Fracture detection using crosshole surveys and …...deduced from other geological and hydrological observations. Analyses of CHS data including modelling with synthetic seismograms

Geophys. J. Znt. (1991) 107, 449-463

Fracture detection using crosshole surveys and reverse verticalseismic profiles at the Conoco Borehole Test Facility, Oklahoma

Enru Liu,’ Stuart Crampin’ and John H. Queen2’ Britkh Geological Survey, Murchkon House, West Mains Road, Edinburgh EH9 3LA, UK2 Exploration Research and Services, Conoco Inc., PO Box 1267, Ponca City, OK 74603, USA

Accepted 1991 July 1. Received 1991 July 1; in original form 1991 April 6

SUMMARYShear waves in combined crosshole surveys (CHSs) and reverse vertical seismicprofiles (RVSPs) at the Conoco Borehole Test Facility, Oklahoma, are analysed toexamine the relationship between shear-wave propagation and natural fracturesystems. The surveys cover a range of azimuths and angles of incidence, and give thepossibility of studying fracture-induced azimuthal anisotropy in some detail.

The data display several features characteristic of seismic anisotropy. Shear-wavesplitting, displaying substantial time delays up to 7 ms, for source-geophonedistances of less than 50 m, suggest large fracture densities. Estimates of fastshear-wave polarizations and time delays confirm the N75”E f 10” fracture strikededuced from other geological and hydrological observations. Analyses of CHS dataincluding modelling with synthetic seismograms suggest that, at least the dominantfracture set, is rotated by 20” from the vertical.

One of the most important results of this study is the positive identification ofguided waves propagating between wells along interfaces with sufficient velocityconstrast in CHS profiles. It appears that combinations of CHSs and RVSPs offerunique possibilities in evaluating fracture parameters at shallow depths. This couldbe important for the study of fluid flow at shallow depths in hydrologicalinvestigations.

Key words: crosshole surveys, fractures, guided waves, reverse VSPs, seismicanisotropy, shear-wave splitting.

1 I N T R O D U C T I O N

In recent years, there have been an increasing number ofreports of observations of shear-wave splitting interpreted asindicating fracture-induced (crack-induced) seismic ani-sotropy. These have usually been observations of reflectionsurveys (Alford 1986; Willis, Rethford & Bielanski 1986)and vertical seismic profiles (VSPs) (Beydoun, Cheng &Toksijz 1985; Crampin et al. 1986; Johnston 1986, amongstothers) in hydrocarbon reservoirs, and of shear wavesrecorded immediately above small earthquakes (Crampin etal. 1980; and many others, reviewed by Crampin 1987).Fractures can be a significant feature of hydrocarbonreservoirs where their presence (either natural, or inducedby hydraulic pumping) may increase the productivecapacity. Many reservoirs with low matrix permeabilitywould not be commercially attractive without a natural orinduced system of fractures. Fractures at usually shallowdepths are also important for the fluid flow in manyengineering and hydrological applications. Recognition and

observation of shear-wave splitting offers the possibility ofusing shear waves to evaluate the fracture parameters:strike, dip, fracture density, and pore-fluid properties(Crampin 1987). Crampin (1990a) has suggested that suchtechniques also offer possible ways of monitoring reservoirdevelopment during enhanced oil recovery procedures.However, reservoir description and monitoring recoveryrequire high-frequency and broad-band seismic data. Apotential technique, as suggested by Nur (1989), is to takeadvantage of the distribution of injection and recoverywells, to monitor the reservoir by mounting crossholesurveys between wells.

As a contribution to such studies, a combination ofcrosshole surveys (CHSs) and reverse vertical seismicprofiles (RVSPs) were investigated at five shallow boreholes(down to 50 m) at the Conoco Borehole Test Facility(CBTF), in Kay County, Oklahoma (Queen & Rizer 1990).The study area is highly fractured with two distinct fracturesets visible at surface outcrops. The Conoco downholerotary source, generating horizontally polarized shear-wave

449

450 E. Liu, S. Crampin and J. H. Queen

radiation, was deployed downhole, and three-componentgeophones were located in wells (for CHSs) and on thesurface (for RVSPs).

The data show several features characteristic of seismicanisotropy. In particular, three-component seismograms inRVSPs display shear-wave splitting with oriented polariza-tions, where the maximum time delay between the splitshear waves is up to 7 ms over source-geophone distances ofless than 50 m. These time delays are large in comparisonwith typical delays of less than 50 ms over source-geophonedistance of between 1000 and 2000 m seen in many VSP datasets. This relatively large time delay suggests either thepresence of large fractures or large crack densities. Theamplitudes on the vertical components in CHSs are large incomparison with the horizontal amplitudes, for both in-lineand cross-line (X-line) horizontally polarized sourceradiation, even for the azimuths where the source andgeophones are assumed to be in the dominant fracturedirection. Modelling with synthetic seismograms suggeststhat these large vertical amplitudes are caused by thenon-vertical alignment of the fractures.

Synthetic modelling also demonstrates that the bulk of theenergy in these particular CHS profiles, which displaysdistinctive particle motion, can be interpreted as guidedwaves (channel waves or interface waves), which aretrapped by impedance contrasts across horizontal interfacesbetween the wells. Such waves are modal phenomenaresulting from interference between direct, reflected,refracted, and mode converted waves, at high incidentangles in a multilayered structure. These guided waves offerwavepaths, where most of the energy is trapped near aninterface, or near a particular layer, which may be useful formonitoring conditions in particular zones of interest, such asreservoirs undergoing EOR.

We determine the fracture parameters for both CHS andRVSP surveys. The results are consistent with the otherindependent measurements from geology and hydrology(Queen & Rizer 1990). We confirm these analyses bymatching fullwave synthetic seismograms to the observeddata sets.

2 SITE GEOLOGY

The CBTF site in Kay County, north central Oklahoma, is ageologically well-characterized area documented by Queen& Rizer (1990). Surface structure consists of low-amplitudefolds overlying an approximately 50 km wide zone ofdifferentially uplifted blocks bordered by northeast andnorthwest trending faults active in the Palaeozoic. Shallowstructure in this area consists of low-amplitude foldsoverlying some of those faults. Surface rocks consistprimarily of limestones and shales of the Lower PermianChase Group. Surface structure in this area is subtle anduniform, characterized by a regional dip of less than 1.5” tothe west-southwest with the velocity structure given in Fig.1. Fig. 2 shows the surface and subsurface fracture patternsin a neighbouring outcrop of the Fort Riley Limestone,where the near-orthogonal sets of near-vertical fractureshave been mapped by various techniques described byQueen & Rizer (1990). There is a systematic set strikingabout N75”E and a non-systematic s e t a t N25”W

CONOCO CBTF SITE

1Ve&ty (L-n/s) 4

Figure 1. Shallow P-wave and shear-wave velocity structurewell-logs at the Conoco Borehole Test Facility, Oklahoma.

from

(non-systematic fractures generally terminate againstsystematic).

