The development of seismic reﬂection sandbox modeling

AAPG Bulletin, v. 85, no. 9 (September 2001), pp. 1645–1659 1645

The development of seismicreflection sandbox modelingDonald H. Sherlock and Brian J. Evans

ABSTRACT

Analog sandbox models provide cheap, concise data and allow theevolution of geological structures to be observed under controlledlaboratory conditions. Seismic physical modeling is used to studythe effects of seismic wave propagation in isotropic and anisotropicmedia, and to improve methods of data acquisition, processing, andinterpretation. By combining these two independent modelingtechniques, the potential exists to expand the benefits of eachmethod. For seismic physical modeling, the main advantages arethat the seismic data collected from these models contain naturalvariations that cannot be built into conventional solid models,which are machined with predetermined structures. In addition, thecost and construction time to build these models is significantlyreduced. For sandbox modeling, the ability to record three-dimensional (3-D) seismic images before the model is manuallysectioned for conventional two-dimensional (2-D) structural inter-pretation allows far more detailed study of subtle 3-D structuresthan previously possible.

In the past other workers have attempted to use unconsolidatedsands for seismic physical models, but these attempts have beenunsuccessful because of the lack of control or understanding of thenatural variations that occur throughout the models. The aim ofour research has been to overcome such problems and to developtechniques to alter the acoustic impedance of sand layers, therebyallowing the subsequent ultrasonic seismic recording of 3-D faultsystems in sand analog geological models.

INTRODUCTION

Analog sandbox models are powerful tools in the study of structuralprocesses in nature and have been used for many years to guide thestructural interpretation of field and seismic data. Reflection seis-mology is the key method in mapping subsurface geology for pe-troleum exploration. Sandbox models, however, have not previ-ously been used to test the correspondence of seismic images ofgeological structures with true geological sections.

The collection of scaled seismic data from physical models,known as “seismic physical modeling,” has two great advantages

Copyright �2001. The American Association of Petroleum Geologists. All rights reserved.

Manuscript received March 22, 1999; revised manuscript received October 3, 2000; final acceptanceNovember 9, 2001.

AUTHORS

Donald H. Sherlock � Department ofExploration Geophysics, Curtin University ofTechnology, P. O. Box U1987, Perth, 6845,Western Australia;[email protected]

Don Sherlock graduated with a B.Sc. (hons)degree in geology from the University ofWestern Australia in 1995 and subsequentlycompleted a Ph.D. in geophysics from CurtinUniversity of Technology in Perth, Australia, in1999. He is currently a research fellow ingeophysics with CSIRO Petroleum in Perth,where he is collaborating with reservoirengineers and geophysicists from CurtinUniversity to develop a physical modelingfacility for seismic monitoring of hydrocarbonreservoir production.

Brian J. Evans � Department ofExploration Geophysics, Curtin University ofTechnology, P. O. Box U1987, Perth, 6845,Western Australia;[email protected]

Brian Evans is an associate professor at CurtinUniversity of Technology. He graduated fromLiverpool as an electrical engineer in 1969and has since completed an M.Sc. degree andPh.D. in geophysics at Curtin University. Brianhas worked on seismic operations throughoutthe world as both a staff geophysicist andgeophysical consultant and is the author ofthe Society of Exploration Geophysicists bookSeismic Data Acquisition in Exploration. Since1985, Brian has lectured at Curtin Universityand is responsible for establishing newresearch projects.

ACKNOWLEDGEMENTS

This study was made possible through the fi-nancial support of Petroleum Geo-Services.

1646 Seismic Reflection Sandbox Modeling

over working with field data. It is orders of magnitudecheaper than performing field surveys, and the geologyis known so its effects on wave propagation can be di-rectly measured and understood. Prior to the researchpresented here, however, all seismic physical modelinghas been performed using solid models comprising pre-determined structures, which imposes constraints onthe realism of the model. Sandbox modeling is a dy-namic process, developing structures that form with allthe idiosyncrasies of natural systems. Hence, the pro-duction of scaled seismic data from such models pro-vides a new modeling concept in understanding three-dimensional (3-D) geology.

In the past, several problems have prevented theapplication of seismic imaging methods to sandboxmodels. The most significant of these are the high rateof energy attenuation of acoustic waves in unconsoli-dated sand and our lack of understanding or control ofthe natural variations in grain packing that occur in themodels. This has limited our ability to study how ul-trasonic reflections can be produced from layers withinsandbox models that have similar acoustic properties.

The fundamental goal of the work presented hereis to address some of the limitations and to move thetechnology forward by understanding how seismic re-flections may be produced within sandbox models in acontrolled and predictable manner. Our results showthat recording a scaled 3-D seismic image over a simplesandbox model before it is manually sectioned for con-ventional two-dimensional (2-D) structural interpre-tation allows far more detailed study of subtle 3-Dstructures than previously possible.

STATE OF THE ART

Sandbox Modeling

Analog sandbox models have proved to be very pow-erful tools in the study of structural processes producedin nature, especially where the phenomena are poorlyunderstood (Vendeville et al., 1987). Such models of-fer cheap, concise data and allow the evolution ofstructures to be observed, leading to a better interpre-tation of structural systems. The model builder cancontrol the boundary conditions and then compare theresults of modeling to natural geological examples, toeither negate or substantiate possible mechanisms forthe development of geological structures. Such modelshave guided the structural interpretation of field andseismic data for more than 60 years (Vendeville and

Cobbold, 1988; McClay, 1989; Withjack et al., 1995).The results of the modeling can be directly comparedwith geological structures for improved conceptual vi-sualization of the processes involved. This type of mod-eling is very difficult to simulate numerically.

