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Bulletin of the Seismological Society of America, Vol. 95, No. 6, pp. 2525–2533, December 2005, doi: 10.1785/0120040227

Characteristics of Near-Fault Ground Motions by Dynamic Thrust Faulting:

Two-Dimensional Lattice Particle Approaches

by Baoping Shi and James N. Brune

Abstract Two-dimensional lattice particle models have been used to simulatedynamic thrust faulting and its effects on near-fault ground motions. The latticeparticle modeling approach has been demonstrated as an efficient way to model thedynamic rupture phenomena observed from a foam rubber experiment on dippingfaults. We constructed a 42� dipping fault model to simulate near-fault ground mo-tions under different site conditions in which different combinations of fault geom-etry (blind fault underlying a sedimentary layer and outcropping thrust models) andnear-surface sedimentary layers were investigated. In particular, dynamic behaviorsbetween a blind fault with an overlying sedimentary layer and an outcropping faultwithout a sedimentary layer were compared. In this simulation, a dynamic slip pulseaccompanied by fault separation was initiated at the deepest part of the fault andpropagated updip along the fault under a subshear rupture velocity. A strong asym-metrical ground-motion pattern on the hanging wall and footwall, caused by near-source rupture effects, was observed. Rupture directivity played an important role indetermining the size and distribution of peak ground velocities and accelerations onthe hanging wall and footwall. In the case of an outcropping thrust without a sedi-mentary layer, the hanging wall underwent a stronger ground motion, caused by thenear-surface breakout phase, as the rupture reached the free surface. In the case of ablind thrust overlying a sedimentary layer, the peak ground particle velocity andacceleration could be much larger on the footwall. This is a result of the amplificationeffect of trapped long-period seismic energy in the sedimentary layer. The seismicenergy emitted from the rupture-stopping phase was incident to the sedimentary layerand radiated under the rupture directivity effect. The radiated long-period seismicenergy was trapped in the sedimentary layer, propagating away from the fault tracetoward the footwall side. The numerical results show that, for an initial slip of 5 to5.5 m, the horizontal peak ground velocity and acceleration could reach about 1.5m/sec and 2g, respectively, on the footwall for a blind thrust with a sedimentarylayer. With the same initial slip level, the peak ground velocity and acceleration wereabout 1. 1 m/sec and 1.5g, respectively, on the hanging wall for an outcropping thrustwithout a sedimentary layer. These results can partially explain the field observationsof precarious rock distributions and overturned transformers in the vicinity of theWhite Wolf Fault during the 1952 Ms 7.6 Kern County earthquake. Furthermore, thecurrent simulation can be used for near-fault strong-motion prediction for large thrustfaults in the Los Angeles Basin or similar tectonic settings around the world.

Introduction

As a complement to an earlier work (Brune et al., 2004),in this study, we carried out thrust earthquake modeling bya 2D lattice particle approach. Four types of thrust modelsreflecting real geologic conditions were considered in thisstudy. We demonstrated that dynamic rupture processes(e.g., radiation pattern and rupture directivity and stoppingphases) play an important role in near-fault ground motions.

Recent paleoseismic studies have revealed the potentialthreat of large active thrust earthquakes, both outcroppingand blind, in the Los Angeles metropolitan area (Shaw etal., 2002; Dolan et al., 2003). Precariously balanced rocksand overturned transformers (Brune et al., 2004) in the vi-cinity of the White Wolf Fault from the 1952 Kern CountyMS 7.6 thrust earthquake indicate that near-fault peak ground

2526 Short Notes

motions are extremely asymmetrical on the hanging wall andfootwall, both for outcropping and blind fault segments(Brune et al., 2004). Ground motions constrained by fieldinvestigations of precariously balanced rocks around theWhite Wolf Fault could provide important additional insightinto expected ground motions of anticipated large thrustearthquakes in the Los Angeles basin and in other parts ofthe world.