Hydrological tests, indicating high permeability in theN75”E direction, suggest that the dominant fracture is alsoin this direction (Queen & Rizer 1990). Experienceelsewhere indicates that this direction will be close to thedirection of maximum horizontal stress (Crampin & Booth1989). The distribution of fractures controls the fluid flowand hence the reservoir porosity and permeability, and sucha system of aligned fractures will necessarily result in

Oriented Sample,4 Road Cut

--J-I-\’ -- y/-

-q- ,i,+ ’ As

-i-

k

e*

\

‘1

L

%F\

Surface fractureE pattern

-30 m

Figure 2. Map of surface fracture patterns at a nearby outcrop ofFort Riley Limestone and rose diagram of fracture orientations(after Queen & Rizer 1990).

anisotropic permeability. Consequently, there is nowgrowing interest in fracture-related reservoir permeability(Gavrilenko & Gueguen 1989; Gibson & Toksijz 1990;Schoenberg 1991).

North central Oklahoma is part of the midcontinent stressprovince, characterized by NE-SW trending horizontalcompression (Zoback & Zoback 1980). Various techniquesincluding borehole break-outs, hydraulic fracturing, andanelastic recovery tests have been used to measure the localstress. The average stress direction is approximatelyN75”E f 20”, which is subparallel to the dominant fracturedirection.

Queen & Rizer (1990) analysed shear-wave splitting in aVSP data set from an adjacent deep borehole in the samearea and concluded that polarization of the leading splitshear waves and azimuthal time delay variation areconsistent with the estimated fracture orientation of N75”E.

3 D A T A S E T S

Figure 3 is a plan of the CBTF site. The five boreholes,GWl to GW5 marked with circles, are shallow 50 m deepwells used for the CHSs and RVSPs profiles reported here.For the CHSs, sources were located at depths between 3 and41 m with about 0.6 m spacing in borehole GW5, andthree-component geophones were deployed in boreholesGWl to GW4 for the CHS surveys at depths ofapproximately 5 to 42 m with a spacing of about 3.7 m. TheRVSP surveys were carried out at boreholes GW3 and GW5(only GW3 data will be analysed here), where the sourceswere located at depths between 1.5 and 38.4 m with about0.6 m spacing. Fig. 4 shows the RVSP recording geometryaround GW3. The recording was carried out in two phases:two orthogonal lines of increasing offset, surface geophonesGl to G4, and G5 to G8; and an equally spaced arc of 160”with offset of 7.6 m, geophones G9 to G16. Note that onlysignals from every other source depth will be plotted for theRVSPs. The detailed source-receiver parameters for CHSsand RVSPs are given in Tables 1 and 2, respectively.

All data were recorded with the Conoco rotary source,which is rotated in both clockwise and anticlockwisedirections and radiating horizontally polarized shear waves.

Conoco Test SiteKay County, Oklahoma

Nt 33-1

l

33-3 l l 33-2

33-4 00 GW-I

0GW-20

GW-50 GW-3

0GW-4 3 0 m

Figure 3. Plan of wells at the Conoco Borehole Test Facility, KayCounty, Oklahoma. The open circles are the shallow boreholes (to50 m) used in the CHS and RVSP experiments reported here. Solidcircles are deep boreholes to 1000 m.

Well Distance Top

GWI

GW2

GW3

GW4

from GWS

(ml52.33

88.66

43.28

52.79

source

depth

W-43

3

3

3

Table 1. Source and geophone positions for CHSs. All data wererecorded with the source in well GW5, and depths are relative totop of GW5.

Source Top Geophoneincrem. geophone increm.

depth

Cm) (m) Cm)0.6 5.39 3.66

0.6 5.39 3.66

0.6 5.57 3.66

0.6 5.39 3.66

Fracture detection using CHS and RVSPs 451

R V S P S U R F A C E G E O P H O N E L O C A T I O N S

16 15A A 14A 0

13 7 AA

6 A5 AA

GW-3 12

8

w0 A

11A

1 10A A

92 AA

3A

4 5mA -

Figure 4. Recording geometry for the RVSP experiments forConoco borehole source tool in the GW3 well. The recording was intwo phases, radial lines, geophone Gl to G4 and G.5 to G8, and anazimuthal arc of 160” at radius 7.6 m, geophone positions G9 toG16.

These are then demultiplexed and sweep correlated beforedecomposing into linear equivalents of radial and transversecomponents (in-line and X-line sources, respectively), whereorientations were based on a compass attached to thesource. The three-component recorded traces have been

Table 2. Geophone posi-tions for RVSPs with sourcein GW3 every 0.6 m from1.5 to 38.4m.Geophone Geophone Geophonenumber azimuth offset

WOW Cm)I 160.5 4.51

2 160.5 7.62

3 160.5 10.72

4 160.5 13.78

5 65.7 4.51

6 65.7 7.62

7 65.7 10.72

8 65.7 13.78

9 141.7 7.62

IO 123.7 7.62

II 105.5 7.62

12 87.5 7.62

I3 51.5 7.62

14 33.5 7.62

I5 15.5 7.62

16 -2.5 7.62


reoriented into vertical, radial (in-line), and transverse(X-line), components with rotations about the vertical(based on a compass attached to the geophone sonde for theCHSs). The source has a frequency band of 50 to 300 Hz.The sampling rate is 1 ms for the crosshole data, but whenplotting the particle motions in polarization diagrams (PDs,or hodograms), the traces were resampled at 0.5 ms using afast Fourier transform, to introduce some smoothing.

