shear-wave polarizations and subsurface stress directions

GEOPHYSICS, VOL. 56. NO. 9 tSEPTEMBEK 1991): P. 1331-1348. 3 FIGS.. I TABLE.

Shear-wave polarizations and subsurface stress directions at Lost Hills field

D. F. Winterstein* and M. A. Meadows*

ABSTRACT

Nine-component VSPs recorded in two wells 862 ft (263 m) apart in the Lost Hills oil field in the southern San Joaquin Valley of California show that the polarization of the faster shear (S) wave is aligned with the direction of maximum horizontal compressive stress as determined from analysis of tiltmeter data. Tiltme- ters monitored fractures that were hydraulically induced in or near the VSP wells. When fractures were induced in a VSP well, fracture azimuths determined from tiltmeter data were N 53”E and N 56”E, respec- tively, in two different depth zones; in the same zones the polarization directions of the faster S-wave were N S8”E and N 59%. When fractures were induced in a well 537 ft (164 m) from the other VSP well, tiltmeter data indicated a mean fracture strike of N 59”E. while the polarization direction of the faster S-wave in that case was N 40”E. The discrepancy between tiltmeter and S-wave polarization angles in this second case may correspond to differences in subsurface structures and horizontal stress directions between the two wells.

S-wave polarization directions were determined by minimizing energy on off-diagonal components of the

2 x 2 S-wave data matrix, accomplished by computationally rotating sources and receivers. Although polarization directions obtained by assuming a homogeneous subsurface were moderately consistent with depth, considerable improvement in consistency re- sulted from analytically stripping off a thin near- surface layer whose fast S-wave polarization direction was about N 6”E. S-wave birefringence for vertical travel averaged 3 percent in two zones, 200-700 ft and 1200-2100 ft (60-210 m and 370-640 m), which had closely similar S-wave polarizations. Between those zones, the polarization direction changed and the birefringence magnitude was not well defined. S-wave polarizations from two concentric rings of offset VSPs were consistent in azimuth with one another and with polarizations of the near offset VSP. This consistency argues strongly for the robustness of the S-wave polarization technique as applied in this area. The S-wave polarization pattern in offset data fits a model of vertical cracks striking N 55”E in a weakly transversely isotropic matrix, where the infinite-fold symmetry axis of the matrix is tilted IO degrees from the vertical towards N 70”E. Such a model is of monoclinic symmetry.

INTRODUCTION

This paper makes four contributions. First, it illustrates. from data with good experimental control, details of vertical S-wave birefringence in subsurface formations for which birefringence is relatively uniform. Second, it shows that polarization directions of the fast S-wave coincided with the direction of fracture strike. and presumably of maximum horizontal compressive stress. as determined from analysis of tiltmeter data recorded during hydraulic fracturing. Third, it introduces concepts of layer stripping and downward continuation for analysis of S-wave birefringence in VSP

data and illustrates how layer stripping clarifies interpretation of birefringence effects where anisotropy varies with depth. Fourth. it shows that subtle but systematic variations in S-wave polarization azimuth observed in offset VSP data could be modeled with a simple, homogeneous medium of monoclinic symmetry consistent with the subsurface. (For characterization of monoclinic media see Winterstein, 1990. under .s~~rz~c’tr~ .~y.vterlz.)

S-wave birefringence. a property of elastic waves in anisotropic solids, is common for S-waves traveling verti- tally in crustal rocks. S-wave birefringence means that two

Presented at the 60th Annual International Meeting. San Francisco. CA. Manuscript received by the Editor October 9. 1990; revised manuscript received March 19, 1991. *Chevron Oil Field Research Company. 1300 Beach Blvd.. P.O. Box 446. La Habra. CA 90633-0446. ’ 1991 Society of Exploration Geophysicists. All rights reserved.

1331

1332 Winterstein and Meadows

S-waves of different polarization travel at different speeds in the same direction; vertical S-wave birefringence implies that the direction of travel is vertical. If a seismic source is oriented so as to excite both S-waves, and if the waves travel far enough, S-wave birefringence will cause observable splitting of the two S-waves. Early models of anisotropic sedimentary rocks by exploration geophysicists were often transversely isotropic with vertical infinite-fold symmetry axes. Such solids are not birefringent for S-waves with vertical raypaths. Earthquake seismologists (e.g., Ando et al., 1983; Booth et al., 1985). however, found evidence for near-vertical S-wave birefringence in earthquake data in the early 1980s. At the same time oil companies recording three-component (3-C) seismic data independently found evidence for vertical birefringence in hydrocarbon-bearing sedimentary basins (cf. Winterstein, 1987). Researchers from Amoco, Exxon, Chevron, and Colorado School of Mines presented evidence for this vertical birefringence for the first time publicly in 1986 at annual meetings of EAEG and SEG (e.g.. Alford, 1986; Willis et al., 1986; Becker and Perelberg, 1986; Frasier and Winterstein, 1986; Martin et al., 1986). Since then much additional evidence for vertical birefringence in sedimentary basins has accumulated (e.g., Brodov et al., 1990; Mueller, 1990; Squires et al., 1989; Winterstein and Paulsson, 1990, Winterstein and Meadows. 1991, hereinafter called Paper II), including results shown here.

A common model for vertical birefringence is extensive dilatancy anisotropy (EDA) proposed by Crampin et al. (1984). The essential feature of this model is that horizontal stresses such as those from plate tectonics create vertically oriented, fluid filled cracks or microcracks that cause vertical S-wave birefringence. The validity of EDA as an expla- nation for vertical birefringence is not established, but it and variants of it have proved useful as a framework within which to record and interpret data. An alternate model, the Nur model (Nur, 1971: Nur and Simmons, 1969). takes unstressed rock to be isotropic with a uniform distribution of randomly oriented cracks. Subsurface stresses preferentially close cracks whose normals are along or close to the maximum principal stress direction, making the rock anisotropic. A third model invokes oriented, open vertical fractures such as joint sets. A single set of vertical. parallel fractures would cause S-wave birefringence indistinguish- able at long wavelengths from that of the EDA model. Whatever the best models prove to be, much of the observed vertical S-wave birefringence almost certainly results in some way from unequal horizontal stresses. Crampin and Bush (1986) pointed out that S-wave birefringence might provide a useful tool for reservoir development. The polarization direction of the fast S-wave in simple cases gives the direction of maximum horizontal compressive stress, a quantity much in demand by those who induce fractures in reservoirs by techniques such as hydraulic fracturing.

Results presented here reinforce the notion that vertical birefringence is caused by horizontal stresses. and that the polarization direction of the fast S-wave lies in the direction of maximum horizontal compressive stress. To our knowledge. there is no convincing evidence yet that the polarization of the fast S-wave for vertical raypaths is ever in a direction other than that of maximum horizontal stress.

except possibly in thin. weakly birefringent layers or near- surface layers. However, it is possible and even likely that rocks exist for which the fast S-wave polarization for vertical travel does not lie along the maximum horizontal stress direction. Rocks with fractures oriented by ancient stress regimes. or rocks of low symmetry with tilted symmetry axes, for example, might constrain the fast S-wave polarization to lie in a direction other than that of maximum horizontal stress (see Lynn and Thomsen, 1990). More measurements are needed to determine whether such rocks exist and, if so, how common they are. There is now good evidence for major changes in S-wave polarization direction with depth (Martin et al., 1986; Paper II). and it would be useful to know whether or not horizontal stresses change accordingly.

A comment on terminology may be helpful. The term “polarization” in the context of seismic waves refers to the shape and spatial orientation of particle trajectories. Here we restrict the term to mean only the spatial orientation of the line along which a particle moves in a linearly polarized wave. Hence “polarization” and “polarization direction,” as used here, both imply the spatial orientation of such a line, the latter term emphasizing the restriction to linear rather than more general (e.g., elliptical) motion. A “polarization change,” then, does not mean.a change, for example, from linear to elliptical motion nor a polarity reversal but only a change in the spatial orientation of the line along which a particle moves.