Motivated by the White Wolf field investigations, weconstructed scenario earthquake thrust fault models using thelattice particle approach (Mora and Place, 1994; Shi et al.,1998, 2003) to simulate dynamic thrusting rupture behaviorwith associated near-fault strong ground motions. Previousstudies with foam rubber experiments (Brune, 1996), latticeparticle modeling (Shi et al., 1998), finite element modeling(Oglesby et al., 1998), and analytical solutions (Madariaga,2003), along with field investigation from several largethrust fault earthquakes (Allen et al., 1998) have shown ex-treme ground motions on the near-fault hanging wall whenthe thrust fault breaks the free surface. Results from thesestudies have also clearly shown that rupture directivity andbreakdown of symmetry with respect to the free surface inthe dipping thrust fault play important roles in stronghanging-wall motion (Oglesby et al., 1998; Shi et al., 1998).

Previous studies have largely neglected an entire classof fault: the so-called blind thrust faults. Geological inves-tigations have indicated that these faults do not extend allthe way to the surface; they shorten in the near surface andare accompanied by folding rather than by fault slip (Suppeet al., 1992; Shaw and Suppe, 1994; Schneider et al., 1996).Oglesby et al. (2000) tested 2D dynamic models of blindthrust and normal faults and compared them to surface-rupturing thrust and normal faults, but their models did notdeal with any sort of low-velocity layer near the surface. Inaddition, the absence of instrumental seismic data from blindthrust faulting creates a gap both in our understanding of thethrusting rupture process and in our ability to estimate near-fault strong ground motion from large thrust fault earth-quakes.

Lattice particle methods, which are similar to the dis-tinct finite-element method, have been successfully used tomodel seismic-wave propagation (Toomey and Bean, 2000;O’Brien and Bean, 2004), tectonic process (Saltzer and Pol-lard, 1992), strike-slip faulting (Mora and Place, 1994,1998), and fracture mechanics (Toomey and Bean, 2002).Recent dynamic simulations of earthquake faulting using 2Dlattice particle modeling have extended results to more com-plicated cases, including the modeling of thrust and normalfault earthquakes, earthquakes with material discontinuitiesacross the fault, earthquakes that include geometrical effectsof the fault model, and earthquakes that include the tectonicconditions of loadings (Shi et al., 1998, 2003).

This article describes a 2D lattice particle approach tomodeling dynamic thrust faulting in which we can includea rough fault interface. Four types of thrust fault modelswere used in these simulations. We focused on the rupturedynamics associated with strong ground motion in the pres-

ence of soft sedimentary layers on the hanging wall as wellas on the footwall.

Results show that rupture directivity, for a blind thrustfault overlain by a soft sedimentary layer on the hangingwall and footwall, has a strong influence on the near-faultground motion on the footwall side of the fault, consistentwith the investigations of precariously balanced rocksaround the White Wolf Fault in California (Brune et al.,2004). As far as we are aware, this effect has not been pre-viously studied, but it may have implications when consid-ering the potential damage on the footwall side of a blindthrust fault overlain by a sedimentary layer, if this phenom-enon occurs in the real world.

2D Lattice Particle Model of a 42� DippingThrust Fault

The lattice particle model is a discrete solid model, be-having like a specific elastic solid. The structure of the modelis similar to the crystal structure in which arrays of particlesobey a certain geometrical law. We considered the close-packed triangular lattice in which each particle has six near-est neighbors and the rest position between particles is r0

when the potential energy is at a minimum. Particles interactwith each other according to a truncated anharmonic poten-tial (modified Lennard–Jones [L-J] potential) (Mora andPlace, 1994; Shi et al., 1998, 2003):

1 2k(r � r ) r � 002�(r) � (1)

12 6r r0 0�e �2 0 � r � rb� � � �� �r r

where r0 is the rest length of the equivalent Hooke’s spring,rb is the cutoff distance equal to 1.112r0, k is the linear springconstant, related to Lame’s constant, in which l � 3/4k�with a Poisson’s ratio of 0.25 (Hoover et al., 1974), ande � r0

2k/36.The corresponding interacting force is obtained by dif-

ferentiating the potential with respect to r (the distance be-tween the two particles considered). More precisely, theforce fij acting on the ith particle due to the interaction withthe jth one is

r � ri jf � F (|r � r |) (2)ij ij i j |r � r |i j

where ri denotes the ith particle position, |•| represents themodulus operator Fij(r � r0) � 0 and kij � �dFij/dr|r0 �0 so as to ensure stability. At the break point, rb � 1.112r0

and beyond, the value of the force function drops to zero,which means that, as the mutual distance |ri � rj| becomeslarger than some threshold rb, the interaction strength is ir-reversibly set equal to 0.

