear-wave splitting. It shows a colour-coded map of the time-delays and frequency spectra. The colour bar

shows the time-delay in milliseconds. The top plot displays the whole depth intervals and bottom plot shows the time-delays for the target

formation.



the previous section. Secondly, we apply the wavelet

transform with a Morlet wavelet to the fast and slow

shear-wave components to obtain time-frequency

spectra (or local spectra) of recorded waves. The

number of samples used in the wavelet transform is

32 samples. Examples from trace number 80 (receiver

depth at 6800 ft (2072 m)) are shown in Fig. 7. We

can see a clear difference in travel times between the

fast and slow shear-waves, and also the difference in

frequency spectra between the fast and slow shear-

waves. Thirdly, we pick the maximum amplitudes and

their corresponding arrival times for each frequency in

the transformed fast and slow components [or their

power spectra]. Finally, the time-delays between split

shear-waves for each frequency are obtained by sub-

tracting the travel-times corresponding to the maxi-

mum amplitudes (or power spectra) of the transformed

fast and slow components. This procedure is repeated

trace by trace for all traces to build complete time-

delay and frequency spectra.

The results from the analysis procedure described

above are given in Fig. 8 (top). It shows a colour-

coded map of the variation of time-delays with

frequency for all depths. The colour bar is the time-

delays in milliseconds. The results confirm the in-

crease of time-delay with depth (colour changes from

light yellow to red) and decrease of time-delays as

frequency increases (colour changes from yellow-red

to light green-yellow). Fig. 8 (bottom) displays the

same colour map as Fig. 8 (top), but highlights the

target interval. Clearly, we see an increase in time-

delays with depths (colour changes from light yellow

to red), and a decrease of time-delays with frequency

(colour changes from red to yellow). This is basically

the confirmation of the result in Fig. 4, where a band-

pass filter was applied. The time-frequency analysis,

thus, can give a continuous variation of time-delays

with frequency.

4. Discussion: mechanisms of frequency-dependent

anisotropy

The phenomenon of seismic anisotropy is now in

widespread use as a tool for investigating fractured

rock, accessing sub-seismic scales of importance to

fluid migration. This advance has significantly in-

creased our ability to measure sub-seismic properties

of the rock-mass from seismic measurements. Esti-

mates of fracture intensity and orientation can be

found using existing equivalent medium theories cited

in Section 1. However, the application of seismic

anisotropy is limited by the necessary theoretical

constraints of dilute concentration and very small

scale-size to wavelength ratios, as heterogeneous

and fractured porous rock may be characterised by

observations in different critical wavelength ranges,

each reflecting different physical mechanisms. This

limitation has not yet been satisfactorily addressed.

We do not claim that frequency-dependent anisot-

ropy is unexpected or indeed surprising. However,

there are very few reports of frequency-dependent

anisotropy in the literature, especially in exploration

geophysics community. Evidence has been reported

before for earthquake data, e.g. by Marson-Pidgeon

and Savage (1997). They show a systematic increase

in time-delay with period, i.e. time-delay decreases

with frequency, which is very similar to the observa-

tion reported in this paper. Marson-Pidgeon and

Savage (1997) offer three possible explanations: (1)

shear-wave splitting resolution versus waveform peri-

od; (2) multiple layers of anisotropy; or (3) seismic

scattering by heterogeneities in the crust. If a proper

mechanism is understood, it may provide the means of

going beyond the concept of the conventional static

equivalent medium theories to potentially map the

size of meso-scale fractures whose lengths are much

larger than microcracks or grain boundary pores, but

less than seismic wavelength, and to extract informa-

tion about fluid flow (or transport) properties in

reservoir rocks. This is a subject in our companion

paper by Liu et al. (2003), where we have presented a

quantitative interpretation and also shown comparison

of synthetic results with the observed frequency-

dependent anisotropy using the multi-scale fracture

model presented by Chapman et al. (2002, this issue).

Here, we discuss the two most likely mechanisms

that can cause velocity dispersion and, hence, fre-

quency-dependent seismic anisotropy and some of the

implications from our study.

4.1. Seismic scattering

It has long been known by earthquake seismologists

that wave scattering is frequency-dependent (e.g.

Leary and Abercrombie, 1994; Wu 1981). It has also

E. Liu et al. / Journal of Applied G

been recognised that heterogeneities will produce ap-

parent anisotropy (Marson-Pidgeon and Savage,

1997). Frequency-dependent anisotropy is unarguably

related to the scattering of seismic waves in heteroge-

neous rocks. A typical example is the wave propaga-

tion in finely layered media as demonstrated by

Shapiro et al. (1994); Werner and Shapiro (1999),

who show that anisotropy differs for waves with

different frequencies. This leads to the conclusion that

heterogeneous materials with certain alignments or

ordered distributions must behave as an anisotropic

medium to elastic waves at some frequencies (e.g.