DATA ACQUISITION

Data sets to be discussed in detail were from nine- component VSPs recorded in the 11-10X and I-9J wells of the Lost Hills oil field in the southern San Joaquin Valley of California. The wells were 862 ft (263 m) apart. By nine- component data we mean records from three orthogonal receiver components that detected waves as if from three separate, orthogonal source polarizations (Figure I). In this paper. except for preliminary processing involving vertical components. we treat only data of the 2 x 2 S-wave data matrix, that is. data from .Y and y sources and receivers, or four of the nine components. (To be precise, our S-wave data matrix is of dimensions 2 x 2 x II. where II is the number of samples in a time series.) Our coordinate frame for recording and processing was a right-handed Cartesian frame with the .I--axis along a source vehicle axis. After determining S-wave polarization directions, we reoriented the frame relative to true north. Figure 2 shows the location of the Lost Hills field and site relative to nearby fields in Kern County. The surveys were conducted in July, 1988, for the II-IOX well and March, 1989, for the I-9J. Wells hydraulically fractured in conjunction with the VSPs were the 12-10 and the I-9J; the 12-10 well was 537 ft (164 m) northwest of the 11-10X (Figure 3).

11-10X well

For the II-IOX well we used two mutually orthogonal Omnipulse air gun sources located 57 and 68 ft (17 and 21 m) from the well and as close to each other as possible. Data were recorded without moving the sources. Source guns were tilted at 45 degrees, and each was fired five times left

S-wave Polarizations and Stress Directions 1333

and five times right for a total of 20 pops per receiver level. Source zero-times were obtained from accelerometers screwed into the baseplates. Locations and azimuths of sources were determined by surveyors after we completed the VSP.

The downhole receiver was a three-component (3-C) SSC K tool with a Gyrodata gyrocompass for determining absolute orientation. With the receiver clamped at 1500 ft (457 m). and sources at VSP positions we recorded several series of source impacts before, during, and after the hydraulic fracturing of the 12-10 well to monitor any changes in S-wave polarization that might result from the fracturing. Fracturing did not detectably affect data of the 11-10X well, although it caused transient changes in data simultaneously monitored in a well opposite the 12-10. We do not discuss these transient effects in this paper and restrict consideration to data acquired after the fracturing. For the regular VSP. after recording at a 1720 ft (524 m) depth, we recorded at increments of 80 ft (24 m) from 1700 to 900 ft (518 to 274 m) with the final level at 800 ft (244 m).

Coordinate

Y

Frame for Recording (2 is up)

X receiver polarizations after alignment with source

l-9J well

For the I-9J well we used a single ARIS’” (ARC0 Impul- sive Source, provided by Western Geophysical) for the near offset portion of the VSP and alternated between two ARIS sources for two rings of offset VSPs. For near offset recording the ARIS was 50 ft (15 m) from the well. For offset recording, we positioned the sources successively at eight points nominally 45 degrees apart in each of two concentric rings nominally 350 and 700 ft (1 IO and 210 m) from the well (Figure 3). Each source position was marked with two 14 in. (0.36 m) rebar pegs whose locations were subsequently surveyed for accurate source locations and azimuths. For near offset recording we built a special ARIS baseplate pad of riprap and road base gravel in order to do all recording without moving the source. We found for the layer stripping process described below that it was important not to move the source. Analysis of data from the ARC0 Group Shoot of 1986 and other data suggested that near-surface S-wave

X X

source polarizations

1 lt source vehicle

Z

2 x 2 S-wave Data Matrix

Receivers X Y Z

----1

I I i I I -----

I I I

I I

I I I

I I I L___L__L__J

FIG. I. Coordinate frame for recording and processing S-wave data, and the meaning of the 2 x 2 S-wave data matrix. The .r-axis was along a source vehicle axis, and receiver axes were computationally rotated after recording to coincide with source axes. The 2 x 2 S-wave data matrix consists of four of the nine data components obtained with three orthogonal sources and three orthogonal receivers. The XY data component, for example, is from the .r source component and the y receiver component.


birefringence, like traveltime, varies rapidly with surface components were gimballed so that two were always hori- location, and even small source moves can make data zontal and the third vertical. We recorded at increments of unusable for detailed layer stripping. For offset recording no 100 ft (30 m) from depths of 2100 to 100 ft (640 to 30 ml for pads were needed because source effort at a given position the near offset VSP but at a fixed 2000 ft (610 m) for the offset was small. ARIS made 20 impacts per receiver level or offset VSPs. After completing the near offset VSP, we lowered the position, five in each of four directions-fore, aft, left, and receiver to the 2000-ft (610-m) level and recorded that level right-with the impactor tilted I5 degrees from the vertical. again. without moving the source, before going to the offset The source vehicle axis pointed towards the well at every VSP locations. The receiver remained clamped at the 2000-ft source location. Source zero-times were obtained from (610-m) level without repositioning for all subsequent offset pulses from an accelerometer atop the impactor that were VSP recording. transmitted to the recording truck via hard-wire connection. The well was a nearly vertical cased and cemented hole

The downhole receiver for the I-9J well was the LRS- 1300 which had not yet been perforated. Maximum deviation from 3-C tool with the Gyrodata gyrocompass attached. Receiver vertical was I. I degree, and the bottom of the hole was

VSP Location Map

T.25 S

T.27 S.

T.26 S.

T.29 S.

T.30 S.

T.31 S.

T.32 S.

R.17 E. R.16 E. R.19 E. Ft.20 E, R.21 E. R.22 E. R.23 E. R.24 E.

T.29 S.

sari Luis

;ern; co. Y T.25 S.

\I \ I I r\ I

_i_- --

7.27 S.

*auroaa uap - - - *

R.17 E. ’ R.16 E. ’ R.19 E. R.20 E. R.21 E. R.22 E. ’ -- *.

R.23 E.

b I . N v 0

0

5

8

10

18

15 Miles

24 kilometers

R.i4 E.’ ’

T.31 S.

T.32 S.

FIG. 2. Location of Lost Hills oil field VSPs in relation to nearby oil fields of Kern County. We conducted nine-component VSPs also in Cymric and Railroad Gap fields south of Lost Hills (Paper II).


laterally displaced only IO ft (3 m) from the top. The fluid level was lowered to about 300 ft (90 m) to prevent tube waves, which were undetectable in both wells.

Tiltmeter surveys

Tiltmeter surveys were conducted by deploying 15 tiltmeters in a nondescript array about the well to be hydraulically fractured. The array extended 500-1000 ft (150-300 m) from the 12-10 and l-9J wells in all directions (Figure 3). The tiltmeters measure tilts of the earth’s surface with a sensi- tivity of a few nanoradians. Fractures artificially induced during hydraulic fracturing cause measurable tilts which are fit to a simple model after subtracting earth tide and other known effects (see Davis, 1983). Hunter Geophysics collected and analyzed all tiltmeter data.

DATA CONDITIONING

We sought to analyze birefringence effects in data that were as close to being unprocessed as possible, but the following data conditioning steps were deemed necessary. The first step was to calculate and apply zero-time correc- tions (statics) based on source accelerometer pulses. The second step was, for each receiver depth or source offset position, and for each receiver component, to sum the five traces of like source polarity and then subtract the corresponding sums for which impacts were azimuthally in opposite directions in order to simulate a source that applied a purely horizontal impulse. Such a source produces vertically traveling S-waves with little contamination from vertically traveling P-waves. A further conditioning step was to rotate the .u-axis of the downhole receiver into alignment with the source axis, accomplished with the aid of gyrocompass and surveyor data. Also, data from the SSC receivers, which were not gimbal mounted, were rotated initially to make the receiver :-axis vertical.

Before analyzing the data for S-wave polarization directions, we computationally rotated the receiver data so as to

-1 1000

600 g

t! s 200 4

5

i - 200 i: 5 2

- 600

-‘““Y

Distance (m)

100 -300 -200 -100 0 100 200 300 7 / I :’ I ‘,. I I 300

SOUPXS :’

,:’ ‘..