Short Notes 2527

The equation of motion for the lattice particle modelhas been described in previous articles (Shi et al., 1998,2003) as

2d ri p d extm � F � F � F � m g (3)i � i � i � i i2dt

where g is the acceleration of gravity, mi is the mass ofparticle i, ri is the spatial position of particle i, and ispF� i

the sum of the interaction forces from particles bonded to i.is an external force applied to the model. is aext dF F� i � i

viscous force used to damp reflected waves from the bound-ary of the model.

Recent studies (Mora and Place, 1994; Shi et al., 1998,2003) have shown that the 2D triangular lattice particlemodel under the modified L-J potential displays elastic–brittle behavior and is, therefore, considered to represent amaterial well suited for quantitative investigations.

A 2D lattice particle model with a planar thrust fault(macroscopic view) and a fractal distribution of roughnessalong the fault was used in this study. The major purpose ofadding roughness inside the fault is to provide a frictionprocess between the hanging wall and footwall. The detailsof how to add roughness on the fault have been discussedby Mora and Place (1994) and Shi et al. (1998). The basicideas and method presented here are not limited to this spe-cific model and can be generalized to study seismic zoneswith arbitrary fault geometry and plate tectonic boundaries.

For the numerical implementation of the model, a finitedifference modified velocity Verlet algorithm (Allen andTildesley, 1987) was used, so that the new positions of theparticles were calculated right after all the interactions hadtaken place.

The geometry of the thrust fault model is shown in Fig-ure 1. The model consists of two blocks that correspond tothe hanging wall and the footwall of the fault. Inside eachblock, particles are connected with elastic springs. The weakfault is formed with roughness added to each particle on bothsides of the fault. Fault resistance to slip is simulated by therough particles colliding with each other. Thrust faulting re-sults from the applied model boundary conditions. The leftand right boundaries of the fault model are rigidly displacedtoward the fault by steady motion with speed V (where V K

Vparticle, and Vparticle is dynamic particle velocity) so that thefault model is under compression in the horizontal direction.The bottom boundary of the footwall is fixed in the verticaldirection, so there is no particle motion in the vertical direc-tion. At the bottom of the hanging wall, only upward particlemotion is allowed.

Figure 1 shows the schematic configuration of the thrustfault models in terms of bonds and particles. Four types offault models, A, B, C, and D, are involved in this study. Inmodel A, the fault breaks to the free surface (outcroppingcase) without an overlying sedimentary layer on the hangingwall or footwall. In model B, a soft sedimentary layer over-lies the fault hanging wall and footwall, and the thrustingstops below or inside the sedimentary layer (blind fault). In

model C, a soft sedimentary layer overlies the fault hangingwall and footwall, but the thrusting or rupture penetrates thesedimentary layer and breaks the free surface. In model D,the soft sedimentary layer overlies the footwall only, and thethrusting extends to the free surface. For each type of model,lattice spacing is 10 m and comprises about 2 � 106 parti-cles, so that the fault model dimensions for the four modelsare 20 km � 7 km, regardless of the differences in faultgeometry and material properties. The shear velocities are3000 m/sec and 1500 m/sec, respectively, for the bedrockand sedimentary layer. The thickness of the sediment layeris about 1200 m.

Simulation Results

Stick-Slip Motion

Initially, when the driving force was applied at the leftand right boundaries of the fault hanging wall and footwall(Fig. 1), the stress built up steadily along the fault, and astable deformation occurred inside the two blocks while thefault surfaces were stuck together. When the shear stressalong the fault exceeded the local threshold value (the bond-ing strength between the two sides of the fault), a transitionfrom stable deformation to stick-slip occurred, and the localparticle connection between the two sides of the fault wasbroken abruptly. As a result, other bonding springs con-necting the particles between the two sides of the fault some-times snapped, forming a macroscopic rupture propagatingalong the fault. The particles inside the rupture zone under-went a local dynamic stress drop, with finite displacementsin the slip and normal directions. If the particles between thetwo sides of the fault encountered a particularly strong con-nection, the local rupture was arrested. In general, rupturesinitiated at the deepest part of the fault and propagated to-ward the free surface at a speed less than shear-wave velocity(Fig. 2). The particle motion along the fault surface exhibiteda generic stick-slip motion accompanied by a localized nor-mal motion with a fault opening mode (Brune, 1996; Shi etal., 1998). The slip and normal displacements were similarto a ramp and pulse function, respectively, with a short risetime (Heaton, 1990). The calculated local rupture length wasabout 250 m to 300 m, much less that the total length of thefault, and this kind of pulse does not extend to the wholerupture. Our numerical solution clearly showed a short slip-pulse length with abrupt local and partial stress-drop behav-ior (Brune, 1970, 1976; Heaton, 1990; Shi et al., 1998). Therupture process was associated with a clear abrupt locking,self-healing fault opening and closing pulse.