Construction of ModelsA conventional sandbox model is constructed by de-positing alternating layers of dry sand consisting of con-trasting colors onto a base. Each layer of sand is typi-cally around 2 mm thick and represents a lithologicallayer within a sedimentary sequence. The layers aresprinkled on by hand as evenly as possible and are ini-tially horizontal to simulate a sedimentary sequenceprior to deformation. Depending on the style of modelbeing built, the base may be solid with a predeter-mined structure, such as a footwall, built in to repre-sent the basement underlying the sedimentary se-quence (Withjack et al., 1995). Alternatively, the basemay consist of a flexible rubber sheet (Harris et al.,1994) or silicone putty (Gartrell, 1997) to simulate theductile lower crust.

Deformation of sandbox models is commonly per-formed by computer-controlled stepper motors oper-ating at a fixed strain rate that is scaled to simulatedeformation over geological time from tectonic forces,although there are also examples where gravity can beused to induce deformation (Gartrell, 1997). As faultsare initiated in the models, more layers of sand areadded to the depressions that form to simulate syn-deformational sedimentation and to prevent the struc-tures from collapsing

Rheology and ScalingRheology describes the response of a material to animposed stress in terms of its elasticity and plasticity.Sandbox models commonly focus on brittle deforma-tion in the upper crust, using dry cohesionless sandgrains; however, they can also incorporate materialssuch as silicone putty or honey, analogous to the duc-tile lower crust and upper mantle. For laboratory re-sults to be considered true analogs of natural struc-tures, it is important that the materials and tectonicprocesses are accurately scaled (Ramberg, 1967).

Horsfield (1977) showed that the rheologicalproperties of moderately cohesive sediments, with fric-tional plastic behavior at the time of faulting, could besimulated with dry sand after scaling down by a factorof between 1:10,000 and 1:100,000. Dry sand has anangle of internal friction � � 30–32�, which is similarto that determined for brittle sedimentary rocks in the

Sherlock and Evans 1647

upper continental crust (Bryerlee, 1978). This valuecan, however, vary significantly depending on the han-dling technique employed (Krantz, 1991) and, as weshow, also has a significant effect on seismic transmis-sion properties. The deformation process obeys theMohr-Coulomb failure criterion for faulting, in accor-dance with deformation mechanisms in the brittle up-per crust (Jaeger and Cook, 1979). The characteristicsof granular material mean that faults develop as dila-tional shear zones (Mandle et al., 1977), and the widthof these is governed by the size and packing distribu-tion of the grains.

The very low cohesive strength of dry sand makesthe models essentially strain-rate independent, and al-lows deformation experiments to be performed over areasonable length of time. Millions of years of tectonicdeformation in sedimentary rocks are commonly sim-ulated in less than a day. Although the cohesion be-tween the sand grains is very small (most authors referto it as “negligible”), it may be important in modelsinvolving fault reactivation (Richard and Krantz,1991).

SectioningThe fundamental approach for the analysis of thestructures formed in analog models is manual section-ing of the model with a knife after deformation hasbeen taken to completion. The most common meansof consolidating the sand sufficiently to prevent themodel from collapsing when sectioned is to saturate itwith a water and gelatin mix. This process providesenough cohesion between the sand grains to allow sec-tions of the model to be cut and photographed for lateranalysis without affecting the internal structure.

Sections can be cut in any orientation, even hori-zontally, but are typically cut vertically in the prevail-ing dip direction to reveal as much information as pos-sible. In this orientation fault throws are at theirmaximum, and features such as antithetic faults, roll-overs, and block rotations are revealed. Typically, sec-tions are cut as closely together as possible to enablethe 3-D geometry to be inferred from the 2-D sections.Most authors cite section spacings of 10 mm; smallerspacings are very difficult to cut by hand. This equatesto scaled dimensions of 100 m to 1 km between sec-tions, which is sometimes barely adequate to map thestructure in three dimensions if the model containscomplex faulting. Nevertheless, having multiple sec-tions from the one geological setting is a luxury un-available in the field and is a fundamental aspect ofsandbox model analysis that makes it so powerful.

Surface ExpressionTime-lapse photography is commonly used to recordprogressive stages of deformation as the model is beingrun. In most cases there is only limited information tobe gained from this because it can record only the sur-face expression of the model. Syndeformational layersof sand are commonly added to the model at progres-sive stages, covering up the faults visible on the surface.The use of lighting at low angles to the surface, how-ever, highlights any visible faults, and photographs ofthis aid in establishing the order that faults are initiatedwithin the model. Although most modeling experi-ments are analyzed from section views, Higgins andHarris (1997) provided an example where a plan-viewapproach was used as the basis for the structuralinterpretation.

Three-Dimensional Computer VisualizationThree-dimensional seismic data are probably the oil in-dustry’s most significant technological advance in re-cent times. Interpretation of these data has been influ-enced by the analysis of analog models. Such models,however, have been analyzed almost entirely by tra-ditional 2-D methods employing mostly cross sections,which commonly makes it impossible to understandthe full 3-D geometry of complex models. Computervisualization software enables serial cross sections froma sandbox model to be digitized, interpolated, and ren-dered in three dimensions to aid in visualizing struc-turally complex geology. This technology has beenused to great effect with salt-related analog models byGuglielmo et al. (1997). This is purely a visualizationtool and does not provide any information that is notalready available from the cross sections of the model.To visualize more subtle structures that may exist be-tween each section, finer spatial sampling is required,which is one of the biggest potential benefits of devel-oping the seismic imaging techniques described in thisarticle.

Computerized X-ray TomographyA recent innovation in imaging structures within sand-box models has been the adaptation of computerizedx-ray tomography, or CT scans, for use with dry gran-ular media. Manual sectioning of sandbox modelsmeans that the model is destroyed and only one ori-entation of sections can be made. CT scans have theadvantage of being nondestructive, and, therefore, theyallow sections to be imaged in several orientations. An-other key benefit of this technique is that it allows theevolution of structures to be observed at progressive


stages of deformation. The CT technique was originallydeveloped for medical imaging (Hounsfield, 1973). Itwas first adapted for use in geology to analyze rockproperties and fractures in core samples (Vinegar,1986; Raynaud et al., 1989). Its use in analyzing analogsandbox models was pioneered by Shell Oil Companylaboratories (Mandl, 1988).