A IRIS ‘..,

0 Omnipulse .:” ‘3 A

,:’ ,:’

;.’ A A A

12.1oe ‘.

. . . . .‘..., A 1 .SJ

0. ‘... A

11.10x: : A A A

,.,......’

tiltmeter ‘., A ,...“’ A

,,... .,.,” .,,...’

‘.., . .

A

A

. . . . .

- 200

100

P !?

-0 s

k!

3 - -100

- -200

I 1 I I I J-300

D - 1000 - 600 - 200 200 600 1000

East-west distance (11)

FIG. 3. Plan view of experimental layout showing AKIS and Omnipulse source positions relative to VSP wells I I-IOX and I-9J. The dotted lines roughly outline the tiltmeter array used for tiltmeter surveys in wells 12-10 and I-9J.

minimize S-wave energy on the vertical components. This rotation. which requires two Euler angles (Winterstein and Paulsson. 1990). tilts the plane of the two nearly horizontal receiver components into the plane of S-wave displace- ments. For near offset VSP data the amount of tilt was small. typically 6-10 degrees. Such a tilt puts the receiver plane out of alignment with the source plane, which was horizontal. However, this misalignment is unlikely to cause problems because of the small size of the tilt and because source radiation patterns put S-wave energy nearly equally into all possible S-wave polarization directions for nearly vertical travel. Whether or not the tilt was applied made no difference in azimuth angles and a negligible difference in lags (0.1 ms maximum) calculated from near offset data. For the offset data a few of the angles differed by I degree. In practice the tilt angles were recalculated and applied at each layer stripping step (see below). but the effects were negligible.

The final data conditioning steps involved amplitude ad- justments and bandpass filtering. An assumption of our principal data analysis technique (see below) is that the components of body waves in the y direction from the s oriented source must be identical to the components of body waves in the s direction from the y oriented source. That is, to diagonalize the 2 x 2 S-wave data matrix by a single rotation angle. it is necessary that the XY and YX data components be identical, where XY indicates data from the .I- source on the y receiver. For nearly vertical rays, and under the assumptions of no differential S-wave attenuation and isotropic receiver response, any differences in total wave energy from the .Y source relative to those from the y source should be attributable to source or near-surface properties. Hence we applied an amplitude adjustment to all data(i.e., data from all three receiver components) of the y source to make them. in a time window corresponding to the S-wave wavelets, to have the same energy as those of the .Y source. For effectiveness of data display we also adjusted the energy of the data in the S-wave time window to be the same at every depth, while taking care not to alter relative amplitudes of data from a given source component. Finally. to eliminate high frequency noise we applied a mild high-cut filter.

METHODS AND MODELS

The objective of data analysis was to quantify subsurface S-wave birefringence or. in other words, to find the natural polarization directions of the two S-waves and the timedelays or lags between them. Natural polarization directions are directions along which anisotropic rocks constrain polarizations of S-waves to lie. The purpose of the analysis was to correlate birefringence effects with formation properties such as direction of maximum horizontal stress. Figure 4 illustrates in simplest terms our experiment and basic model.

Symmetry axis of the medium

For arbitrary ray directions in anisotropic rocks of low symmetry, one needs a great deal of information to interpret S-wave time lags and polarizations. However, if the rocks have vertical two-fold symmetry axes, analysis is straight- forward if raypaths are vertical. and polarization directions relate in simple ways to symmetries of the rocks. Our initial assumption was that the rocks had vertical two-fold symme-


try axes and that their symmetry properties did not change with depth. Hence, in order to have raypaths as close to the symmetry axes as possible, we positioned the near offset sources as close to the wells as possible. The two concentric rings of offset VSPs were to serve primarily as a check on our assumption of vertical symmetry axes. Modeling showed that, if the vertical direction is not a symmetry axis, S-wave polarizations at small offsets can vary asymmetrically with azimuth if the rocks are of orthorhombic or lower symmetry. This is true even if there is a set of vertical cracks (Figure 5). On the other hand, if there is a vertical two-fold symmetry axis, such S-wave polarizations will have two-fold symmetry.

The question of symmetry axis orientation at Lost Hills is relevant because the oil field sits atop an anticline. In the vicinity of the VSP wells the subsurface dip determined from electric log correlations is about 12 degrees downward towards N 7S”E (Figure 6). A dip in structure, however, does not necessarily imply a corresponding tilt of rock symmetry properties. The polarization patterns of Figure 5 would be similar to those expected at Lost Hills (apart from a rotation) if vertical cracks paralleling the strike of the anticline had been introduced into a transversely isotropic (TI) matrix such that the infinite-fold axis of the matrix tilted 20 degrees from the vertical in a direction perpendicular to the cracks. Removing the tilt of the TI matrix would give a vertical two-fold symmetry axis and, roughly speaking, would shift the pa:tern so that the point at (-0.25, 0) would move to (0, 0). The actual offset VSP polarization pattern, discussed below, presents a picture different from either of these models.

Polarization analysis

To determine natural polarization directions of the subsurface rock, we applied several different rotation methods as

VSP Shear-Wave Recording

FIG. 4. VSP recording designed for the study of vertical S-wave birefringence. Unequal horizontal stresses in an otherwise isotropic medium make the medium anisotropic with preferred directions. An arbitrarily oriented horizontal displacement from a surface source propagates in the vertical direction as a fast S-wave (S, ) and a slow S-wave (SZ), with S, polarized along the direction of maximum horizontal compressive stress.

well as hodogram analyses. The most reliable method was to find the angle at which S-wave energy on off-diagonal components of the 2 x 2 S-wave data matrix was a minimum (Alford. 1986), a method we call the “Alford rotation” method. All other methods had significant deficiencies (Win- terstein, 1989). We implemented Alford rotations by choos- ing time windows that included only the leading portions of the first arrival S-waves and then calculating energy (sums of squares of amplitudes) on the o%diagonal components at rotation angle increments of one degree. Figure 11 below indicates what we mean by “leading portions.” We included only the leading portions of wavelets because earlier observations showed that, after rotation to the angle which minimized off-diagonal energy, the codas of diagonal wavelets differed from one another, for unknown reasons, much more than did their leading edges. Hence the leading edges are more interpretable than the codas. Using time windows gives a considerable signal-to-noise ratio (S/N) advantage over methods which calculate from individual points and lends stability and consistency to the answers. In most cases results are insensitive, within limits, to the length of the timewindow. An assumption of the Alford rotation method, generally not valid, is that S-wave polarizations are orthogonal. However, the assumption is strictly valid along any two-fold symmetry axis and is a good approximation close to

-2 -1 0 1 2 x (distance)

FIG. 5. Polarization pattern for the fast S-wave in a homogeneous solid with no vertical symmetry axis. Line segments show polarization directions that would be recorded on horizontal receiver components from surface sources offset laterally from the receiier by the indicated distances. Re- ceivers are one distance unit vertically below the center of the Dlot. The dotted circle indicates a source offset of 700 ft (216 m) when the receiver is at 2000 ft (610 m). The message is that, without a vertical symmetry axis, polarizations can vary with azimuth considerably even when source offset is small. The anisotropic medium was synthesized by introducing vertical cracks barallel to the g-axis into a transversely isotronic medium whose infinite-fold axis had been tilted 20 degrees from the vertical towards negative X.


such an axis. We rotated sources by the same angle as receivers, appropriate for vertical rays along a vertical symmetry axis in a homogeneous anisotropic medium.

The differences in arrival times of fast and slow S-waves (the lags) were computed by crosscorrelating waves on the 2 X 2 S-wave matrix diagonals after rotating to the angle that minimized off-diagonal energy. In homogeneous birefringent rock, lag increases linearly with depth.