A space–time plot of the particle slip propagation andvariation for fault model A (outcropping without sedimen-tary layer) along the upper 3 km of the fault hanging wall isshown in Figure 2. Arrowed lines with slopes equal to P-,S-, and Rayleigh-wave velocities are shown for reference.The rupture velocity is limited by the Rayleigh velocitywhen the rupture propagates and approaches the free surface.Near the free surface, slip displacement increases greatly,reaching about 7 m, because of (1) the free surface effect

2528 Short Notes

Figure 1. A schematic configuration of the lattice particle model of a thrust fault.The boundary between the hanging wall and the footwall is defined as B, the intersec-tion of the fault plane and the free surface for the outcropping case, and B�, the pro-jection of the fault trace on the free surface for the blind fault case. Four fault modelshave been constructed in this study: (1) outcropping thrust fault without a sedimentarylayer, (2) blind thrust fault with an overlying sedimentary layer on the hanging walland footwall, (3) outcropping thrust fault with an overlying sedimentary layer on thehanging wall and footwall, and (4) outcropping thrust fault with an overlying sedi-mentary layer on the footwall only. The particles represented by the circles are bondedwith each other through a specific interaction potential. The fault surface between thehanging wall block and footwall block is made relatively rough by adding some to-pography to the fault surface. The rough topography has a fractal property. Therefore,the particles between the hanging wall and footwall sides have weaker bonds than theparticles within each block. In the initial particle configuration on the fault surface, thevoids (or gaps) along the fault indicate that the particles occupying these locations haveno interactions with other particles surrounding thorn owing to the initial roughnesseffect applied along the fault.

(Oglesby et al., 1998), (2) the fault opening related to theshear and normal stress reduction (Brune, 1996), and (3) thetrapped kinetic seismic energy at the tip of the fault hangingwall (Shi et al., 1998). A large vibration near the tip of thehanging wall was also observed in a recent foam rubber ex-periment (Brune, 1996) and numerical simulation (Shi et al.,

1998). In this study, the average final slip distribution alongthe fault is about 5.5 m, corresponding to a seismic momentmagnitude of Mw 7.6 derived from the empirical relationlog(D̄) � a � b � Mw (Wells and Coppersmith, 1994),where D̄ is the fault final slip, and a and b are constants withrespective values of �5.46 and 0.82.

Short Notes 2529

Figure 2. Slip variation during rupture propagation along the fault on the hangingwall side. The arrowed lines with slopes equal to the P-, S-, and Rayleigh-wave veloc-ities are shown for reference.

Rupture Propagation

Figure 3 shows the kinetic energy (proportional to ve-locity squared) propagation pattern from thrust fault modelsA, B, C, and D. In each column, five frames show the energyradiation pattern related to the rupture process. The rupturepropagates similarly for models A, B, C, and D in the deeppart of the fault (frame a) and generates a similar final slipdistribution corresponding to a seismic moment of 2.82 �1027 dyne cm. This is because the rupture process is mainlycontrolled by the significant dynamic change in shear stress,and the near-surface effect is quite small and does not affectthe rupture. Frames b, c, d, and e in Figure 3 show the seis-mic energy distributions around the fault as the ruptures ap-proach or reach the free surface with and without a sedi-mentary layer. The asymmetrical particle motion patternsimply that the dynamic process near the free surface is morecomplicated than commonly assumed from kinematic dis-location modeling. In model A, the kinetic energy is con-tained in the hanging wall block, shown in frames b and cin Figure 3, when the rupture reaches the free surface, andpropagates away from the tip of the fault on the hangingwall (frames d and e in Fig. 3). Therefore, a stronger shaking