Computerized tomography is based on a set of at-tenuation profiles recorded from an x-ray beam. Ab-sorption of x-radiation by any substance depends on itsbulk density and atomic weight. The lower the densityof the material, the more transparent it is to x-rays. Ifthe materials used are relatively homogeneous, the re-sultant attenuation is roughly proportional to the localdensity (Desrues et al., 1996). Faults develop in gran-ular materials as dilational zones and can result in adensity contrast of around 30% (Colletta et al., 1991),and so they show up as areas of lower attenuation inthe CT scan. Old faults that die out tend to recovertheir initial density, and so it is possible to visualize thefault chronology and emphasize out-of-sequencemechanisms.

Recording a successful CT image from a sandboxmodel is far from simple. The images contain consid-erable noise that is a result of density variations thatinevitably occur from the nonuniform sorting of thesand (Mahmood, 1996). We show that this is a prob-lem that also affects the seismic response in sandboxmodels.

Seismic Physical Modeling

The collection of scaled seismic data from physicalmodels, known as “seismic physical modeling,” has twogreat advantages over working with field data. It is or-ders of magnitude cheaper than performing field sur-veys, and the geology is known so its effects on wavepropagation can be directly measured and understood.Such models, however, incorporate several simplifica-tions and are restricted in their complexity.

Once a model has been built, ultrasonic trans-ducers are used to record 2-D and 3-D seismic dataunder computer control in a known x, y, and z co-ordinate system. This capability offers great poten-tial as a scientific tool to understand the seismicexpression of various structural styles, and offers in-sight into future methods of 2-D and 3-D seismicacquisition and processing for improved target map-ping. In 1991, a physical modeling system was con-structed at Curtin University in Perth, Australia,where it is being used for studying the 3-D effects

of seismic wave propagation in isotropic and aniso-tropic media.

Prior to the research presented here, all seismicphysical modeling had to be performed using solidmodels, which are constructed with predeterminedstructures built into the model. This restriction im-posed constraints on the realism or natural variationwithin the model. Sandbox modeling is a dynamic pro-cess, developing structures that form with all the idi-osyncrasies of natural systems. Hence, the productionof seismic profiles from such models would provide anew modeling concept in understanding 3-D geology.Developing the ability to apply such technology to co-hesionless sand models also reduces the cost and timeinvolved in construction of a physical model.

A major problem in the past that has preventedthe application of seismic imaging methods to sandboxmodels has been the severe energy attenuation ofacoustic waves as they travel through the sand matrices(Purnell, 1986). This is due to several factors such asenergy loss caused by friction between grains in theunconsolidated matrix, an unrealistic ratio of grain sizeto seismic pulse wavelength, and problems of unevenpore-space distribution. In sandbox modeling, the sandis poured onto the model by hand, and therefore, it isimpossible to achieve a completely uniform applica-tion of the sand grains. The heterogeneity of the grainpacking arrays means that every sandbox model isunique. This is both an advantage and a disadvantagein that it adds a degree of realism to the model due tonatural variation but also that the seismic response ofeach model is not consistently repeatable. Thisprompted seismic experiments on samples of grainmixes within consolidated matrices, such as siliconrubber (Purnell, 1986), and resins (Zhang et al., 1996),where grain distribution was more controllable. A fun-damental goal of this work, however, was to overcomesuch problems and move the technology forward.

Scaling and Velocities for Seismic Physical ModelingMost marine seismic data are within in the frequencyrange of 10 to 100 Hz. Therefore, a scale of between1:10,000 and 1:100,000 could be modeled with a 1MHz transducer, which was used for most of this re-search. When scaling physical models, the main rulethat must be followed is that the ratio of geologicalfeature size to wavelength must be the same in bothfield and model. The larger end of this range (1:10,000)was chosen for the sandbox models presented here tominimize problems associated with the grain size towavelength ratio. A typical model area of 300 � 200


mm and depth of around 100 mm represents field di-mensions of 3 � 2 km and a depth of 1 km.

The quartz sand used in most of these models hasa mean grain size of 200 lm and a maximum of 300lm, which, although a good analog for sedimentaryrocks in terms of its deformational behavior, is not idealin terms of the seismic response. A grain size of 200lm represents the equivalent of a 2 m diameter boul-der, which is around one eighth of the seismic wave-length used in these experiments. Grains larger thanthis behave as individual reflectors and contribute tothe significant amount of noise that occurs in thesemodels from scattering of the signal. Therefore, largergrain sizes should not be used. Although the grain sizeto wavelength ratio cannot be scaled realistically, theindividual grains are below the limit of the seismic res-olution and, hence, do not change the seismic expres-sion of the model structures. This is, however, a sig-nificant limitation if the goal is to relate the acousticproperties of individual layers measured at ultrasonicfrequencies to the properties of similar unconsolidatedsands measured in the field at seismic frequencies.

Finer grain sizes are desirable to reduce the degreeof scattering, but this in turn creates other problemswhen saturating the models in preparation for the seis-mic surveys because of the reduced permeability. It isnecessary to develop techniques that ensure that finergrained models can be fully saturated before they canbe used successfully for seismic imaging. Methods un-der consideration to achieve this in future models areto saturate the models while in a vacuum chamber orto use wetting agents to reduce the air-water interfacialtension, which in turn allows the water to permeateinto the smaller pores.

Many modeling materials have velocities muchlower than true rock velocities, and because of this thetime scale is commonly specified independently of thedistance scale. Note that both the distance scale andtime scales are, in a sense, arbitrary, because both thehorizontal and vertical axes can be stretched orsqueezed by resampling when displaying the seismicsection.