GW5-GWl(4 In-Linelxx I I

GeophoneX-Line Vertical Depth

I IXY I I I Ixz I I 1 Cm)

10

E 207+ 30

is 40

2cn

10

E7 20A

30

40b 150 0 150 0 150

TIME IN MSEC

GWS-GWI (X-LINE SOURCE)

R-T PLANE V-T PLANE2, M

l 514.63 H NT2

v-7

15.85 H N- W-

17.07 H N- 3

r

18.29 H N- ap

r

19.51 H N-C%

*ET-

20.73 H N- 8

r

21.95 H N-B

*$7-

23.16 H N-

T

24.38 H “-7

r

25.60 HN ?

26.82 H N-

7

28.04 H N-F

0 50 0

R-T PLANE

14.63

PLANE

Npe[;+mi

15.85

17.07

18.29

19.51

20.73

21.95

23.16

24.30

25.60

26.82

20.04

25 75 25 75

TIME IN MSEC TIME IN MSEC

3.1 Crosshole data

Figure 5 shows six-component (two source orientations andthree-component recordings) geophone gathers and selectedPDs, to geophones at a depth of 23.7 m in wells (a) GWl,(b) GW2, and (c) GW4 from a range of source depths inGW5 (Table 1). The numbers in the top left corners of someof the PDs indicate the gains applied to the original signals

GW5GW2 GeoDhone(b) In-Line

-s

(I)

10

2 2032 30

40I I I I I I I I I I0 150 0 150 0 150

TIME IN MSEC

GW5GW2 (X-LINE SOURCE)

Figure 5. Observed common geophone gathers and selected PDs for CHS profiles to geophones at a depth of 23.7 m in wells (a) GWl,(b) GW2, and (c) GW4 for a source at a range of depths every 1.2 m from 3 to 40 m in well GW5. The seismograms are -displayed in asix-component format (two source orientations and three-component recordings), where X and Y are the in-line and X-line components,respectively. All depths are relative to the top of the GW5 well, and three-component sections display true relative amplitudes for each sourceorientation. The arrow marks a shear-wave reflection from the basement. The 10 ms PDs are displayed for the horizontal R, T, and thetransverse vertical T, V planes for the X-line source orientation. The numbers in the top left corners of some of the PDs indicate the gainsapplied to the original signals relative to the unnumbered PDs.

GW5GW4 GeophoneCc) In-Line X:Lmelxx I I / I I

I I I I I k I0 150 0 150

TIME IN MSEC

Vertical Depth(m)

GWS-GW4 (X-LINE SOURCE)

R-T PLANE

20.73

23.16

TIME IN MSEC

Figure 5. (continued)

relative to the unnumbered PDs. Note that we displaycommon geophone gathers because they typically showmore regular variation between different paths thancommon source gathers. The reason for this is that theanisotropic polarizations at any geophone are necessarilydominated by the anisotropic structure near to the geophonesite, so that records in common geophone gathers have allbeen filtered (modified) by the same near-geophonestructure. Common source gathers, where the waveformsare dominated by possibly different near-geophone struc-tures, usually show much more variation from path to path.Note also that the waveforms of the seismograms for thein-line sources are more complicated than from the X-linesources because of reverberations and mode’ conversions inthe multilayered structure (Fig. 1). This is so even for

Fracture detection using CHS and RVS?s 453

synthetic seismograms (see Fig. 14, below). Consequently,we display PDs only for the seismograms from the X-linesources. The seismograms and PDs from these X-linesources show almost equal amplitudes on the horizontalradial and transverse components. All figures in this papershow true relative amplitudes unless specified otherwise, sothat amplitudes of radial, transverse, and vertical com-ponent seismograms and PDs may be directly compared.

A reflection from the basement is marked in Fig. 5(c)(visible only on some components). Apart from this arrival,almost all signals display several or many cycles of almostmonotonic particle motion on all three components, and it isneither possible nor appropriate to search for separate bodywave arrivals.

A remarkable feature of the seismograms is that thedominant energy is on the vertical components for bothin-line and X-line horizontal source orientations. This is soeven in Fig. 5(b), where the ray paths between sourceborehole (GW5) and geophone borehole (GW2) arebelieved to be approximately in the plane parallel to thedominant fracture directions (Fig. 2). The CBTF siteappears to have relatively uniform horizontal layering, andit is unlikely that the local structure can produce such strongvertical components. It is also unlikely that such anomalousvertical components are due to the rotary sources, whichhave been thoroughly calibrated elsewhere. However,examples of synthetic modelling show possible explanations:strong vertical components may be generated in an isotropicmedium if a X-line source is not strictly in the horizontalplane (or an in-line source is not strictly radial) (Section6.1), or in an anisotropic (cracked) medium if there arenon-vertical cracks in the rockmass (Section 6.2). Since theexpected deviation of these shallow wells is small, the mostprobable explanation of the dominant vertical energy isthough to be non-vertical cracks in the rockmass.

The seismograms in Fig. 5 show marked variations ofamplitude with source depth. The largest amplitudes appearto be associated with sources at depths near to levels wherethere are interfaces with strong impedance contrasts. Suchsources may generate guided waves tied to high contrastinterfaces which act as waveguides channelling the energyparallel to the layering. Lou & Crampin (1991) suggest thatalmost any solid/solid interface can support such guidedwaves if appropriate source and geophone depths, andsource polarizations and frequencies can be selected. Thismeans that although initial arrivals in Fig. 5 could be bodywaves, the large-amplitude reverberations over many cyclesare normal-mode guided waves. Note that in some records(e.g. Fig. 5c), there is a sudden decrease of shear-waveamplitudes from the X-line source for sources in the lowerpart of the Fort Riley Limestone layer. This may be due tothe existence of large fractures at this azimuth. The effectsof large fractures on amplitudes are now under investi-gation, and will not be discussed here.

These guided modes would separate into a family ofRayleigh waves, with elliptical motion strictly in thevertical/radial plane, and Love waves, with linear motionstrictly in the horizontal transverse plane, if the structureconsisted of plane horizontal isotropic layers. In contrast, ina structure of horizontal anisotropic layers, the distinctfamilies of Rayleigh and Love modes combine into a singlefamily of generalized modes (Crampin 1970; Crampin &


Taylor 1971) with elliptical 3-D particle motion. The PDsdisplay elliptical motion with major axes inclined to thevertical and radial directions depending on the symmetrydirections through the particular anisotropic structures. Suchmotion is typical of the single family of generalized modescharacteristic of modal propagation in structures containingazimuthal anisotropy (Crampin 1975, 1981).