Layer stripping

The motive.-We had expected S-wave polarization directions to remain constant with depth, but data analysis showed that they did not. Polarizations at Lost Hills field changed relatively little, but polarization changes in Cymric and Railroad Gap fields to the south were large and unmis- takable (Paper II). A layer stripping method developed for data from those areas proved useful also for Lost Hills data.

Layer stripping involves simply subtracting anisotropy effects in a layer in order to analyze anisotropy effects in the layer immediately below. S-wave splitting is cumulative, so that if anisotropy changes with depth, effects of anisotropy above the change, unless removed, will persist in the changed region and confuse analysis there. As Figure 7 shows, each S-wave in an upper layer excites two S-waves in a lower layer with different polarization directions. Until appreciable lag accumulates between the two S-waves in that lower layer, polarization analyses tend to continue to give answers for the upper layer and thereby cause what we call the inertia effect. Although wave polarization changes instantly when a wave enters a region with different natural polarization directions, recorded wavelet shapes change slowly and preserve information about their past travels through other regions. Hence if in polarization analysis one uses a significant fraction of an arriving wavelet. as we did, one sees effects of present as well as past polarizations. A way to avoid the effects of past polarizations would be to use only the portion of the faster S-wave wavelet in the lower layer that came in ahead of the slower S-wave. Our attempts

to use this approach have been defeated by low S/N in such early. low-amplitude portions of wavelets.

What hurts the effectiveness of Alford rotations below a polarization change is distortion of signal on the off-diagonal components of the 2 x 2 S-wave data matrix. Accuracy of analysis by Alford rotations depends, at least in principle, on having signal amplitudes of off-diagonal XY and YX components identical at common times. If they are not identical, the data do not fit the model, and the matrix cannot be diagonalized by rotating sources and receivers by the same angle. If signal on XY components differs systematically from that on YX components, there will be systematic errors in calculated azimuth angles. But changes of polarization with depth cause just such systematic differences in signal on XY and YX components. Specifically, when coordinate axes are rotated into the natural coordinate frame of the upper layer, the signal on one of the two off-diagonal components lags that on the other by the time delay imposed by the birefringence of the upper layer. The lag tends to make the Alford rotation analysis insensitive to polarization changes and thus generates the inertia in azimuth angle determinations. Layer stripping removes this lag.

The model.-Layer stripping assumes certain subsurface properties. For example, S-wave polarizations must remain practically constant within a layer. Polarizations hence are assumed to change discontinuously at layer boundaries, and S-wave lag in a given layer increases monotonically from zero at the upper boundary to some finite value at the lower boundary. If polarizations were to change continuously with depth, the meaning of polarization analyses after layer stripping would be unclear. Also, each layer must be thick enough, and its birefringence large enough, to determine the correct polarization direction and maximum lag for that layer. The layer stripping procedure can, of course, handle isotropic layers, for which there is no birefringence. For such layers, however, any calculated polarization directions are meaningless. Wave propagation is also assumed to be close enough to a symmetry axis or plane in every layer so

Wells

FIG. 6. Contour map of Lost Hills anticline based on shallow electric log markers. Contours are superposed on the section line grid. In the vicinity of the VSP wells, dip is about I2 degrees downward to the east.


that rotation of sources and receivers by a single angle can do a good job of diagonalizing the 2 x 2 S-wave data matrix.

The procedure.-To do layer stripping we rotate all the data from below the depth at which polarization change occurs by the azimuth angle determined down to that depth and then apply a static shift to remove the lag between the two S-waves at that depth. The process simulates putting a source at the depth where the polarization change occurs, such that the simulated source polarizations are oriented along natural polarization directions (assumed orthogonal) of the upper medium. After layer stripping, rotation analysis is repeated as before, and further layer stripping (i.e., “downward continuation”) is applied if indicated by consistency checks or other cues in the data.

Layer stripping should be effective for surface seismic as well as VSP data, but it may be necessary to use information from VSPs to layer strip surface data. Surface data alone may be inadequate because (I) signal-to-noise ratios are lower than in direct arrival VSP data, and (2) reflection events, which the method would have to rely on, do not necessarily occur close to where polarization changes occur.

Where to strip.--Layer stripping, in contrast to methods involving the calculation of propagator matrices or transfer functions from depth to depth (Nicoletis et al., 1988; Lefeuvre et al., 1989; Cox et al., 1989), encourages the user to judge where to do the stripping on the basis of a preconceived model. The user ordinarily will have criteria in mind for judging from analysis results where polarization directions change and hence where to pick layer boundaries. Layer stripping is thus an interactive process.

Cues in data that S-wave polarization directions have changed often appear as persistent changes with depth in either the azimuth angle or the slope of the lag curve. Lags are often sensitive indicators of change. When polarization direction changes, the slope of the lag curve usually changes abruptly and thus may serve as the interpreter’s principal cue. Calculated azimuth angles, in contrast, tend to be sluggish indicators of polarization change. especially below a thick birefringent layer. At the bottom of such a layer the lag between the S-waves may be quite large. When the waves cross into the layer below, properties of the S-wave wavelets remain much the same as they were in the layer above, despite possible large changes in wave polarizations. The angles from Alford rotation analysis consequently tend to remain the same for some distance below the interface (the inertia effect).

If the polarization change is small-l&20 degrees, for example, it may not be signaled by a change in the slope of the lag curve. For this reason it is wise to layer strip at arbitrary levels as a test for polarization changes that may be masked by the inertia effect (see Paper 11). It is always possible, of course, to do the layer stripping at arbitrary intervals without regard to cues in the data. Most of the timehowever, such a practice would lead to unnecessary data manipulation. It is usually necessary in any case to treat data in blocks of several levels at a time (Lefeuvre et al., 1989). because it is impossible to determine birefringence effects if the two S-waves have not traveled long enough in the birefringent medium to have accumulated a significant lag. What magnitude of lag is significant depends on signal-to-

Layer Stripping Rationale

surface SOURCE

wwr anisotropic layer

s2

*

Sl

wper natural coordinate frame

lower anisotropic layer

4------l., _ si* Pi Sl

Sl lower __.____I

cooratnate --- -

waves waves sourced sourced by S, by S,

FIG. 7. S-waves traveling vertically downward through anisotropic layers with different natural polarization directions. S, and S2 waves of the upper layer will act as independent sources. generating two sets of S’, and Ss waves at the interface. Layer stripping removes the time delay between the two effective sources at the interface, causing the primed waves to behave as if the interface had been at the surface.


noise ratios, but in noisy data birefringence analysis is aided by large lags between S-waves.

In analyzing the Lost Hills VSP data we encountered a thin (-100 ft, -30 m) near-surface layer in which S-wave natural polarization directions were significantly different from those below it. In that case lags could not serve as an indicator of polarization change because not enough of them were mea- sured in the near-surface layer to define a trend. The lag imposed by that layer was sufficient to contaminate azimuth angle analysis, and evidence for a change in polarization was readily apparent in systematic variations in calculated azimuth angles (see Figure 12 below). Because the data did not contain sufficient information about vertical S-wave birefringence of the upper layer, it was necessary to formulate ad hoc criteria, described in the Results section, for stripping that layer.

Details of the procedure.-The first step is to calculate polarization directions and lags for all the conditioned VSP data. The next step is to look for cues in the angle and lag trends that indicate the level where S-wave polarization is likely to have changed. Everything above that level is defined to be the upper layer. We then rotate source and receiver axes, say the x-axes, into alignment with the natural polarization direction of the fast S-wave in the upper layer. The rotation is applied to all data at and below the level where the polarization changed. We denote this as a rotation from the x-_v coordinate frame, which is the initial coordinate frame of the sources, into the x,-y’ frame, the frame of the S-wave polarizations. Ideally, after this rotation, no signal remains on the X’Y’ or Y’X’ components of the upper layer; and signal on Y’Y’ components is the same as on X’X’ components except for a time delay.