Data Recording and ProcessingThe physical modeling system used for this research(Figure 1) comprises a personal computer (PC) drivingan ultrasound pulser unit, using ultrasonic piezoelec-tric transducers for the source and receiver. Movementof the transducers is controlled in three dimensions bystepper motors that are driven by the PC in an x, y,and z coordinate system.

Once a model has been built using dry granularmaterials, it is saturated and placed in a large tank ofwater. Ultrasonic transducers are positioned over themodel to simulate a marine environment, thereby re-cording acoustic waves. Any configuration of 2-D or3-D seismic data can be collected under computer con-trol. The data for the models in this article were col-lected at zero offset, using the same transducer for bothsource and receiver. Conventional surveys using vari-able offsets and common midpoint (CMP) stacking canalso be performed, which is necessary to image themore complex structures that are found in typicalsandbox models. To do so, however, presents furtherproblems that are related to the particular type of high-energy transducer that is needed for sandbox models(Sherlock, 1999).

The output from the receiver is fed into a 12-bitanalog-to-digital converter and then stored on disk ordownloaded over the network directly onto an Exabytemagnetic tape in SEG-Y format. The volume of datacollected is similar in size to that collected in the field.Hence a large disk and tape capacity is a prerequisiteto recording, plus the requirement of processing dataon fast computers.

Data processing is performed using interactiveworkstations networked to a Sun 1000E processorwithin the Department of Exploration Geophysics atCurtin University and uses the Landmark softwarePROMAX. Complex processing steps were not requiredbecause of the simple structure of the models pre-sented here. For example, it was not necessary to in-clude techniques to remove multiple reflections fromthe data because the source and water depth were de-signed such that all multiples would arrive at travel-times later than the primary reflections of interest.More sophisticated processing sequences can, how-ever, be easily implemented when required to betterimage more complex models as they are developed.The only processing applied to the recorded data forthe display of the data and calculation of the reflectioncoefficients was a gain function to recover the ampli-tudes lost through spherical spreading of the sourceenergy and absorption. Three-dimensional visualiza-tion is performed on a Silicon Graphics workstationand uses the Paradigm software VOXELGEO.

Seismic Reflection Theory

Conventional theory states that for a seismic reflectionto result between two layers of rock there must bean acoustic impedance contrast. Acoustic impedance


Figure 1. Schematic diagramof the components that makeup the physical modeling sys-tem at Curtin University ofTechnology in Perth, Australia.

(Z) is defined as density (q) times velocity (V). There-fore, a seismic reflection should result whenever thereis a change in rock density or velocity. The strength ofthe reflection, that is, the percentage of energy re-flected, is dependent on the reflection coefficient (Rc),which is defined by the formula

(Z � Z )2 1cR �(Z � Z )2 1

where Z1 and Z2 are the respective upper and lowerlayer acoustic impedances.

With consolidated rocks, velocity is mainly influ-enced by density (which is dependent on mineralogy,porosity, and fluid type), degree of cementation, pres-sure, and temperature. The relationship of these fac-tors to velocity is described by the Biot-Gassman equa-tion (Biot, 1956a, b). In the case of unconsolidatedsediments, however, the influence of these factors isless clear. Density no longer plays a significant role, and


the major factors become pressure, temperature, andframe rigidity. Bell and Shirley (1980) showed that thetype of loose material makes no difference to the com-pressional wave (P-wave) velocity. Talwani et al.(1973) showed that loose sediments exhibit hysteresis,that is, the velocity change with increasing pressure isreversible whereas the porosity change is not. Thisdemonstrates that the velocity is not dependent onporosity.

At room temperature and pressure, the major in-fluence on loose sediment velocity is the rigidity of thesediment frame (matrix) and fluid type. For the pur-pose of this article, the fluid used is always fresh waterand so can be neglected. The rigidity of the sedimentmatrix can be expressed in terms of the bulk modulus(K), which is defined as

2qVK �

1 � Q

where V is the P-wave velocity, q is the density, andQ is the rock quality factor. For materials of similardensity and velocity, the bulk modulus is approxi-mately inversely proportional to Q, which can bethought of as the ability of the sediment to transmitseismic energy. Q is also related to the attenuation co-efficient (�), which is the exponential decay constantof the amplitude of a plane wave traveling in a ho-mogeneous medium. They are related as follows:

1 �V�

Q qf

where f is the dominant frequency. The grain packingand degree of consolidation govern Q. In unconsoli-dated sands the packing is dependent on grain shapeand sorting.

EXPERIMENTS

Sand Velocities

When considering measured velocities of unconsoli-dated sands in the laboratory it is important to keep inmind several factors:

1. The low total pressure (atmospheric) and zero ef-fective pressure (confining pressure minus porepressure) mean that the rate of energy absorptionthrough friction between the grains is extremely

high. This requires that the length of the sand sam-ple used for velocity tests be kept small to allow atransmitted pulse to be recorded between ultrasonictransducers, which subsequently results in highmeasurement errors.

2. A fraction of a percent of gas is known to have sig-nificant effects on velocity (Domenico, 1976), andit is difficult to ensure that all of the air has beenexpelled from the samples.

3. Velocities are calculated from first-arrival travel-times, and it is assumed that the ray path traveledis the shortest direct path, but this is not necessarilythe case (Wyllie et al., 1958). The direct path mayin fact be slower than the waves through the fluidin the matrix, or be attenuated by the transitionsbetween fluid to grain, to the point of being imper-ceptible. The fastest waves may be those that travelonly in the sand grains and follow a longer zig-zagpath through sand grain contacts.

4. The sands used by different researchers may havesimilar average grain sizes, but they are not the samesamples. Subtle variations in sorting and grain shapemake little difference to the porosity and densitybut have large effects on the frame rigidity and sub-sequently the velocity.