on the hanging wall side of the fault than on the footwallside is expected because of the multiple reflecting stresswaves trapped in the wedge-shaped hanging wall of the fault(Brune, 1996; Shi et al., 1998). In model B, when the rupturereaches the bottom of the sedimentary layer, the seismic en-ergy carried from the rupture front (stopping phase) goesthrough the sedimentary layer toward the footwall side ofthe fault, because of the directivity effect. The trapped seis-mic energy in the sedimentary layer propagates away fromthe tip of the fault on the footwall side. In other words thesediment acts as a waveguide. Resultant large near-fault par-ticle motion on the footwall is expected because of the fur-ther site amplification caused by the thin soft sedimentarylayer. In model C, the seismic radiation pattern is more com-plicated than that in model A because the trapped seismicenergy in the sedimentary layer also affects the rupture pro-cess. The trapped seismic energy propagates away from thetip of the fault, traveling both on the hanging wall and thefootwall. In this case, because rupture extends to the faultoutcrop, the hanging wall breaks away from the footwall,causing a large opening vibration of the hanging wall; thisphenomenon is similar to the result in model A. Conse-

2530 Short Notes

Figure 3. Snapshots of the particle velocities in a cross section perpendicular to thefault trace for thrust fault models A, B, C, and D. Columns 1–4 represent fault modelsA, B, C, and D, respectively. Frames a–e show the kinetic energy radiation patternsrelated to the rupture process. The resultant radiated energies shown in these frames havebeen normalized to the maximum kinetic energy derived from the dynamic rupture.

quently, the near-fault ground motion is further amplified bythe soft sedimentary layer. In model D, although the faultextends to the free surface, the resultant rupture pulse diesgradually in the updip direction when the rupture propagatestoward the free surface along the fault, because there is amaterial contrast between the hanging wall and the foot wall.In other words, the rupture process strongly depends on themost favorable direction of slip motion in the more compli-ant medium when a material contrast occurs (Weertman,1980; Andrews and Ben-Zion, 1997). Therefore, the incon-sistency between the rupture direction (updip direction) andthe slip direction (downdip direction) of the complaint me-dium (soft sedimentary layer on the footwall) decelerates thepulse-shaped rupture process during updip rupture propa-gation. Compared with models B and C, the resultant near-fault ground motion is much smaller in model D.

Near-Fault Particle Motions on the Free Surface

Figure 4 shows the particle velocity profiles on thehanging wall and on the footwall for thrust models A, B, C,and D (shown in Fig. 1). In model A (Fig. 4, column 1), inwhich the fault breaks the free surface without a sedimentary

layer, the largest velocity pulse corresponds to the particlevelocity at the tip of the hanging wall when the rupturereaches the free surface (breakout phase). The breakoutphase, along with the P-, S-, and Rayleigh-wave phases, arein general agreement with the analytical solution, as dis-cussed by Madariaga (2003). The Rayleigh wave convertedfrom the hanging wall breakout phase travels away from thefault trace along the free surface without spreading (Mada-riaga, 2003). This generalized surface wave dominates thenear-field particle motion. In model B (Fig. 4, column 2), inwhich the thrust fault is buried below the sedimentary layeron the hanging wall and footwall, the rupture is arrestedbelow or inside the sedimentary layer. The radiated energyfrom the stopping phase is incident to the sedimentary layer,and is trapped inside the layer, traveling away from the faulttrace along the free surface on the footwall side. Note thatlarge particle velocity amplitudes, both in horizontal andvertical directions, can occur on the footwall side becauseof the forward (updip) rupture direction. In model C (Fig. 4,column 3), in which the fault goes through the sedimentarylayer and breaks the free surface, the particle velocity fields,both on the hanging wall and the footwall, are further am-

Short Notes 2531

Figure 4. Particle velocity profiles along the free surface for the four thrust faultmodels. These figures show the breakout (or stopping) phases, along with the P-, S-,and Rayleigh-wave phases when the ruptures approach the free surface or enter thesedimentary layer. The x and y components represent the horizontal and vertical particlemotions, respectively.

plified by trapped surface-wave energy inside the layer, andthey have a longer time duration, compared to model A. Inmodel D (Fig. 4, column 4), in which the thrust fault breaksthe free surface and a sedimentary layer overlies only thefootwall side of the fault, the particle velocity fields, bothon the hanging wall and the footwall, are quite different. Theparticle velocities on both walls are relatively weak com-pared with the other three thrust fault models, because of theearlier arrest of rupture caused by near-surface material con-trast on the two sides of the fault. The particle motion on thefootwall side, with the trapped surface-wave energy, lastslonger compared with the results from model A. In fact, thiskind of waveguide effect caused by a sedimentary layer canbe modeled with current dislocation theory if we define therupture model exactly (e.g., a crack-like rupture or pulse-like rupture).