Next we apply the static shift, which means we time shift the Y ‘X’, Y ‘Y’, and Y ‘Z’ components from all depths at and below the bottom of the upper layer by the amount needed to eliminate the time delay between X’X’ and Y’Y’ wavelets at the bottom of the upper layer. Eliminating this lag is equiv- alent to positioning .Y’ and .v’ sources at the top of the second layer. The initial rotation before layer stripping will not have properly minimized energy on the X’Y’ or Y’X’ components of the lower layer because the effective x’ and y’ source polarizations acted as though they were excited at diferent depths (different times). The Alford rotations which follow the stripping, however, should do a good job of minimizing energy on those off-diagonal components down to the bottom of the second layer. Also, Alford rotations after stripping should cause lags to increase from a value of zero at the level where change occurs to progressively larger values. Of course, data will not ordinarily be recorded precisely where a change occurs, so even in principle the lag should not always be strictly zero at the level closest to the interface.

After completing the Alford rotation analysis of all data below the upper layer, we look once more at angle and lag trends for evidence that further layer stripping is needed and, if so, we continue the process downward. We also do layer stripping at arbitrary levels as consistency checks.

RESULTS

Near offset VSP data

Data from the 1720 ft (524 m) level of well I 1-10X are shown in Figure 8 as recorded and in Figure 9 after rotation

to minimize energy on the off-diagonal components. The similarity of the two S-wave wavelets after rotation is noteworthy, as are the relatively low amplitudes of the off-diagonal components. This set of traces is one of our better examples of how well real data can fit the simple model.

Data from well I-9J comprise a much more complete set than do those of well 11-10X. The near offset traces are

1.0 --

2 g 1.2 -- ._ k

1.4 --

FIG. 8. The four S-wave components from the 1720 ft (524 m) depth of the 11-10X well after properly combining data from different source pops but before any rotation.

X’X’ X’Y’ Y’X’ Y’Y’

o~81-t 1.0

f

Lag: 28 ms I__. ____

1.4t

1.8 t

FIG. 9. Traces of Figure 8 after rotation to minimize energy on off-diagonal (X’Y’ and Y’X’) components. The final azimuth angle of the fast S-wave polarization was N 40”E. The lag of 28 ms was determined by crosscorrelation.

1340 Winterstein

shown in Figure 10 after rotating receivers into alignment with the source. Figure I I shows the same data after rotation to minimize energy on the off-diagonal components in the analysis window indicated. Low amplitudes within the analysis window on the off-diagonal components at all depths suggest the rotation criterion worked well for this data set, and that the subsurface S-wave polarizations were relatively uniform.

Initial rotation analyses gave azimuths for the 11-10X data that were nearly constant over their relatively limited depth range. In contrast, analyses of the l-9J data gave azimuths that showed a substantial and systematic change with depth (Figure 12). The change in polarization azimuth with depth was counter to expectations from models and led us to suspect that a near-surface layer with a different polarization azimuth was contaminating analysis of deeper data. The strongest indication that S-wave polarizations in the near- surface layer were different from those at greater depths is the azimuth of I3 degrees at 100 ft (30 m), shown in Figure 12. Subsequent angles show a systematic increase in azimuth angle, to 31 degrees at 200 ft (60 m) and from there up to about 60 degrees at 2100 ft (640 m). The change is not erratic, as might be expected from random errors, but smooth, indicating a possible systematic error that might be eliminated by stripping off a near-surface layer.

Initial rotation analyses gave a lag of 9.6 ms at 100 ft (30 m) and 6.5 ms at 200 ft (60 m), below which level the lag increased monotonically down to 800 ft (240 m). We assumed the 9.6 ms value at 100 ft (30 m) was aberrant,

2ioo Ii00 r1bo sbo 160

540 488 335 183 30

Depth

Y 0

Depfh

FIG. IO. Two-by-two (2 x 2) S-wave data matrix from the I-9J VSP after aligning receivers with sources but before Alford rotations. If the subsurface had been isotropic with horizontal layering, no signal would have appeared on off-diagonal (XY and YX) components.

and Meadows

Receiver -b X' 8

2

i

V’

SflSlYSiS

window (

11 21'00 16bo lb0 6bO lb0

m 640 466 336 163 30

Depth

21130 16bO llb0 660 lb0 ft

640 466 335 163 30 m

Depth

FIG. I 1. Data of Figure IO after Alford rotations. Energy of off-diagonal components is small in the analysis window. Increase in S-wave lag with depth is apparent in S-waves on diagonal components.

Depth (m)

2 30 Z a

20

10

0

+++ + +++ + ++++ ++ + + +

+ + +

+

+

I I I I

2000 1500 1000 500 I

Depth (ft)

FK. I?. Polarization azimuths of the fast S-wave as determined from the initial Alford rotation analysis of l-9J data, before any layer stripping. The systematic increase in angle with depth results from contamination by a thin near-surface layer.


possibly because the raypath had a significant horizontal component at that small depth. Consequently we chose 6.5 ms as the amount to strip off initially after rotating source and receiver x-axes to 13 degrees, the azimuth calculated at the 100 ft (30 m) depth.

Stripping simplified the picture considerably. Instead of S-wave polarization azimuths varying more than 25 degrees for depths below 100 ft (30 m), as they did before stripping, they now clustered tightly about 60 degrees with standard deviation of 2.8 degrees. The first five azimuths, however, showed a systematic drop which looked as suspicious as the previous systematic rise in azimuth. Hence we suspected the initial angle and lag were not optimal. To explore the depen- dence of the azimuths on initial angle and lag, we stripped off the near-surface layer using several other starting angles and lags. Results in Figures I3 and I4 show that calculated azimuth angles were insensitive to starting angle but sensitive to starting lag. We chose an angle of 6 degrees and a lag of 5 ms as the best values. Comparing data analyses before and after stripping off the near-surface layer (Figure 13) illustrates how a highly birefringent, thin layer can contaminate analysis of data recorded more than a thousand feet below it.

Variations in S-wave lags with depth after stripping off the near-surface layer (Figure 15) indicate a significant change in birefringence at about 700 ft (210 m). The lags rise uniformly, then level off and drop before continuing to rise again. If the subsurface were homogeneous, the lags would increase at a constant rate, while if the rock became isotropic. lags would remain constant. The only way lags can diminish, as they do from 900-1200 ft (270-370 m). is for anisotropy to change.

90

80

70

c = e 60

‘tj ;; 50 $

5 40 E I r” 30 a

20

10

0

r t

600

Depth (m)

400 200 0 I I I

AAAAA ++

Amount stripped 0 0 ms 0 5 ms + 6.5 ms A 10 ms

Initial angle: N6”E

2000 1500 1000 500 0 Depth (ft)

FIG. 13. Polarization azimuths of the fast S-wave of I-9J VSP FIG. 14. Polarization azimuths of the fast S-wave of l-9J VSP data after stripping off the indicated lags. We chose 5 ms as the best value for eliminating effects of the near-surface

data as a function of initial rotation angle. We chose 6

layer. degrees as the best initial angle, but results are obviously insensitive to initial angle.

Layer stripping down to 700 ft (210 m) and then perform- ing Alford rotation analysis showed that there was no significant change in azimuth and no consistent increase in lags until below 900 ft (270 m). Azimuth changed between 900 and 1200 ft (270 and 370 m). but changes in lags there were inconsistent and small, reaching a maximum of 2. I ms. The zone from 900-1200 ft (27@-370 m), then, caused too little S-wave splitting to have a significant impact on polarization analysis below 1200 ft (370 m). The final layer stripping of the I-9J data hence involved stripping off the zone from 90&1200 ft (270-370 m). Note that the azimuth change in this zone was undetectable before layer stripping (Figure 12).

Results of layer stripping analyses from the surface to 2100 ft (640 m) are summarized in Figures 16 and 17. Except for the near-surface layer and the zone from 700-1200 ft (210- 370 m), the subsurface at the I-91 well proved to be rather uniformly birefringent.