5. The effects of velocity dispersion, whereby differentfrequencies travel at different velocities are not fullyunderstood. In most cases with pulse measurementsthe first arrival is assumed to be the dominant fre-quency or the highest frequency. Liu and Nur(1996), however, suggested that the first break isthe lowest frequency.

6. Vibration applied to the loose sand packages makesa significant difference to the packing of the grains.This is illustrated by observing a sand velocity of1600 ms�1 before vibration, compared with 1730ms�1 measured from the same sample after vibra-tion, which is consistent with measurement bymany researchers, both in situ and in the laboratory.

For these reasons, estimated errors for velocitymeasurements are commonly on the order of 100ms�1, depending on the frequency used. Chotiros(1995) estimated an error of �300 ms�1 below 15kHz. We recorded velocities of individual sand samplesused in the models (all without vibration) using acous-tic pulse transmission measurements (1 MHz), and allsamples were within the range 1600 to 1700 ms�1,varying less than the estimated measurement error.These measurements are considered accurate enoughto demonstrate that the reflections produced in the


pure sand models are not primarily a result of the ve-locity contrast between different layers. Velocities ashigh as 2000 ms�1 were recorded for mixtures of sandand clay (kaolin) powder. The sands tested in this ar-ticle were assumed to have no gas content, and at-tempts were made to ensure this. Nevertheless, it isnot known for certain that all of the air was expelled,particularly with the less permeable sand and claymixtures.

MODELS

The standard sand used as a basis for these modelscomprised subrounded pure quartz grains. This sand ispoor to moderately sorted with a maximum grain sizeof 300 lm and an average around 200 lm. The porositywas measured by weighing a known volume of the sandunder room-dry and fully saturated conditions. Thestandard sand has a porosity of 35% and a saturateddensity of 2.05 g cm�3. Other variations of sands usedwere made from sieved fractions of the standard sand.There was little variation in the measured porositiesand densities except when a very narrow range of grainsizes was used, in which cases the porosity was as highas 38%.

All of the models were constructed in the samemanner, with the only variations being the particularsand used in each of two layers. The first sand (lowerlayer) was poured into a container with dimensions ap-proximately 200 � 100 mm and a depth of 50 mm.At a depth of 20 mm the sand was graded flat to pro-duce a horizontal surface. The second sand (upperlayer) was then carefully sprinkled on top so that thesurface of the first sand was not disturbed. The modelswere then saturated with water and placed in a largewater tank in preparation for the seismic experiments.A 2-D zero offset seismic line was then recorded overeach of the models using a 1 MHz piezoelectric trans-ducer as both the source and receiver. A scale factor of1:10,000 was applied so that the recorded data couldthen be analyzed with conventional seismic data pro-cessing software.

Reflection coefficients were estimated from theamplitudes recorded at the layer interface relative tothe surface. The rate of energy attenuation within thesands has not been precisely determined at this stage,and therefore, it is likely that significant errors exist inthe estimated reflection coefficients. In the followingexamples, the resulting reflections were very strongand the observed amplitudes indicate reflection coef-

ficients around 0.2, which is at least 10 times greaterthan that predicted from the calculated acousticimpedances.

Example 1: Change in Grain Size

ResultsThe first example comprises the standard sand for thetop layer whereas the sand for the bottom layer wassieved so that its average gain size was halved to 100lm. The porosity of this lower sand was reduced to30%, and the density was subsequently raised toaround 2.1 g cm�3. The measured velocity of this sanddid not change perceptibly, and the estimated reflec-tion coefficient was 0.02. Because the depth to thelayer interface is the same in all of the examples (20mm), the velocity of the overlying sand could be easilychecked from the two-way traveltimes between themodel surface and the first reflection and was consis-tently between 1600 and 1700 ms�1. Figure 2 showsthe seismic section recorded over this model; the ob-served reflection coefficient was at least 0.2, which isan order of magnitude greater than that predicted fromthe acoustic impedances.

InterpretationThis first example shows that it is possible to producea strong reflection between unconsolidated sedimentswith nearly identical density and velocity, using only avariation in grain size. The reflection coefficient is atleast an order of magnitude larger than that predictedfrom the calculated acoustic impedance contrast. Wesuggest that the reflection is not a result of a change ofcharacteristics between the different sands used, butinstead a consequence of the interaction of the twomixtures at the layer interface. McGeary (1961)showed with experiments on the mechanical packingof spheres how the packing of grains altered dependingon the sorting of grain sizes. From these results it isconcluded that the porosity at the interface of the twosand layers may be as low as 10%. A precise estimateis not possible because the actual figure is strongly de-pendent on the amount of settling that occurs, whicharranges the grains into the most stable packing order.Although the porosity change does not directly alterthe acoustic properties, it is the effect on the rigidityof the grain packing that produces the contrast.

The strong reflection is interpreted to be a resultof the change in grain packing that occurs at the inter-face between the two layers. This effectively creates athird layer of around one grain thickness, where the


Figure 2. Schematic diagram and scaled seismic section of atwo-layer sand model where the strong reflection from the layerinterface is caused by a contrast in grain size between layers.The data has been scaled by a factor of 1:10,000; g.s. � grainsize.

Figure 3. Schematic diagram and scaled seismic section of atwo-layer sand model where the same sand is used for bothlayers. The reflection from the interface is caused by the changein grain packing that occurs from the action of grading a flatsurface on the lower layer. g.s. � grain size.

packing is more dense and subsequently the porosity isreduced and the frame rigidity is increased. This thirdlayer is analogous to a thin bed in the real world, suchas a low-porosity shale lens between two high-porositysands. Although this layer is too thin to be resolved asan individual layer in the seismic data, the sharp changein acoustic properties produces a reflection. The fol-lowing experiments show that either a change in av-erage grain size or simply a change in grain sorting canproduce such a reflection.