The observed particle motions for selected traces shownin Fig. 5 are elliptical in both vertical and horizontal planes.Such elliptical particle motions are typical of thepropagation of normal generalized mode surface andchannel waves propagating in structures with azimuthalanisotropy (Crampin 1975) indicating that the seismogramsin Fig. 5 are dominated by guided waves. The variationswith direction of propagation of these patterns of elliptical

RVSP-Gil GeoDhoneDepth

WC

10

i+.-7 20

E

30

al nn

gI I I ‘II I I I-

O ’cn10

E‘-

220

3 0

40

0I I I I I I I

150 0 150 0 150

TIME IN MSEC

@) Depth0-Q

15.24

17.68

20.12

22.56

24.99

27.43

29.87

32.31

In-LineR

!sclT

f3J

I3

B

%

X-Line

R

4

d@

H

4

P

+

w

&

1

Figure 6. (a) Observed six-component common-geophone gathersfor in-line and X-line RVSPs sources at a range of depths every1.2 m from 1.5 to 36 m in well GW3 recorded at surface geophoneGil. Sections of each component are separately normalized.(b) Polarization diagrams of horizontal particle motion of theshear-wave arrivals for in-line and X-line source orientations atspecified depths.

motion are characteristic of the orientation of theanisotropic structure, and in some cases may be directlyindicative of a particular anisotropic symmetry orientation(Crampin 1975, 1981).

The ringing nature of the signal on the two horizontalcomponents of the CHS from GW5-GW2 in Fig. 5(b) is ofspecial interest because this azimuth is believed to be in thedirection of the dominant fracture set (N75”E). Queen &Rizer (1990) reported a similar phenomenon from a VSPdata set in an adjacent deeper well. This wave could be afracture-related tube wave, which requires further study.

3.2 RVSP data

In the analysis of the RVSP data, we examine a selection ofthe data, which appears to be reasonably consistent with thewhole data set. Fig. 6(a) shows six-component seismogramsfor the RVSP to geophone Gil (see Fig. 4 and Table 2),and horizontal PDs at a range of depths from in-line andX-line sources.

Arrivals from the most shallow sources display stronglydispersed surface-wave motion. At least two generalizedmode wavetrains appear to be present, with motion on allthree geophone components. The fracture-induced aniso-tropy in near-surface layers is expected to be complicated(Crampin 1990b). We have not attempted to match any ofthe RVSP data sets with synthetic seismograms as the detailsof the comparatively high-frequency (150 Hz) records arelikely to be dominated by this near-surface structure.

4 ISOTROPIC BODY WAVE RAY TRACING

The shallow isotropic velocity structure at the CBTF site inFig. 1, listed together with the estimated attenuation Q inTable 3, has several pronounced velocity contrasts of up to50 per cent. The high-velocity Fort Riley Limestone layerbetween about 15 and 30 m may lead to severe ray bending

Table 3. Structure of the untracked matrix at theConoco Borehole Test Facility. Isotropic velocityfrom Fig. 1, and attenuation, Q, from Section 6,below.

Layer

I

23456789IOIII21314I5I6I7

Thickness "P(m) (m/s)6.4 710I.2 9144.9 17060.03 30480.06 17061.2 4115

2.4 1829

11.6 411.5

5.5 2212

2.7 29024.3 20115.2 30783.0 42363.7 2453IO.1 41157.6 2194

Q) 4115

“s P Q(m/s) (gm/cm’)

190 2.00 10457 2.00 20356 2.00 20914 2.00 20305 2.00 202072 2.42 50762 2.42 502072 2.42 50914 2.42 201219 2.50 20823 2.24 201584 2.48 100

2182 2.59 100

1006 2.42 1002118 2.47 100

902 2.43 100

2118 2.64 100

CRQSSHOLE

0aFigure 7. Ray tracing through the isotropic structure in

RVSP

(b)

Fig. 1 forcommon geophone gathers in: (a) CHSs to geophones at 9, 20, and38 m; and (b) RVSPs to a geophone at an offset of 7.6 m.

at the high-impedance limestone/shale contrasts above andbelow the limestone. Fig. 7(a) shows isotropic shear-waveray tracing for common geophone gathers at three depths inCHSs. The bending results in the ray paths being close tovertical outside the Fort Riley Limestone, and close tohorizontal within the limestone, and indicates why theguided waves have such substantial amplitudes. These twoextreme orientations of ray paths account for much of theirregular amplitudes of the arrivals.

Figure 7(b) shows similar ray tracing for commongeophone gathers for the arc of RVSPs. The range of anglesof emergence is small, and the ray paths are close to verticalfor nearly all source positions. This means that the arrivalsat the surface are within the shear-wave window for nearlyall source depths deeper than about 10 m, so that the effectof interactions of the shear waves with the free surface willbe minimized (Yardley & Crampin 1991). It is expected thatthe orientations of fluid-filled inclusions and fractures maybe distorted by near-surface stress anomalies (Crampin1990b). However, since the surveys cover only compara-tively shallow depths (less than 50 m), for the purposes ofthis preliminary investigation of the RVSPs, we shall assumea uniform crack distribution in the uppermost 50 m.

5 ESTIMATING FRACTURE PARAMETERS

Although the bulk of the energy of the signals in the CHSsections is in guided waves, we shall attempt to analyse theweak shear-wave splitting by automated techniques, Thetwo parameters most commonly used to describe shear-wavesplitting are the polarization of the leading shear wave, andthe time delay between the faster and slower split shearwaves. Under relatively general conditions (Crampin 1987))the former can indicate the direction of the strike of thenearly vertical micro- or macro-fractures, and the latter is a


measure of the degree and extent of the anisotropy.MacBeth & Crampin (1991) reviewed some of theautomated techniques for determining these twoparameters.

We shall try to evaluate shear-wave splitting from bothCHS and RVSP data sets. However, there are two reasonswhy it is easier to evahrate splitting in RVSPs (and VSPs)than in CHS profiles. The ray paths in VSPs and RVSPs areusually close to vertical and consequently have nearly normalincidence to approximately horizontal interfaces. Thisminimizes the disturbing effects of the interactions of theshear waves with interfaces (Liu & Crampin 1990). Morefundamental is the fact that there are no directions in nearlyhorizontal ray paths in CHS experiments which have thedistinctive polarizations of nearly vertically propagatingshear waves in VSPs and RVSPs (Liu, Crampin & Booth1989). The shear-wave polarizations along nearly verticalray paths are approximately parallel to the strike of thevertical inclusions, which is approximately subparallel to thedirection of maximum horizontal compressional stress(Crampin 1987). A further difficulty is that it is usuallydesirable to examine shear waves in a range of azimuthaldirections. At some expense, it is usually possible to lay outgeophones in the desired configuration in VSP experiments,whereas in CHS experiments the range of azimuths islimited by the available boreholes.