As a check on the validity of layer stripping, it is useful to monitor VSP traces closely after each stripping to determine whether the results fit simple layer stripping models. We have found that seismic data usually fit better after layer stripping than before. For example, Figure 18 compares off-diagonal components at the deepest levels before and after layer stripping. Wave amplitudes in the figure relative to trace spacing are four times those of Figure I I. According to the model, amplitudes of the S-wave direct arrivals should be zero after Alford rotations. Figure I1 shows that amplitudes of off-diagonal, direct-arrival S-waves are low relative to those qf S-waves on the diagonals, but they are clearly lower after layer stripping than before.

9a

80

70

10

0

‘r It

I -

I -

/ -

-

600

Depth (m)

400 200 0

A

Initial angle

0 1”

0 6” + 13"

A 31"

Amount stripped = 6.5 ms

2000 1500 1000 500 Depth (ft)

0

30

25

L


Offset VSP data

Offset data of the l-9J experiment gave remarkably consistent S-wave polarization azimuths (Figure 19), the mean azimuth being 55 degrees and the standard deviation 6.3 degrees. The consistency results from the high SIN, from the relative simplicity of anisotropy in that area and from the fact that the near-surface layer had little influence on data recorded 2000 ft (610 m) below it. The lags, posted above the short, dotted lines indicating azimuths and source locations in Figure 19, are much less consistent than the azimuths and vary systematically along the northeast-southwest polarization direction of the fast S-wave. It is likely that the variation in lags originates in shallow raypath segments, because variations of the magnitudes indicated would be unlikely to originate from portions of raypaths in close proximity, such as those at depth, which converge on the receiver.

Support for this proposed correlation between lag variations and shallow raypath segments comes from comparing lags of the 11-10X VSP with those of the near offset I-9J VSP. The increase in 1 l- IOX lags between 1200-1700 ft (370-520 m) resembles that of the l-9J (Figure 15). The absolute magnitudes, however, are lower in the I-9J data by about 8 ms, consistent with the lag variation observed in Figure 19. Part of the difference in absolute lag (up to 4 ms) appears to result from a relatively small decrease in 11-10X lag in the anomalous zone from 900-1200 ft (270-370 m), but the rest must occur shallower in the section.

MODELING OFFSET VSP POLARIZATION AZIMUTHS

Although polarization azimuths of the offset VSPs were remarkably consistent (Figure 19), modeling the subtle but

600

Depth (m)

400 200 0 1 I 1

+$ +

+ + +

+ +

+ ++++ ++ +

+ +

+ +

2000 1500 1000 500 0 Depth (ft)

FIG. 15. Lags between S-waves of the I-9J VSP after stripping off the thin near-surface layer. Smooth increases in lag indicate uniform S-wave birefringence, but any change in a trend, such as that below 700 ft (210 m), signals a possible change in S-wave polarization.

0

152

305

E B

451

610

762

m

North East South

1 ---

1500

2000 I-

0 50 n

+ 7”,5 ms 0 0”,5 ms

l 700, 2.1 ms o 69”, 1.6 ms

Tulare SS and conglomerate

San Joaquin shale

top diatomite

I I I 100 150 200

Azimuth angle (de!)

FIG. 16. Summary of polarization angles of the fast S-wave versus depth for two independent layer stripping analyses of I-9J VSP data. Angles and lags posted alongside the data points indicate values of layer stripping parameters applied at the top of the layer. For example, the near-surface layer was stripped off with an initial rotation angle of either 7 degrees or 0 degrees, indicated by the different symbols, and a static of 5 ms. (These angles unlike the others are relative to the source azimuth, which was N 6”E.) Layer stripping parameters for deeper layers are given relative to the parameters for the layers immediately above them. The similarity of the two sets of results shows that a 7 degree difference in initial rotation angle had little effect on answers at deeper levels.

0

152

305

5

%

457

610

762

Tulare SS and

501

San Joaquin shale

1500 top diatomite

2000

2500 I / 0 5 10 15

Lag (ms)

-70 m n

FIG. 17. S-wave lag versus depth for the layer stripping sequence indicated by circles in Figure 16. Except for the thin surface layer and an anomalous zone from 700-1200 ft (210-370 m), the subsurface is rather uniformly birefringent.


systematic variations proved surprisingly informative. For example, the flaring out of polarization azimuths to the south and northwest (Figure 20) could be modeled only by incor- porating a small symmetry axis tilt to the east or northeast.

For modeling of offset polarization azimuths we assumed a single homogeneous anisotropic layer whose stiffnesses came from crack sets of various orientations. Crack set properties were from Hudson’s first-order approximation (Hudson, 1981) for cracks filled with weak material. We do not believe that anisotropy in rocks of the uppermost 2000 ft (610 m) at Lost Hills originates in sets of oriented. penny- shaped cracks, but Hudson’s formulation provides a conve- nient way of getting stiffness tensors for modeling. Although the anomalous near-surface layer may have perturbed calculated azimuths at a depth of 2000 ft (610 m), we did not have enough information to strip off the layer for offset VSP data. Near offset data suggest the effect of the near-surface layer had a negligible effect at that depth anyway.

The modeling program we used calculates wave polarizations along straight line rays from the sources to the receiver. It iterates on phase-velocity directions until it finds the appropriate group velocity (ray) direction. Sometimes it is necessary (but not in this case) to guide the iteration interactively if a desired ray lies too close to a point singularity. This program also generated the polarization pattern of Figure 5.

The consistency of observed polarization azimuths in offset VSP data, in combination with lag information from the near offset VSP, suggests a transversely isotropic (TI) model with 3 percent vertical birefringence and a horizontal

after first

rotation

after layer

stripping to 1200 ft (366 m)

11 2100 1700 1300 m 640 518 396

Depth

infinite-fold symmetry axis. Results for this model are shown in Figure 20. where the solid bars show azimuths from real data (Figure 19) and the dotted from the model. The strike of vertical “fractures” was along N 5S”E. The rms deviation from observations was 6.3 degrees. It is clear from the figure that the discrepancies are small but systematic.

Independent evidence actually ruled out a TI subsurface with a horizontal infinite-fold axis (TIH). Figure 21 shows crosshole S-waves from a downhole source in the 12-10 well recorded (by B. N. P. Paulsson) in the 1 I-IOX well. Receiver coordinate frames have been rotated to separate the two S-waves. The horizontal birefringence at the recording depth is about I4 percent, much larger than the vertical birefringence. The horizontal birefringence is not equally large at all depths. and Paulsson’s source was not suited for consistent measurements of it: but its presence indicates that some Lost Hills rocks are definitely not TIH. Hence proper modeling must incorporate media of lower symmetry than TI.

Our best fit, which brought the rms deviation of model from observations down to 3.!I de- rpps~ b. __<. was~obtained with a monoclinic medium created by introducing vertical cracks striking N 55”E into a weakly anisotropic TI matrix, where the infinite-fold axis of the matrix was tilted 10 degrees from the vertical towards N 70”E. Weak TI anisotropy means in this case that v’L/Chh/C44 was 1.025. The fit is shown in Figure 22. At some point, model refinements only improve the fit to noise, and we believe that our best model reached that point.

analysis window a_tiaI

time (s)

analysis window for layer stripping

time (s)

2100 640

1700 516

Depth

1300 ft 396 m

FIG. 18. Off-diagonal components of the 2 x 2 S-wave data matrix of the l-9J VSP after Alford rotations. Traces are from depths below 1200 ft (370 m). In the analysis window, signal amplitudes are lower after layer stripping (bottom) than before (top). an indication that layer stripping improved the fit to the seismic model.


Distance (m) Distance (m)

-300 -200 -100 0 100 200 300

-600

D -200 -100 0 100 200 300 h

17’ Lag in Ills

23 . . .-

23. 17 I ..’ 24 25 I’ ,....’ ” 30. 13.