Example 2: Same Grain Size, Change in Packing

ResultsA clearer illustration of the significance of localizedchanges in grain packing is shown in Figure 3, which

shows a reflection from an interface where the samesand was used for both layers of the model. As withthe other models, the top surface of the lower sandwas graded to be horizontal before the upper sand wasadded, but in this case the same sand was used againfor the upper layer. The resulting reflection coefficientis approximately 0.1.

InterpretationIn this case there is no contrast in grain size betweenthe two layers that can create the third layer that hasbeen suggested as the reason for the strong reflectionin the first example. Although the reflection coeffi-cient of around 0.1 is half that of the first example, itis still a very strong reflection that must have beengenerated by a contrast in properties at the layerinterface.


Figure 4. Schematic diagram and scaled seismic section froma sandbox model containing four layers of different sand andclay mixtures.

Our interpretation of this result is that it must havebeen caused by the action of grading the flat surfaceinto the lower sand layer before the upper layer wasadded. This flat surface was created artificially withinthe models by dragging a board over the surface of thesand at a fixed level. Although this action is not anal-ogous to any geological process, it was performed toensure that the interface was perfectly horizontal andat the same depth within every model. In this way, itis possible to accurately compare differences in the in-terval velocity of each model, and it allows the inter-face to be interpreted unambiguously in models withvery subtle reflections or low signal-to-noise ratios. Wesuggest that the process of grading the flat horizoncauses localized changes in the grain packing and sort-ing at the interface between the two sands. As theboard is dragged along the sand surface the smallergrains fall into the cavities of the larger grains, resultingin a more tightly packed grain matrix at the interface.Results of repeated experiments in which the intensityof this grading process was varied support thisconclusion.

Example 3: Multilayer Reflections from Sand and ClayMixtures

ResultsHorizontal layers comprising mixtures of sand andclay (kaolin) were shown to produce strong reflec-tions within models of pure sand. Kaolin appears tostiffen the contacts between the quartz grains (Hanet al., 1986). This has the effect of raising the acous-tic velocity by raising the bulk modulus of the grainmatrix. Limitations on the energy output of thetransducers and the high rate of absorption throughthe uncemented grains make it very difficult to imagemultiple layers at this stage. Various combinations ofmixtures at different depths were tested in an at-tempt to achieve the best balance of reflected andtransmitted energy, thereby allowing as many layersto be imaged as possible. Figure 4 shows a 2-D seis-mic profile recorded over a model containing fourreflecting horizons plus the model surface. The depthto the first layer is 20 mm (200 m scaled), and eachsubsequent depth interval is progressively smaller toensure that any multiple reflections that are gener-ated between layers arrive after the last primary re-flection of interest. The third and fourth horizons areseparated by just 2 mm (20 m scaled) and are diffi-cult to resolve because of the resonant nature of theseismic signal.

InterpretationManually sprinkling the sand into the model containerresults in a natural sorting of the grains. This is analo-gous to the way fining-upward sequences are depositedin fluvial systems, with the larger grains coming to restfirst and finer grains depositing farther down stream.The result is that each single body of sand depositedwithin a particular layer in the model is effectively afining-upward sequence, which has major implicationson the grain packing within the layer. This effect in a


container is sufficiently profound to result in low-amplitude reflections within each of the sand layers,which were initially assumed to be homogeneous.

Evidence that these reflections are a result of thenatural segregation of the grains as they are depositedis provided by the fact that the greatest effect occurswhen the sand is poorly sorted. Such reflections can beclearly seen between the main horizon reflections inFigure 4. This effect is reduced when using well-sortedsands, such as the lower sand in Figure 3, where thereis less variation in grain size and subsequently less sort-ing possible.

Example 4: Reflections from Natural Variations in Sorting

The natural sorting of the sand grains illustrated in theprevious example can be exploited to produce a strongcoherent stratigraphic-style reflection throughout asandbox model. Figure 5 shows an interpretation ofthree horizons from a 3-D seismic volume recordedover such a model. The 3-D survey was recorded witha zero-offset configuration whereby the same trans-ducer is used for both the source and receiver and theseismic waves are transmitted and reflected vertically.The upper and lower horizons are reflections fromlayer interfaces in the model where there is a contrastin grain sizes. The middle horizon has been interpretedfrom a reflection that has been generated within a sin-gle body of sand that exists between the upper andlower horizons. This reflection was generated inten-tionally by exaggerating the effects demonstrated inthe previous examples. The middle sand was depositedas two separate scoops of sand taken from the samebucket. Each scoop was slowly sprinkled into themodel container to allow the natural sorting of grainsto occur. This effect could be seen with the naked eyeas the larger grains tended to rise to the top of thescoop and fall into the container first, leaving a greaterproportion of the finer grained fraction to fall in last.This created a natural fining-upward sequence withinthe layer, resulting in a contrast in packing at the in-terface with the following scoop of sand.

Wedge Model

An example of the resolution possible from seismicsandbox modeling is shown in Figure 6. The modelcomprises a three-layer case where the top sand layerlies on an angular unconformity so that the middle sandlayer forms a wedge that pinches out at the unconfor-mity. The seismic display is a close-up of this pinch-

out, with a field of view approximately 10 mm2 (100m2 in scaled terms). The unconformity is clearly im-aged, and tuning effects can be seen as the middle layerpinches out. These tuning effects are a result of inter-ference between the reflections from the upper andlower interfaces of the wedge. In addition, a much sub-tler depositional feature of the sand onlapping onto theunconformity is also imaged.

Gas/Fluid Contacts

The use of sands in seismic physical modeling allowsdifferent fluids to be incorporated for the first time,providing an analog of hydrocarbon reservoirs. Figure7 shows the seismic data recorded over a sandboxmodel where a pocket of air has been trapped underan impermeable shale anticline. A flat spot can beclearly seen at the contact between the trapped air andthe underlying water. Similar experiments are cur-rently being developed with models that contain moretransitional and subtle contacts between oil and water.