We shall apply two automated techniques (Alford 1986;Li & Crampin 1991) to estimate the polarization and timedelay of the shear-wave splitting in a selection of the CHSand RVSP data sets. We will discuss how the fractureorientation, density, and dip can be inferred from theobserved data. Other fracture parameters, such as theeffective aspect ratio of the fractures, would require a morecomprehensive analysis of the whole RVSP data set.

5.1 Fracture orientation in CMSs

The CHS surveys cover a range of incidence angles at fourazimuths, from sources in GW5 to geophones in GWl-GW4(Fig. 3). We only processed records from the two geophoneslocated at depths of 34.4 and 38.1 m, respectively. These arebelow the Fort Riley Limestone and the ray tracing in Fig.7(a) indicates that the ray paths to these geophones areclose to vertical, which is the reason why the recordedwaveforms are considerably less complicated than those atother geophones. The polarizations, estimated by thelinear-transform technique (Li & Crampin 1991), are shownin Fig. 8 for ray paths from all source depths in the fourCHS profiles. (Note that all azimuthal angles in this paperare measured clockwise from north, unless specifiedotherwise.)

The estimated polarizations are scattered, but in generalthere is a consistent alignment of between N60”E and N90”Eat each azimuth. This is not surprising. Polarizations at anygeophone are determined by the anisotropic symmetry ofthe structure within a wavelength or two of the geophone,and the common geophone gather to the lowest geophone inFig. 7(a) (the lowest geophone location in Fig. 8), divideinto two very narrow ranges of directions. Ray paths to thegeophone from sources above the base of the Fort RileyLimestone at about 28 m are about 30” from the vertical,whereas those from below the limestone base are almost

456 E. Eiu, S. Crampin and J. H. Queen

GW5-GWI GW5-GW2

10

s5zZ 20

5

8cl

3C

Figure 8. Estimates of the variation with source depth of the faster split shear-wave polarizations in the four CHS offsets. Polarizations areshown for the bottom two geophones at depths of 34.4m (star) and 38.1 m (circle) as estimated by the linear-transform technique of Li &

30

Polarization (Degrees) Polarization (Degrees)0 30

GW5-GW3 GW5-GW4

II ”I. .,“I 1. ,. .I..

I 0 30 60 90 120 160

Polarization (Degrees)

Crampin (1991).

horizontal. This means that the measured polarizations inFig. 8 are principally determined by the anisotropicproperties in these two directions. Note that the alternationbetween directions 90” apart in profile GWS-GWl isexpected from time to time in shear-wave splitting. If thepolarization of the initial faster split shear wave is missed,for any reason (for example noise or low excitation), thenearly orthogonal polarization of the slower split shear wavemay be identified.

The measurements of polarization show a possible minormodification at around source depths of 28 m at the base ofthe Fort Riley Limestone dividing into two ray pathdirections, but otherwise display remarkable consistency,particularly between the estimates from the two geophones.Since the wavelengths at the geophones are probably lessthan lOm, this consistency suggests the details of thefracture-induced anisotropic structure are comparativelyuniform at the CBTF site, so that analysis in terms of auniform anisotropic orientation in all layers (except possiblyvery near-surface) is probably valid. However, because thewavelengths are so short and the ray paths to the geophonessample such a narrow range of directions, the differences inthe estimated polarizations between the four CHS profiles,could well be due to comparatively minor irregularities inthe interfaces in Fig. 1. Fig. 9 is a histogram of thepolarization directions in Fig. 8 and shows considerablescatter, as is expected from such complicated ray paths.There is a minor peak around 45” and a broader maximumaround N70”E f 15”. The minor peak is associated with theGWS-GWl profile, but the broader maximum is at theexpected orientation of fractures from independent geologi-cal and hydrological observations, and is consistent withorientations derived from an adjacent deep VSP experiment(Queen & Rizer 1990).

geometry are given in Table 2 and Fig. 4. Fig. 10 shows thepolarizations of the leading split shear waves estimated bylinear-transform technique (circle) and by the Alford (1986)technique (stars). The ray tracing in Fig. 7(b) shows that,for source depths below 10 m, the ray paths to the surfacegeophones are within 30” of the vertical and are within theshear-wave window. Ray paths from sources above about10 m are outside the shear-wave window so that surfacerecordings are not representative of the waveforms of theincident wave (Booth dz Crampin 1985). For most of theazimuths, the polarizations of the leading split shear wavesare N75”E f 15”, and only few azimuths (to GlO, G13, andG14) show irregular scatter, probably due to localirregularities of structure near the geophones. Severalazimuths also show the 90” alternation mentioned in theprevious section.

With the above exceptions, the polarizations in Fig. 10again show remarkable consistency, and indicate polariza-tions close to those displayed for the deeper geophones inthe CHS profiles in Fig. 8. Fig. 11(a) is a histogram of the

CROSSHOLE DATA - POLARIZATIONS50

5.2 Fracture orientation in RVSPs0

0 30 60 90 120 150 180A N G L E F R O M N O R T H I N D E G R E E S

We estimate polarizations of the RVSPs in the arc of Figure 9. Histogram at 5” intervalsgeophones from north (G16) to N160”E (G2). Details of site the CHS data sets in Fig. 8.

I., ., ., .. ,, ,,0 30 60 90 120 150

Polarization (Degrees)

of the estimated polarizations of


G2 G90

GlO Gil G12

0 30 60 90 120 150 180 0 30 60 90 120 150 160 0 30 60 90 120 150 160 0 30 60 90 120 150 160 0 30 60 90 120 150 180

G13 G14 G15 G16

0 30 60 90 120 150 180 0 30 6 0 90 120 150 180 0 30 6 0 90 120 150 180 0 30 6 0 90 120 150 IPolarization (Degrees) Polarization (Degrees) Polarization (Degrees) Polarization (Degrees)

0 3 0 6 0 90 120 150 160

Polarization (Degrees)Figure 10. Estimates of variation with source depth of faster shear-wave polarizations for RVSP azimuths to the arc of geophone positionsfrom geophones G16 and G2. Circles denote measurements using the linear-transform technique of Li & Crampin (1991), and stars those ofAlford (1986).

polarizations in Fig. 10. Since the RVSP records aredisplaying polarizations determined by the shallow struc-ture, the agreement between the shallow polarizations inFig. 11(a), and deeper polarizations in Fig. 9, is again strongconfirmation that the anisotropic symmetry structure of theCBTF site is comparatively uniform in all layers belowabout 15 m.