-. 25 ‘-

.6

11.10x 32 . . . ,/ 1-9J 20. 0 ,’

32 : 33. _’ 30 .’ 20

, ,’ ,..’ _’

30 ,..’ 30

,

-1000 L -1000 -600 -200 200 600 1000

300

200

100 P 2

0 S !Z

3 -100 -

- 200

- 300

30

- 600

-1200

c

c

c

/ 1.

L 21 -1200 -800 -400 0 400 800 I

East-west distance (11) EasCwest distance (11)

FIG. 19. Polarization azimuths of the fast S-waves from two concentric rings of offset VSPs around the l-9J well. The receiver was at a fixed depth of 2000 ft (610 m). S-wave lags, posted above the dotted lines indicating azimuth, generally increase from upper right to lower left (northeast to southwest).

FIG. 20. Polarization azimuths of the fast S-waves from a TI model with horizontal symmetry axis (dotted) superposed on azimuths from offset VSP data of Figure 19 (solid). Although fit is good in most places, it deteriorates to the south and to the northwest for source locations in the outer ring.

Lost Hills Cross-Hole S-Wave Data After Rotation

225 250 275

Rotation Angles: 40,490, loo

interwell Distance: 532 ft

Source Depth: 1760 ft

Receiver Depth: iTJO-*

time (ms)

FIG. 21. Crosshole S-wave data recorded at 1740 ft (530 m) in the 1 I-10X well from a vibrator source at 1760 ft (536 m) in the 12-10 well. The lag between the two S-waves implies about I4 percent horizontal birefringence. This magnitude of horizontal birefringence means that subsurface symmetry cannot be TIH.


Nevertheless, modeling involved many significant variables, and because we could not exhaustively test all possible com- binations, we cannot claim that our best fit is unique or even believable. First of all, we know that the subsurface is inho- mogeneous, but the model which gave a good fit to the data is homogeneous. The good fit apparently means that overly simplified models sometimes do the job in birefringence anal-

ysis as well as they do in other kinds of seismic data analysis. There are good reasons for believing that our best model

has merit, however. First, the vertical S-wave birefringence is relatively uniform with depth and thus appropriately modeled as homogeneous. Second, without the TI matrix, the fit is visibly worse (Figure 20), and such modeling ignores plain evidence for horizontal S-wave birefringence (Figure 21). That the TI matrix should be weakly anisotropic (2.5 percent) does not conflict with crosshole data, which so far are ambiguous on this point. Strengthening the anisotropy of the TI matrix causes the peripheral polarization azimuths to the northwest and southeast (Figure 22) to flare out more and thus fail to fit observations. Removing the IO degree tilt of the TI matrix causes the flaring to be as noticeable to the northeast as to the southwest, whereas measurements show it mainly to the southwest. Finally, the fact that the fit is slightly better when the tilt of the TI matrix is I5 degrees south of the “fracture” strike agrees with what is known about subsurface structure in the vicinity of the I-9J well, namely, that the tilt is more easterly (N 75”E from log data) than northeasterly (see Figure 6). The significance of the need for tilting the TI matrix is that, in this case, symmetry properties of the anisotropy tilt with the subsurface structure.

Distance (m)

-300 -200 -100 0 100 200 300 I c 300

/ / -- 200

/ // / .- 100 P

‘4’

r

-- 0 ? / l-9J

/ 8

.A 3

j .j 1’ ---100 -

’ /

.- - 200

-- 300 -

-1200 -800 -400 0 400 800 1200

East-west distance (ft)

FIG. 22. Polarization azimuths of the fast S-waves from a monoclinic model (dotted) superposed on azimuths from VSP data of Figure 19 (solid).~ The model was obtained by introducing vertical cracks at N 55”E into a weakly transversely isotropic matrix, where the infinite-fold symmetry axis of the matrix tilted 10 degrees from the vertical towards N 70”E. This model is consistent with knowledge about the subsurface.

In summary, although a significantly different model might fit the polarization data as well as the model we used, it probably would not fit independent information on the subsurface as well. Our model, because it fits available geologic knowledge in addition to the VSP data, is probably as accurate as a homogeneous model can be. A remaining unanswered question is whether or not elastic constants from the Nur model would fit the data as well as those from Hudson’s formulation.

DISCUSSION AND COMPARISON WITH TILTMETER DATA

Consistency of S-wave polarization azimuths

S-wave polarization azimuths are consistent for a given anisotropic layer; that is, in the near offset VSP they are consistent from 200-900 ft (60-270 m) and from 1200-2100 ft (370-640 m). Consistency is noteworthy because each calculated azimuth is the result of an independent set of measurements. The lesser consistency in the deeper zone is expected, because layer stripping removes the inertia that builds up in polarization determinations as the lag between the S-wave wavelets increases. The high overall consistency in polarization azimuth results from several factors: consistency in subsurface properties. high S/N in VSP direct arrivals and the fact that waves along vertical raypaths satisfied the model assumptions employed in data analysis. The consistency in azimuth justifies the layer stripping model, which assumes that S-wave polarizations remain constant over appreciable depth ranges.

Layer stripping was effective and important for eliminating effects of a thin, near-surface anisotropic layer that had natural S-wave polarizations different from those of deeper materials. Layer stripping was less important for dealing with a change in anisotropy from 700-1200 ft (210-370 m)

wi

200 m

E

7 4 100m _

Layer

S,.wave polarization

N15”W

S,.wave polarization

N30”E

Layer 2

1” ~I

700 m

FIG. 23. VSP model of MacBeth and Crampin (1991). Polar- ization of the fast S-wave in the shallow layer differs by 45 degrees from that in the deeper layer.


because of the small change in lag there. It is evident from data analysis (Figures 12 and 13) that the anomalous near- surface layer adversely affected polarization analysis down at least to 1500 ft (460 m) and to a serious degree down to about 600 ft (180 m); but the effect is small at the deepest levels. Birefringence of deeper formations will overcome contamination from a near-surface layer when the lag from the near-surface layer is small compared with a wavelength and when the lag between S’, and S’, is much larger than the lag from the near-surface layer.

rotations appear to be so robust despite flagrant violations of model assumptions (i.e., in that XY and YX data components were often obviously dissimilar) is a question that deserves further attention.

We have not modeled effects of the anomalous near- surface layer, but MacBeth and Crampin (1991) have practically done it for us. The upper two layers of their “Test C” come close to representing our near-surface layer and the layer below it: S-wave polarizations in their upper layer are at 45 degrees from those of the lower layer, and the upper layer imposes a lag of 4 ms on the S-waves (Figures 23 and 24). Their method of determining polarization angles is a variant of the Alford rotation method. applied without layer stripping. In calculating S-wave azimuths in their second layer they obtained large systematic errors just below the interface between the first and second layers, but their calculated azimuths gradually converged on the correct angle. Their results with synthetics thus closely parallel ours with real data before layer stripping as shown in Figure I2 and help to justify our interpretation.

The consistency of azimuth calculations from the offset VSP data of the I-9J well is a remarkable confirmation of the robustness of analysis by Alford rotations, to our knowledge the most spectacular of many such confirmations. Each such fast S-wave polarization azimuth was determined first relative to the source azimuth. which varied from location to location. The final pattern became clear only upon correcting individual source azimuths to true north. Hence the consistency cannot be accidental; yet it occurred despite appreciable dissimilarity, in many cases, of the off‘-diagonal components of the 2 x 2 S-wave data matrix. The consistency in azimuth angle of the Alford rotation method was also higher than that from any other polarization analysis method, including-or perhaps especially-hodogram analysis. which was often misleading (Winterstein, 1989). Why Alford

0

700 1 0 30 60 90 120 150 180 0 5 10 15 20

Angle (deg) clockwise from north Lag (ms)

FIG. 24. Azimuth angles (left) and lags (right) of S-waves after analysis by MacBeth and (‘rampin (1991), without layer stripping, of synthetic data from the model of Figure 23. Solid lines show expected values, dashed lines show values actually calculated. Calculated angles in the lower layer converge towards correct answers as lags in the lower layer exceed those in the upper layer.