Rift Graben

The aim of the next model is to demonstrate the abilityto record a seismic image from a more conventionalstyle of sandbox model, where the structures are cre-ated by actively deforming the model, rather than con-trived as in the previous examples. Figure 8 shows theapparatus used to produce a simple rift graben. A plas-tic sheet underlies half of the sand in the container andis attached to a moveable end wall. As the wall wasslowly pulled away, a rift developed in the middle,which was continuously infilled to simulate synriftsedimentation and to prevent the structure fromcollapsing.

A 3-D seismic survey was performed by running50 parallel 2-D profiles at spacings of 1 mm (10 mscaled). The reflecting horizon and faults were inter-preted on a workstation and are displayed in a 3-Dvolume form in Figure 9. The image clearly defines arift graben bounded by normal faults. The position ofthese faults varies laterally along the strike of the gra-ben, which is also seen on time slices of the model.Two small raised blocks are visible on the base of thegraben, which trend orthogonally to the strike of therift, along with a small displacement fault, which canbe seen on the upper reflecting horizon to the west.

After the seismic data were recorded, the modelwas physically sectioned with a knife at spacings of10 mm, corresponding to a section along every tenth


Figure 5. Schematic diagramand 3-D visualization of threereflecting horizons within asandbox model. The reflectionsfor the upper and lower hori-zons are generated by a con-trast in grain size between lay-ers. The middle reflection is aresult of natural sorting of thesands as they are depositedinto the model.

seismic line. The model sections reveal the gross formof the faults but are unable to resolve the finer detailsof the model that are seen in the seismic interpretation.Without the seismic data, these subtle details wouldremain undetected, which illustrates the improvementin resolution that is possible using this new technology.

DISCUSSION

The effects of the small-scale heterogeneitieswithin thesandbox model shown do not arise in other studies ofvelocities and attenuationwithin sand, because they areinvariably experiments involving acoustic transmission,

Figure 6. Schematic diagramand scaled seismic section of athree-layer sandbox model con-taining an unconformity. Theseismic display is a close-up ofthe pinch-out in the model.Note the tuning effects of thewaveform as the middle sandlayer gets thinner and also theseismic expression of the topsand layer onlapping theunconformity.

Figure 8. Schematic diagram of the apparatus used to gen-erate a simple rift structure within a sandbox model. As the rightend wall is extended, extra sand is added to the graben as itforms, simulating synrift sedimentation and preventing the struc-ture from collapsing.

‹Figure 7. Schematic diagram and scaled seismic display of ananticline sand model. A pocket of air is trapped under an im-permeable seal, creating a flat spot at the air-water contactwithin the model.


Figure 9. A 3-D interpretation of the sand and clay (shale) horizon reflection. Detailed features such as the raised blocks in thegraben and the small throw fault to the west were not apparent in the manually cut sections of the model.

not reflection. The heterogeneities exist within anyone sample, and therefore, the effects on velocity andattenuation are averaged over the length of the sam-ple that the transmission is being recorded through.Calculations of parameters such as the bulk mod-ulus from these results do not indicate how the mod-ulus may vary at any one point within the sample.With the experiments presented here, however, anyreflections recorded must be a result of a changewithin the model, which can only be from localizedvariations in grain packing. The reflections are anal-ogous to seismic stratigraphic effects and complicatethe assumptions on attenuation because, although theenergy is being reflected and not absorbed, it has thesimilar effect of reducing the amount of energy thatis transmitted through to the layer boundary. Thesestratigraphic reflections are highly sensitive to themanner in which the sand is poured into thecontainers.

This technology, although still in its infancy, is ap-plicable to all forms of sandbox models. The high de-gree of resolution demonstrated in these simple modelssuggests this technique could potentially help with the

interpretation of more complex models that prove dif-ficult to interpret from sections alone. New forms ofsandbox models that incorporate different fluids canalso be considered for modeling hydrocarbon reser-voirs. Other issues that are currently challenges for theseismic industry, such as subsalt imaging or time-lapseseismic could also be examined within a controlled lab-oratory environment using this technology.

CONCLUSIONS

Seismic physical modeling experiments with uncon-solidated sand packages have shown that seismic re-flections can result at boundaries between layers ofequal density and velocity. Conventional theory sug-gests that a contrast in acoustic impedance betweenadjacent layers be required to produce such a reflec-tion. We suggest that, although two different sand lay-ers may have similar or identical acoustic impedances,there is effectively a third layer at the interface itselfwhere the combination of the sands produces the re-quired acoustic impedance contrast.


Developing techniques to combine the methods ofanalog sandbox modeling and seismic physical model-ing have shown the potential to expand the benefits ofeach method. For seismic physical modeling, the abil-ity to use sandbox models dramatically reduces the costand time involved in construction of models while add-ing a degree of realism not previously possible. Forsandbox modeling, the ability to record seismic imagesover them allows far more detailed interpretation ofthe structures.

Closer study of the seismic sections reveals that itis not only possible to accurately map the structure ofthe reflecting horizons in three dimensions, but thatmore subtle depositional features within each sandlayer can also be imaged. This shows that as well asadapting these methods to the wide range of existinganalog sandbox model varieties, there is the potentialto develop new styles as well.

REFERENCES CITED

Bell, D. W., and D. J. Shirley, 1980, Temperature variation of theacoustical properties of laboratory sediments: Journal of theAcoustical Society of America, v. 68, p. 227–231.

Biot, M., 1956a, Theory of propagation of elastic waves in a fluidsaturated porous solid: I–low frequency range: Journal of theAcoustical Society of America, v. 28, p. 168–178.

Biot, M., 1956b, Theory of propagation of elastic waves in a fluidsaturated porous solid: II–high frequency range: Journal of theAcoustical Society of America, v. 28, p. 179–191.

Bryerlee, J., 1978, Friction of rocks: Pure and Applied Geophysics,v. 116, p. 615–626.