5.3 Fracture density in RVSPs

Estimates of time delays in the CHSs show a large scatter aswould be expected from the complicated ray paths, and theyare not shown here. The time delays estimated for the arc ofRVSPs by the linear-transform technique have less scatterand are shown in Fig. 12 with a histogram in Fig. 11(b). Ingeneral, 150 Hz signals through such multilayered structureswould be expected to display multiple splitting, causingproblems in identifying consistent delays. Consequently, theestimates still display considerable scatter, but the timedelays originating from source depths between about 10 and30 m are relatively stable for some of the geophones. Themaximum time delay is 7 ms in the direction of N87”E toG12. This is close to the direction expected for the strike ofthe fractures, N75”E, and there is weak symmetry about thisdirection (Fig. llb).

For RVSP source locations in the Fort Riley Limestone,Fig. 7(b) shows that the ray paths are incident at the surfaceat less than about 20” to the vertical. We assume thatcracks/fractures are uniformly distributed and the crackorientation does not change with depth. This assumption isjustified on the basis that the surveys only cover a depth

(a) RVSP DATA - POLARIZATIONS100 , I

B60

2

2 40

20

090 120 150 1eo

ANGli FROivl NORTH IN DEGREES

UN R V S P D A T A - T I M E D E L A Y S8,

ti120

ANGLE FRO-ii NORTH IN DEGREES150 180

Figure 11. (a) Histogram at 5” intervals showing estimatedpolarization directions at all azimuths. (b) Average time delayprofile between depths of about 10 and 30 m.


0

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Figure 12. Measured time delay variation with source depth for all RVSP azimuths. The time delays show large scattering, but they arerelatively stable between depths of about 10 to 30 m (corresponding to the Fort Riley Limestone interval in Fig. 1).

range of less than 50 m, and the comparatively uniformpolarizations throughout the structure in Figs 8 and 10.Assuming that the maximum time delay of 7 ms isrepresentative of the maximum delay through the alignedfractures, using estimates of the shear-wave velocities in Fig.1, and ray paths in Fig. 7(b), a conservative estimate of thecrack density is between CD = Nu3/V = 0.10 and CD =0.15, where N is the number of cracks of radius a in volumeV (Hudson 1980, 1981; Crampin 1984). In our modelling inthe next section, we shall assume an average crack densityof CD = 0.12. Note that the amount of differentialshear-wave anisotropy, in per cent, is approximatelyequivalent to the crack density times 100 (Crampin 1987).

5.4 Fracture inclination

There are several reasons why it is not possible to estimatethe inclination of the fracture to the vertical directly fromeither the CHS or RVSP data sets as recorded. If the CHSprofiles had recorded split shear waves instead of a mixtureof split shear waves and guided waves, it would have beenpossible to identify inclinations to the vertical comparativelyaccurately by analysing PDs in directions within f15” of thecrack strike (Liu et al. 1989). However, the information willstill be contained in the wavetrain of the guided waves but,in most cases, can only be extracted by fullwave modellingwith synthetic seismograms. The inclination of cracks to thevertical can seldom be obtained from RVSPs (or VSPs) as,except for comparatively large inclinations to the vertical,inclinations to the vertical cause only minor changes in

behaviour of the waveforms along ray paths within f30” ofthe vertical (Crampin 1981).

The strong alignment of leading split shear waves in thedirection of the known dominant fracture system in Figs 8and 10 suggests that any deviation of fractures from verticalmust be less than 20” f 5”. However, the strong coupledenergy on vertical and radial components from a transversesource in the CHS profile from GW5-GW2 (believed to bein an azimuth close to the strike of the inclusions) (Fig.5b) indicates that the geometry is not parallel verticalfractures. We will show in the next section that fracturesinclined at 15” to 30” to the vertical, dipping towards thesouth, can give a reasonable match of the strong verticalcomponents observed in Fig. 5.

6 ANISOTROPIC MODELLING

The behaviour of seismic waves in anisotropic material maybe unfamiliar, and it is difficult to specify anisotropicbehaviour exactly without modelling observations withsynthetic seismograms. It is suggested that matchingrecorded waveforms with fullwave synthetic seismogramsmust be the most complete confirmation that anyinterpretation of the anisotropy is correct. We now presentsynthetic seismograms for the CHS data based on ourprevious estimates of anisotropic parameters.

The source time function is: F(t) = exp (at/d) cos (ot);where w = 2nf is the circular frequency; and d is thedamping factor of the source function. In our model of the


CBTF seismograms, the peak frequency is f = 250 and thedamping is d = 5.

We found that it was necessary to introduce relativelystrong attenuation in order to match the relative amplitudesand the dominant frequencies of the different arrivals. Inour model, the average isotropic attenuation factor (qualityfactor) Q is estimated to be 20 f 10 for the relatively softshales immediately above and below the Fort RileyLimestone, and 50 f 10 within the limestone (see Table 3).This relatively high attenuation may be attributed to theshallow depth and highly fractured rocks within therockmass.

Matching observed to synthetic seismograms provides anempirical technique for crude estimations of attenuation incomplicated structures, where estimates of attenuation aredifficult to obtain quantitatively. Note that we expect thatthe in situ attenuation at the CBTF site will be controlled bythe fractures and the fracture geometry. This wouldnecessarily result in an anisotropic attenuation with a strongvariation of attenuation with direction. Although themechanism for specifying anisotropic attenuation, by realand imaginary elastic constants, has been identified(Crampin 1981), anisotropic attenuation has not yet beensuccessfully formulated in a realistic rockmass. Conse-quently, at this stage, we assume an isotropic attenuation(constant Q) in our model.

We model fullwave synthetic seismograms using theANISEIS modelling package (Taylor 1987, 1990), and try tomatch synthetic to observed seismograms in order to obtainan approximate estimate of the effect of fractures on seismicshear waves.

6.1 Isotropic modelling and effects of source orientations

In a homogeneous isotropic structure with horizontallayering, wavefields from an in-line (radial) and X-line(transverse) source orientation will be separated, and haveparticle displacements confined to sagittal planes, andhorizontal transverse directions, respectively. In this section,we examine the extent to which the 3-D coupling can bemodelled with an isotropic structure.