Subsurface stress directions

Correlating S-wave polarization directions with in-situ horizontal stress directions requires reliable measures of the latter, which can be difficult to obtain. At Lost Hills field, reservoir engineers had investigated a number of stress direction indicators, including wellbore breakouts, interference tests, tiltmeter surveys, hydraulic fracture break- through, passive seismic monitoring, FMS logs, and anelastic strain relaxation. Passive seismic monitoring, FMS logs. and anelastic strain relaxation proved useless as stress direction indicators, and interference testing, which consists of monitoring pressure variations in wells surrounding an artificially pressured well, wel-e ambiguous. Wellbore breakouts and fracture breakthroughs indicated that the maximum horizontal stress was roughly northeast-southwest, but variances were too large to permit confident planning of reservoir development. Analyses of tiltmeter data obtained during hydraulic fracturing gave consistent answers, but because answers depend on what may be an excessively simple model, further confirmation was desired. When polarization directions of the fast S-wave coincided with fracture strike deduced from analyses of tiltmeter data, credibil- ity of both methods increased considerably.

Three tiltmeter data analysts, corresponding to hydraulic fracturing at three different depth levels, were performed for the I-9J well, and five such analyses, corresponding to various stages of fracturing at three different depth levels, were performed for the 12-10 well. Results are in Table I and are also summarized graphically in Figure 25. Close agree- ment with fast S-wave polarizations is obvious for the I-9J well. The 20 degree discrepancy for the 11-10X well is believed to correlate with changes in subsurface structures such as fault surfaces. Error estimates are not shown because those given by tiltmeter data analysts were for random errors (typically +4 degrees). while the most significant


errors here are likely systematic, from failures of overly eas, and from these it should be possible to formulate good simple models to represent subsurface formations properly. theories of causes.

Causes of anisotropy CONCLUSIONS

The dominant orientation of the fast S-wave polarization direction, at about N 60”E, is roughly perpendicular to the strike of the Lost Hills anticline and is thus consistent with a tectonic origin. That is, tectonic stresses which formed the anticline apparently persist today. A northeasterly stress direction is consistent with observations discussed by Zo- back et al. (1987) that indicate maximum horizontal compressive stress is perpendicular to the San Andreas fault in this part of California. The fault, which lies about 20 mi (30 km) to the southwest, trends northwest-southeast.

Why anisotropy should vary with depth here is unknown. The S-wave polarization directions in the near-surface layer are unlikely to be controlled by tectonics: that is, it is difficult to visualize how tectonic stresses could act in a different direction in a thin surface layer than in a thick section immediately below it. Possibly the near-surface material responds in nonrandom fashion to weathering processes.

The disparate polarization directions from 90&1200 ft (270-370 m; Figure 16) are even more difficult to explain. The changes in lag trends with depth (Figure 15) establish beyond doubt that anisotropy in that zone differs from zones above and below. Lithology is much shalier from 710-1250 ft (215-380 m) than elsewhere in the section, with a tight blue clay from 95&l 100 ft (290-335 m); but there is no obvious cause for a change in vertical S-wave birefringence. We speculate that some past stress perturbation left a lasting imprint on small-scale structures of that layer. Or possibly an environment analogous to that of the present-day surface layer imposed its own nonrandom structures, independently of tectonic stresses, which were somehow preserved beneath the subsequent sedimentary load.

Hickman et al. (1988) point out that variations of stress magnitude and direction with depth have been observed elsewhere but have seldom been adequately explained. They suggested that a major stratigraphic discontinuity or slip on a fault might abruptly change stress magnitude or orientation. Further VSP measurements of S-wave birefringence will give a clearer picture than we now have of the variability of subsurface velocity anisotropy in tectonically active ar-

We have shown clear examples of vertical S-wave birefringence in carefully recorded VSP data from the uppermost 2100 ft (640 m) of sedimentary rock in the Lost Hills oil field. The birefringence is obvious because lags between the two S-waves increase monotonically over two depth zones, 20&700 ft and 1200-2 100 ft (60-2 10 m and 370-640 m) in the I-9J well, and this increase is visually evident in plots of X’X’ and Y’Y’ data after applying Alford rotations. Except for a thin near-surface layer and an anomalous zone from 700-1200 ft (210-370 m), the birefringence is almost uniform with depth. Similar but less complete examples of vertical S-wave birefringence are evident in data of the 11-10X VSP. Azimuths of the fast S-wave polarizations calculated by Alford rotation analysis are consistently near N 60”E in the two zones of uniform birefringence in the I-9J well and near N 40”E in the 11-10X well. Offset VSP data recorded at the 2000 ft (610 m) level in the I-9J well also gave very consistent azimuths with a mean of N 55”E. Systematic deviations from the mean were fit well by a simple, homogeneous model of monoclinic symmetry that is compatible with available information on the subsurface. The consistency of the offset VSP results speaks eloquently about the robustness of S-wave polarization measurements at Lost Hills. The high consistency in both offset and near offset results indicates that measure-

l l l l l

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32-268121 E 0 33-268121 E

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D

l

Table 1. Results of tiltmeter data analysis for Lost Hills 12-10 and l-9J wells. Depths are to centers of perforated intervals, 80-170 ft high.

Fracture Fracture S-wave Depth Azimuth Dip Azimuth

Well (ft) (deg) (deg) (deg) - -

l l I l

l l l

l l

12-10 2000 12-10 2000 12-10 2000 12-10 1785 12-10 1620 1-9J 2078 I-9J I898 I-9J 1753

60 53 59 63 61 56

::;

73 NW 73 NW 70 NW (well:) 87 NW 40 (I 1-10X) 87 NW 39 (I 1-10X) 82 NW 59 84 NW 58 86 NW 55

l l l

-;- l l

FIG. 2.5. Well locations in the Lost Hills oil field with lines showing polarization directions of the fast S-waves from two VSPs (solid) and strikes of induced fractures from tiltmeter surveys (dashed).


ments have good repeatability and, where systematic errors are not a concern, that they give high accuracy.

In the case where the fracturing was induced in the VSP well itself (i.e., the I-9J well), the polarization direction of the fast S-wave agreed closely with the strike of hydraulically induced fractures determined from analysis of tiltmeter data. In the case where the fracturing was induced in a well 537 ft (164 m) to the northwest of the VSP well, there was a discrepancy of about 20 degrees, explainable in terms of lateral changes in subsurface structures. Hence S-wave birefringence is a useful tool at Lost Hills for predicting the strike of induced fractures. Tiltmeter data, in contrast, cannot predict fracture strike in a given well because such data must be recorded during the fracturing.

A simple layer stripping procedure enabled us to evaluate accurately the variations in S-wave birefringence with depth. A highly birefringent near-surface layer with S-wave polarization directions different from those of underlying layers caused systematic errors in S-wave polarization azimuths over an interval of more than 1000 ft (300 m) below it. Such errors were effectively eliminated by stripping off that near-surface layer. Further layer stripping uncovered a layer at 90&1200 ft (270-370 m) with S-wave polarization directions unlike any others in the section. Besides clarifying data interpretation, the layer stripping caused data after rotation analysis to comply better with expectations from simple anisotropic models and thereby bolstered our confidence in its validity.

ACKNOWLEDGMENTS

We thank those who aided with planning and data acquisition, especially Clint Frasier, who suggested the offset VSP configuration as a check on interpretability of near-ofTset VSP data. We thank also Paul Donoho and John Fairborn, who made the MicroMAX accessible as a useful field tool. and numerous others, both in Chevron operating companies and at Chevron Oil Field Research Company, without whose timely help the experiments could not have been success- fully completed. Bharat Gael’s enthusiastic consultation and support were extraordinarily helpful, and Louis Klonsky and Dale Julander provided important background information. Indispensable operational support was provided in the field by Don Wheeler, Al Smith, and the field ofice staff. We thank Chevron Oil Field Research Company for supporting the research and for permission to publish.

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