Chesnokov et al., 1998). The presence of a heteroge-

neous medium instead of a homogeneous isotropic

medium can produce frequency-dependent anisotropy,

in which the influence of heterogeneities decreases as

frequency increases. The scale of heterogeneities can

be constrained by the fact that they need to be small

enough to cause effective anisotropy instead of scat-

tering. This requires a quasi-homogeneous propagation

regime which can be expressed mathematically as ka

«1 (for example, say ka < 0.1, e.g. Sato and Fehler,

1997), where k is the wavenumber, and a is the scale-

length of the heterogeneities. For the data presented in

this paper, the dominant frequency is f = 25 Hz, and the

average shear-wave velocity is about V= 7000 ft/s

(2133 m/s). We expect that scale-lengths smaller than

about 10 m (V/fc 2133/25� 0.1) would cause effec-

tive anisotropy. Heterogeneities larger than 10 m will

cause scattering of seismic waves, and so reduce the

time delays due to effective anisotropy (the discussion

here follows that of Marson-Pidgeon and Savage,

1997).

Chesnokov et al. (2001) present a model based on

the correlation approach addressing frequency depen-

dent anisotropy when there is order in the orientation

of contrasting inhomogeneities. Anisotropy can only

be observed when the wavelengths of propagating

waves (P or S) are much greater than at least one (of

possibly many) scale lengths associated with the sizes

of inhomogeneities, i.e., in the case where the assump-

tions of the long wavelength approximation are satis-

fied. As frequency increases and wavelengths become

commensurate with these scale-lengths, anisotropy

becomes smaller and smaller. Beyond a certain tran-

sition frequency, it becomes minimal, with the prop-

agation being better characterised by discrete scatter-

ing effects.

4.2. Fluid flow in fractured porous rock

The other likely cause of frequency-dependent an-

isotropy is related to the fluid flow in fractured porous

rock. There have been several studies aimed at predict-

ing the velocity dispersion in porous rock and, hence,

variation of anisotropy with frequency. Bayuk and

Chesnokov (1998) investigate the correlation of elastic

wave anisotropy of P- and shear-waves and transport

properties of cracked porous rock and conclude that

seismic waves can be used to distinguish fluid proper-

ties (oil and gas) of reservoir rocks. Chapman et al.

(2002) have developed a model by placing a set of

aligned fractures into porous media, based on a squirt

flow model. Coupled fluid flow motion occurs on two

scales: the grain scale and the scale of the fractures. A

consequence of this is that the predicted anisotropy

becomes frequency-dependent, with the form of the

dependence related directly to the fracture scale. Pre-

vious estimates of the squirt flow frequency have given

high values, typically between the sonic and ultrasonic

bands. This has led to the suggestion, implicit in

Thomsen’s (1995) equant porosity model, that at seis-

mic frequencies, there should be little dispersion.

Chapman et al. (2002) demonstrated that in the pres-

ence of larger scale fractures, substantial frequency

dependence may be expected in the seismic frequency

ranges and, therefore, it is not safe to treat seismic

frequency as a low frequency limit. Tod and Liu (2002)

have presented an alternative model that describes a

fluid flow mechanism between elliptical cracks (bed-

limited cracks) that produces a frequency dependence

in the resulting effective material parameters, and

hence in the shear-wave splitting. They demonstrate

that the effects of fluid flow (either gas or liquid) are

non-negligible and, thus, an important factor contrib-

uting to observed frequency-dependent anisotropy.

eophysics 54 (2003) 319–333 331

5. Summary

We have provided observational evidence showing

the variation of shear-wave anisotropy with frequen-

cy from analysis of multicomponent VSP data in a

fractured gas reservoir. There is no apparent varia-

tion of polarisation with frequency, which is not

surprising as we do not expect that stress pattern

and, thus, spatial distribution of fracture orientation


would change with frequency. Time-delays between

split shear-waves, which are proportional to fracture

density, show a decrease as frequency increases. We

have presented a processing technique based on the

time-frequency representation of transient signals to

extract time-delays and frequency information. Time-

frequency analysis of shear-wave splitting enables us

to detect multiple arrivals in time, and variations in

shear-wave splitting with frequency. The method we

have proposed in this paper can be used to analyse

anisotropy and shear-wave splitting.

Acknowledgements

We thank John A. Hudson, Simon Tod (Cambridge

Univ.), Kurt Nihei, Seiji Nakagawa, Larry Myer, Ernie

Majer, Tom Daley (Lawrence Berkeley National Lab.),

and our colleagues Alexander Druzinin, David Booth

and Russ Evans for their comments on this manuscript.

We thank Professor Dirk Gajewski for many insight

discussions and for reminding us of the limitation of

band-pass filtering technique used to produce Figs. 3

and 4, and Claudia Vanelle and an anonymous reviewer

for their constructive comments that have significantly

improved the readability of our paper. The VSP data

presented here were acquired as part of the US DOE

project (Contract number DE-AC21-92MC28135).

The Seismic Unix code ‘sufilter’ of the Colorado

School of Mines was used to perform band-pass

filtering, and the BGS/EAP SWAP package was used

for anisotropic parameter estimation from shear-wave

data. This work was supported by the Natural En-

vironment Research Council (UK) through project

GST22305 as part of the thematic programme Under-

standing the micro-to-Macro Behaviour of Rock Fluid

Systems, and Edinburgh Anisotropy Project (EAP),

and is published with the approval of the Executive

Director of the British Geological Survey and the EAP

sponsors.

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Observation and analysis of frequency-dependent anisotropy