A possible explanation of the strong radial and verticalcomponent energy from the X-line source in Fig. 5(b),where the ray paths are approximately in the plane of thedominant fractures, might be that the energy from theX-line source is not strictly confined to the X-line direction.It is believed that this anomalous vertical energy is unlikelyto be due to the source orientations [particularly as theX-line energy from the in-line source in Fig. 5(b), iscomparatively weak], however, the following exampledemonstrates that in multilayered structures the sourceorientation is crucial and strong vertical component energymay be generated even if the source is misaligned by as littleat 10” to 20”.

Figure 13 shows an example of synthetic seismogramscalculated for a horizontal plane-layered structure with theisotropic velocities in Fig. 1 (Table 3) (the model geometryis the same as GW5-GW2 CHS profile to a geophone at adepth of 23.7 m). The two source orientations are with thein-line source rotated 20” clockwise from the radialdirection, and the X-line source rotated 20” from thehorizontal plane. A remarkable feature is that although the

GeophoneIn-Line X-Line 4”p;”

m

10

F20

l.ii 30

a, 40” I5

I I I I I I I I

6310

kz3 20

ic30

40

c- ’I I I I I I

150 0 150 0 150

TIME IN MSEC

Figure 13. Common geophone gathers for a CHS profile to ageophone at 23.7 m depth in the isotropic model in Fig. 1 and Table3. Seismograms were calculated for two sources: an in-line sourcerotated 20” clockwise from the radial direction, and a X-line sourcerotated 20” from the horizontal.

X-line energy is only 30 per cent of in-line energy for the‘in-line’ source, the two horizontal components have almostequal displacements when the source is within the Fort RileyLimestone. Similarly, the vertical and X-line displacementsare similar for a ‘X-line’ source in the Fort Riley Limestone.This strong cross-coupling demonstrates that apparentlyanisotropic cross-coupling effects may be the result ofcomparatively minor source misalignments or structuralirregularities. Note that in an isotropic structure the effectswould be independent of azimuth of propagation and that isclearly not the case in Fig. 5.

6.2 Anisotropic modelling

In an anisotropic structure, particle displacements will becoupled in three dimensions, except when the propagation isconfined to a vertical plane of anisotropic symmetry. In thissection, we attempt to derive a structure that can explain thepronounced cross-coupling in the CHS profile in Fig. 5(b),which is believed to be parallel to the strike of the fractures,and hence in a symmetry direction.

We obtained an approximate match of arrival times, andamplitudes of synthetic to recorded seismograms by usingthe velocities and empirical attenuation of the isotropicmodel in Table 3. Anisotropy was introduced by simulatingparallel fluid-filled fractures using the formulations ofHudson (1980, 1981) as adapted by Crampin (1984). Theseformulations model the seismic effects of distributions ofcracks with dimensions much smaller than a seismicwavelength (the long-wavelength limit) by calculatingeffective elastic constants. The formulations are strictly validin the long-wavelength limit and can only approximate tothe effects of the possibly large fractures believed to bepresent at the CBTF site. In each layer, we assume a crackdensity CD = 0.12, with the fractures striking N75”E anddipping 70” to the SE (20” from the vertical).

Figure 14 shows synthetic seismograms for commongeophone gathers to a geophone at 23.7 m for CHS profiles:( a ) GWS-GWl; ( b ) GW5-GW2; a n d ( c ) GW5-GW4,which can be directly compared to the recordedseismograms in Fig. 5. The synthetic seismograms display


GWS-GWl GeoDhone GW5GW2 GeophoneIn-Line Depth

Cm)(W In-line X-line Vertical Depth

(ml

I I I I I0 150 0-o ol-

I I150


Z, M

14.63

15.85

18.29

20.73

23.16

24.38

25.60

26.82

28.04

GWS-GWl (X-LINE SOURCE)

R-T PLANE V-T PLANE


GW5-GW2 (X-LINE SOURCE)

14.63

15.85

17.07

18.29

20.73

23.16

24.38

25.60

26.82

28.04

R-T PLANE

Hiq~~j

I.0 I: I n 115’ 2’H c dbwd=-76L

25 75 25

V-T PLANE

NzJJJJJ

Figure 14. Synthetic common geophone gathers and selected PDs modelling CHS profiles in Fig. 5, with the isotropic model in Fig. 1 andTable 3 with each layer pervaded by parallel cracks striking N75”E and dipping 70” to the SE. The cracks have a crack density, CD = 0.12, andnegligible aspect ratio, AR = 0.001.

many of the characteristic features of the recordedseismograms, and the agreement is considered to be a goodfirst-order match. The seismograms show several interestingfeatures as follows.

(1) Amplitudes of the vertical component are large forboth in-line and X-line source orientations, when the sourceis in the Fort Riley Limestone. For X-line source, whenthere is no vertical energy excited, the amplitudes of thevertical component is typically 1.5 to 2 times those of thetransverse component. In Fig. 14(b), where the profile fromGW5-GW2 is almost along the strike of fractures, so that in

an isotropic structure the X-line source would produce novertical motion, the synthetic seismograms show particularlylarge amplitudes on the vertical components. We havemodelled (not shown) several different angles of dip, andfound that seismograms from the model with fracturesdipping 75” to 70” to the SE give the best match of syntheticto recorded behaviour.

(2) The PDs in Fig. 14 are for the same selection ofX-line source depths as in Fig. 5, and show a similar type ofelliptical particle motion. Again, the wavefields from in-linesources are more complicated than those from the X-linesources and are not shown here. Shear-wave splitting cannot


GW5GW4In-Line

GeophoneX-Line

IXY I I IVertical Depth

(ml

iI3c2

10

E‘3 20

>i

30

40I I I I ’ I

1500 *I I I I I

0 150 0 150

TIME IN MSEC

2, M

14 63

20.73

23.16

24.38

25.60

26.82

28.04

GW5-GW4 (X-LINE SOURCE)

R-T PLANE V-T PLANEANIbEIS 1

Figure 14. (continued)TIME IN MSEC

be seen despite the large fracture density used for themodelling, and the records display the elliptical, sometimesalmost planar, motion typical of generalized mode wavephenomena (Crampin & King 1977).