The horizontal peak particle velocities and accelerationsfor fault models A, B, C, and D along the free surface aredisplayed in Figure 5. In all cases, the thrust faulting pro-duces strong asymmetrical ground motion across the faulttrace on the hanging wall and footwall. Near the fault trace,the ground motions are much higher on the hanging wallthan on the footwall in fault models A and C, and there is alarge discontinuity in particle displacement, velocity, and

acceleration from the hanging wall to the footwall. In modelB, the peak ground motions, both in terms of horizontal ve-locity and acceleration, are continuous from the hangingwall to footwall under the fault model definition shown inFigure 1. In this case, the ground motions both on the hang-ing wall and footwall (peak horizontal velocity and accel-eration) are usually larger compared with model A. In modelD, the largest peak ground motions, both in terms of velocityand acceleration, occur on the footwall side. The unusuallyhigh peak particle velocity (�2.4 m/sec) and acceleration(�3.0g) near the fault trace on the hanging wall in model Cis related to the particle motion patterns, in which the bondsof some particles with their neighbors are broken, causingconnections between the main blocks of the hanging walland footwall to be lost; therefore, these particles could movefreely under gravity force. The complicated rupture processinvolved in these models plays an important role in affectingnear-fault particle motions.

Conclusions

Using a 2D lattice particle approach, four types of thrustfault models were adopted to simulate thrusting dynamicrupture with associated near-fault ground motion. Our re-

2532 Short Notes

Figure 5. Horizontal peak particle velocity and acceleration distributions along thefree surface for the four thrust fault models. The zero point along the horizontal axiscorresponds to the fault trace on the free surface (outcropping fault) or the projectionof the fault trace to the free surface (blind fault). The negative and positive parts of thehorizontal axis correspond to the hanging wall and the footwall, respectively.

Short Notes 2533

sults suggest that geometrical differences and material dis-similarity in the upper part of the thrust faults (exposed withor without a sedimentary layer, and buried inside the sedi-mentary layer) can significantly affect the thrust-faulting dy-namics, mainly because of differences in the assumed faultproperties. The near-fault ground-motion patterns exhibitedin these models are, in general, consistent with field obser-vations of precariously balanced rocks and overturned trans-formers in the vicinity of the White Wolf Fault from the1952 Kern County earthquake (Brune et al., 2004) in whichsome parts of fault segments are buried under a sedimentarylayer both on the hanging wall and footwall, and other faultsegments are exposed at the free surface, with or without asedimentary layer. The dynamic features in the present nu-merical simulations differ greatly from those assumed in tra-ditional dislocation models. In fact, if these features occurin the real Earth, they can provide us insight into the dy-namic rupture process of thrust faulting, as well as provideuseful information on ground-motion constraints from largethrust faults such as might occur in the Los Angeles basin,the New Madrid seismic zone, and other parts of the world.In addition, the rupture phenomen a that we have derivedfrom this study can also be useful for improving earthquakesource model descriptions used in dislocation models.

Acknowledgments

We wish to express our appreciation to Mrs. Margaret Luther Smathfor her attentive review of the original manuscript. We are grateful to Dr.Stefan D. Nielsen, Dr. Deborah E. Smith, and Dr. David D. Oglesby fortheir helpful comments and suggestions. This work was supported by theSeismological Laboratory, University of Nevada, Reno, and by NSFCGrant No. 40474031 to School of Earth Sciences, Graduate School of Chi-nese Academy of Sciences.

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School of Earth SciencesGraduate School of ChineseAcademy of SciencesBeijing Yuquan Road #19Beijing 100049, P. R. China

(B.S.)

Seismological Laboratory, MS 174University of Nevada, RenoReno, Nevada 89557-0141

(J.N.B.)

Manuscript received 22 November 2004.