Chotiros, N. P., 1995, Biot model of sound propagation in watersaturated sand: Journal of the Acoustical Society of America,v. 97, p. 199–214.

Colletta, B., J. Letouzey, R. Pinendo, J. F. Ballard, and P. Bale, 1991,Computerized x-ray tomography analysis of sandbox models:examples of thin-skinned thrust systems: Geology, v. 19,p. 1063–1067.

Desrues, J., R. Chambon, M. Mokni, and F. Mazerolle, 1996, Voidratio evolution inside shear bands in triaxial sand specimensstudied by computed tomography: Geotechnique, v. 46,p. 529–546.

Domenico, S. N., 1976, Effect of brine-gas mixture on velocity in anunconsolidated sand reservoir: Geophysics, v. 41, p. 882–894.

Gartrell, A. P., 1997, Evolution of rift basins and low-angle detach-ments in multilayer analog models: Geology, v. 25, p. 615–618.

Guglielmo, G. J., M. P. A. Jackson, and B. Vendeville, 1997, Three-dimensional visualization of salt walls and associated fault sys-tems: AAPG Bulletin, v. 81, p. 46–61.

Han, D., A. Nur, and D. Morgan, 1986, Effects of porosity and claycontent on wave velocities in sandstones: Geophysics, v. 51,p. 2093–2107

Harris, L. B., R. I. Higgins, M. C. Dentith, and M. F. Middleton,1994, Transtensional analogue modelling applied to the Perthbasin, Western Australia, in The sedimentary basins of WesternAustralia: Proceedings of the Petroleum Exploration Society ofAustralia, p. 801–809.

Higgins, R. I., and L. B. Harris, 1997, The effect of cover compositionon extensional faulting above re-activated basement faults: re-

sults from analogue modelling: Journal of Structural Geology,v. 19, p. 89–98.

Horsfield, W. T., 1977, An experimental approach to basement con-trolled faulting: Geologie en Mijnbouw, v. 56, p. 363–370.

Hounsfield, G. N., 1973, Computerized transverse axial scanning(tomography): British Journal of Radiology, v. 46, p. 1016–1022.

Jaeger, J. C., and N. G. W. Cook, 1979, Fundamental rock mechan-ics: London, Cambridge University Press, 593 p.

Krantz, R. W., 1991, Measurement of friction coefficients and co-hesion for faulting and fault reactivation in laboratory modelsusing sand and sand mixtures: Tectonophysics, v. 188, p. 203–207.

Liu, X., and A. Nur, 1996, A new experimental method for studyingvelocity dispersion in rocks (abs.): Society of Exploration Geo-physicists 66th International Meeting, Expanded Abstracts,v. 2, p. 1683–1686.

Mahmood, T., 1996, ATLAS 3D analogue modelling of extensionalfault systems plus field applications: Ph.D. thesis, University ofAdelaide, Australia, 187 p.

Mandl, G., 1988, Mechanics of tectonic faulting: models and basicconcepts: Amsterdam, Elsevier, 407 p.

Mandle, G., L. N. J. D. Jong, and A. Maltha, 1977, Shear zones ingranular material: Rock Mechanics, v. 9, p. 95–144.

McClay, K., 1989, Analogue models of inversion tectonics, in M.Cooper and G. D. Williams, eds., Inversion tectonics: London,Geological Society, p. 41–59.

McGeary, R. K., 1961, Mechanical packing of spherical particles:Journal of the American Ceramics Society, v. 44, p. 513–522.

Purnell, G. W., 1986, Observations of wave velocity and attenuationin two phase media: Geophysics, v. 51, p. 2193–2199.

Ramberg, H., 1967, Gravity, deformation and the Earth’s crust: NewYork, Academic Press, 452 p.

Raynaud, S., D. Fabre, F. Mazerolle, Y. Geraud, and H. J. Latiere,1989, Analysis of the internal structure of rocks and character-ization of mechanical deformation by a non-destructivemethod: x-ray tomodensitometry: Tectonophysics, v. 159,p. 149–159.

Richard, P., and R. W. Krantz, 1991, Experiments on fault reacti-vation in strike-slip mode: Tectonophysics, v. 188, p. 117–131.

Sherlock, D. H., 1999, Seismic imaging of sandbox models: Ph.D.thesis, Curtin University of Technology, Perth, Western Aus-tralia, 323 p.

Talwani, P., A. Nur, and R. L. Kovak, 1973,Compressional and shearwave velocities in granular materials to 2.5 kilobars: Journal ofGeophysical Research, v. 78, p. 6899–6909.

Vendeville, B., and P. R. Cobbold, 1988, How normal faulting andsedimentation interact to produce listric fault profiles and strati-graphic wedges: Journal of Structural Geology, v. 10, p. 649–659.

Vendeville, B., P. R. Cobbold, P. Davy, J. P. Broun, and P.Choukroune, 1987, Physical models of extensional tectonics atvarious scales, in M. P. Coward, J. F. Dewey, and P. L.Hancock,eds., Continental extensional tectonics: Geological Society ofLondon Special Publication, v. 28, p. 97–107.

Vinegar, H. J., 1986, X-ray CT and NMR imaging of rocks: Journalof Petroleum Technology, v. 38, p. 257–259.

Withjack, M. O., Q. T. Islam, and P. R. LaPointe, 1995, Normalfaults and their hanging-wall deformation: an experimentalstudy: AAPG Bulletin, v. 79, p. 1–18.

Wyllie, M. R. J., A. R. Gregory, and G. H. F. Gardner, 1958, Anexperimental investigation of factors affecting elastic wave ve-locities in porous media: Geophysics, v. 23, p. 459–493.

Zhang, M., D. A. Ebrom, J. A. McDonald, and R. H. Tatham, 1996,Comparison of experimental velocity measurements with theo-retical results in a solid-solid composite material: Geophysics,v. 61, p. 1429–1435.

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The development of seismic reﬂection sandbox modeling