(3) A reflection from the basement, marked with arrow inthe YY component of Fig. 14(c), is similar to that observedin the YY component of Fig. 5(c). This arrival, showing asingle cycle of wave motion, is the only body wave arrivalthat can be easily identified in Fig. 14. Body waves withwider angles of incidence interact with the interfaces andbecome incorporated in modal solutions (Lou & Crampin1991).

(4) The three-component seismograms show similarmarked variations in amplitude with source depth as therecorded profiles in Fig. 5 (ignoring the occasional dead- -channel in Fig. 5), where sources at different levels generate

substantially different signals at the 23.7 m geophone. Insome cases, the patterns of low-amplitude arrivals are verysimilar to that in Fig. 5.

(5) The occasional synthetic channel waves in Fig. 14shows oscillatory motion due to difficulties in choosingwholly appropriate sampling, window length, and integra-tion paths. The ray paths in Fig. 7 indicate the wide range ofarrivals that may be incorporated in the model solutions.The recorded profiles in Fig. 5, also show similar oscillatorymotion, often from similar source locations. Theseoscillations are presumably due to difficulties in combiningthe rotary borehole source to give in-line and X-line sourcepolarizations. It is interesting that very different processingprocedures should have similar effects on records fromsimilar source depths.

Although the waveforms in the PDs do not match those inthe recorded profiles in detail, the overall character of theseismograms and profiles is in good agreement with therecorded profiles.

7 DISCUSSION

We have demonstrated that fracture-induced seismicanisotropy determines many characteristic features ofthree-component seismograms in the CHS and RVSPprofiles at the CBTF site, and have shown that thebehaviour of the seismograms and waveforms may beinterpreted in terms of the crack geometry. Shear-wavesplitting in the RVSP over the Fort Riley Limestoneinterval, demonstrates a large fracture density of parallelnear-vertical fractures with a crack density of between 0.10and 0.15. Although the crack density is not well resolved,since the formulations for cracks are not strictly valid forlarge fractures, it does suggest substantial fracturing presentin the Fort Riley Limestone. Previous geological studies inthe area have suggested that two near-orthogonal fracturesystems are present at the surface (Queen & Rizer 1990).We find no evidence for this in either the CHS or RVSPprofiles, which indicate parallel near-vertical cracks in therockmass sampled, which is essentially below 10 m.

Matching the waveforms of the CHS profiles withsynthetic seismograms shows that the bulk of the seismicenergy propagates as modes of guided waves channellingenergy along interfaces between the wells. The patterns offractures cause these generalized modes to couple betweentransverse, radial, and vertical motion. In particular, thepronounced vertical motion, from the horizontally polarizedshear-wave sources in the CHS profiles, is caused by thefractures being as much as 20” away from the vertical. Thisdoes not conflict with our previous claim of a near-verticalfracture model since shear-wave polarizations from such adipping fracture model do not produce a significant change-in polarization direction of the split shear waves from anessentially vertical fracture model. Such dipping fractures inthe near-surface are expected from the near-surface stressanomalies (Crampin 199Ob), and the relatively large crackdensities and dipping fractures obtained in this study areconsistent with these previous studies. The consistency ofthe crack strike derived by different techniques from theCHS and RVSP profiles lends confidence to theinterpretations.

The broad similarities of the shear-wave polarizations


estimated by the automatic techniques in Fig. 8, forstructure below the Fort Riley Limestone, and Fig. 10, forthe near-surface structure, suggest there is some overalluniformity of the crack structure at the test site. They alsosuggest that modelling the overall structure within a uniformcrack distribution has some validity. However, thediscrepancies in detail between recorded and synthetic PDsindicate that the geometry is more complicated than theparallel near-vertical fracture system that has beendeveloped in this paper, some may well be due to the noise.However, the first-order match of the synthetic to therecorded CHS profile data set does suggest that the parallelsystem is approximately correct, and that at least thedominant fractures are not strictly vertical. Queen, Sinton &Buller (1990) and Rizer (1990) suggested that the fracturesystems are complex in this area, and it is probable that anysignificant further improvement to the detailed modelling ofthis small rock volume would require minor irregularities inthe interfaces to be taken into account, and that is beyondthe scope of this present study.

Fractures can have a very strong effect on seismicattenuation. We have demonstrated that attenuation isnecessary to get any sort of match between syntheticseismograms and field observations. The effects onattenuation of large fractures have not yet beeninvestigated, but is clearly of paramount importance, and isa serious limitation to our modelling.

8 CONCLUSIONS

This study clearly demonstrates the effects of fracture-induced seismic anisotropy in CHS and RVSP profiles. Wehave shown that synthetic seismograms can in general, if notin detail, reproduce many of observed characteristic featuresof the three-component seismograms by assuming a uniformsystem of stress-aligned cracks throughout the CBTF site.Only a single near-vertical fracture system is modelled, butthe consistency of the modelling does suggest that a singleparallel near-vertical fracture system, striking N75”E, isdominant, and that a biplanar crack structure is not requiredby the data as modelled here. We have confidence thatmany parameters of fracture-induced seismic anisotropy canbe inferred from CHS profiles, and can be modelled withsynthetic seismograms. One important result of this study isthe positive identification of guided waves in CHS profiles.The analysis of the guided modes may be an important newtool for CHS investigations.

We conclude from this study, that the combination ofcrosshole surveys and reverse VSPs is an effective way toinvestigate fracture-related seismic anisotropy at shallowdepths. This could be important for the study of fluid flow atshallow depths in hydrological investigations.

ACKNOWLEDGMENTS

We thank Applied Geophysical Software Inc. and MacrocLtd for approval to use the ANISEIS package forcalculating the fullwave synthetic seismograms. J. B. Sintonand P. L. Buller, with JHQ, of Conoco did most of the earlyanalyses of RVSP data. The necessary pre-processing(including the rotary source decomposition) of the data wascarried out at Conoco. We thank W. D. Rizer for geological

information, P. Wild for assistance with data processing,and X. Y. Li, M. Lou, C. D. MacBeth, and X. W. Zeng fordiscussions on techniques for measuring shear-wavesplitting. We also thank J. H. Love11 and two anonymousreviewers for their comments to improve the manuscript.This research was supported by Conoco Inc. and the NaturalEnvironment Research Council, and is published with theapproval of Conoco Inc. and the Director of the BritishGeological Survey (NERC) .

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Fracture detection using crosshole surveys and …...deduced from other geological and hydrological observations. Analyses of CHS data including modelling with synthetic seismograms