Marmousi2: An elastic upgrade for Marmousi

The original Marmousimodel was created by a con-sortium led by the InstitutFrançais du Pétrole (IFP) in1988. Since its creation, themodel and its acoustic finite-difference synthetic data havebeen used by hundreds ofresearchers throughout theworld for a multitude of geo-physical purposes, and to thisday remains one of the mostpublished geophysical data sets. The advancement in com-puter hardware capabilities since the late 1980s has made itpossible to perform a major upgrade to the model and dataset, thereby extending the usefulness of the model for, hope-fully, some time to come. This paper outlines the creationof an updated and upgraded Marmousi model and data setwhich we have named Marmousi2.

We based the new model on the original Marmousi struc-ture, but extended it in width and depth, and made it fullyelastic. We generated high-frequency, high-fidelity, elastic,finite-difference synthetics using a state-of-the-art model-ing code made available by Lawrence Livermore NationalLaboratory as part of a U.S. Department of Energy researchproject. We simulated streamer, OBC, and VSP multicom-ponent shot records with offsets up to 15 km.

We have found these data suitable for a wide variety ofgeophysical research including calibration of velocity analy-sis, seismic migration, AVO analysis, impedance inversion,multiple attenuation, and multicomponent imaging. As partof this project, the Marmousi2 model and data set are avail-able to other researchers throughout the world.

The Marmousi2 structural model. We created the Mar-mousi2 model by first reconstructing the original Marmousimodel. The original Sierra Geophysical format horizon fileshave been lost with the passage of time, so we needed to

recreate the horizon segments from the gridded represen-tations of the model provided to us by colleagues at IFP.

Once these horizons were regenerated, we expandedthe model from 9.2 km to 17 km in width and from 3 km to3.5 km in depth to better simulate long-offset acquisition ina deepwater setting (Figure 1). The original Marmousi modelis close to the center of Marmousi2. We extended the hori-zons in the original model to fit the expanded model andadded 41 new horizons, bringing the total number of hori-zons in Marmousi2 to 199. Since we are interested in eval-uating amplitude preservation for AVO analysis, theaugmented Marmousi2 model now includes several addi-tional structurally simple, but stratigraphically complex fea-tures outside the original zone of complex structure (Figure2). We also inserted several reservoirs to explicitly modelchannels and other hydrocarbon traps in both the originaland new part of the Marmousi2 model.

Since deepwater exploration (including OBC acquisi-tion) is now of significant interest, we replaced the previ-ous ~32-m water layer with a 450-m water layer. For the samereasons, the original “hard water bottom” effect was reducedby adding two flat transitional layers with thicknesses of 25m and 30 m above the original water bottom. As a result,the original Marmousi structures are approximately 473 mdeeper in Marmousi2.

We did not change layer thicknesses from the original

Marmousi2: An elastic upgrade for MarmousiGARY S. MARTIN, GX Technology, Houston, USAROBERT WILEY and KURT J. MARFURT, University of Houston, USA

156 THE LEADING EDGE FEBRUARY 2006

Figure 1. P-wave velocityfor (a) original Marmousiand (b) Marmousi2. Modelis shown to scale withoutvertical exaggeration.

model. Typically the sediment layers have a thickness in therange of 20-100 m, although minimum thickness ultimatelyapproaches zero at pinchouts and truncations.

Seismic resolution is defined in terms of seismic wave-length, λ=V/f, where λ is the seismic wavelength, V is thevelocity, and f is the dominant frequency. The resolvable limitis normally expressed as λ/4.

Example values of seismic resolution and the corre-sponding resolvable limit for representative shallow, mid-dle depth, and deeper parts of the model are shown in Table1. A range of dominant frequencies, compatible with typi-cal surface seismic data and the actual modeling wavelet,is used for illustration. The wavelet itself is discussed indetail in a later section, and is shown in Figure 8.

Table 1 shows that while some formations will be indi-vidually resolved, the majority of reflection events will becomposites consisting of the interference of more than oneformation in our earth model. Thus, although our 199 hori-zons define formations that are coarser thanin the real earth, the resulting events willmostly be composites.

Layer properties. The original Marmousimodel was an acoustic model—i.e., it onlysupported the propagation of compressional(P-) waves. Marmousi2 is a fully elastic modelthat supports not only compressional waves,but also shear waves, converted waves, andall manner of guided waves including thosetraveling along the sea floor. To define thismodel we needed to assign a shear velocityas well as the original compressional velocityand density to each layer.

In order to assign reasonable shear veloc-

ities, lithologies were first assigned to each layer. TheMarmousi model was based upon geology from the NorthQuenguela Trough in the Quanza Basin of Angola, andalthough the lithologies were not assigned in the model(except for salt and water), the lithologies were described(Versteeg, 1994). The section is primarily composed of shaleunits, with occasional sand layers. The core of the complexfaulted area is an anticline that is composed of marl. Anunconformity and a partially evacuated salt layer separatethe marls from the deeper anticlinal units, which are alsomostly shales with some sand.

We assigned lithology to Marmousi2 (Figure 2) using thefollowing policies. The salt and water layers from the orig-inal model are preserved. The first two layers (transitionallayers) are shale, and possess properties consistent with softmodern sediments. All layers containing hydrocarbons mustbe sand. The anticline above the salt is composed of marl—i.e., carbonate rich shales. All other layers are either sand or

FEBRUARY 2006 THE LEADING EDGE 157

Figure 2. Marmousi2 model, structural elements, horizons, and lithologies.

shale, with the majority of lay-ers being shale. The sand layerswere picked out by analyzingthe density of the original modelassuming that sands are typi-cally less dense than shale.

Regardless of the designatedlithology, the layers were initiallygiven a P-wave velocity identicalto the original Marmousi model.We defined the P-wave velocityusing either a constant velocity ora simple compaction model of V= V0+kz, where z is depth belowsea level, k is a “compaction gra-dient” term, and V0 is the veloc-ity intercept at datum. Sincevelocity gradients account forcompaction due to overburdenloading (and thus water depth isirrelevant), we adjusted the veloc-ity definitions accordingly usingthe following equation: V0 new = V0

old - (k*468) where 468 is the repo-sitioned average depth of theoriginal waterbottom in meters.Thus, the gradients (k) areunchanged, but the intercepts atdatum (V0 values) are reduced.The new layers were assigned P-wave velocities similar to theneighboring units. We displayour final P-wave velocity modelin Figure 3.

Given the lithology and the P-wave velocity, we applied theGreenburg and Castagna (1992)transforms to obtain the S-wavevelocity (Figure 4), and the Cas-tagna et al. (1993) transforms forobtaining the density (Figure 5).We reproduce these transforms(which are defined for water-wetsediments) in Table 2, which alsoshows the values for the otherlithologies in the model.

The P-wave velocity of thesalt layer was reduced signifi-cantly from the value in the orig-inal model (5500 m/s). Wereduced the value to 4500 m/s,which is a more commonly usedvelocity for salt. Correspondencewith velocity modeling expertsat Elf Acquitaine working inAngola confirmed that the pre-vious figure was probably toofast.

We calculated the propertiesfor the marl units using the equa-tions given above for shale andlimestone. Using the Voight-Reuss-Hill method (related byHilterman, 2001), we describedthe marls as 70% shale and 30%limestone.


Figure 3. Marmousi2 P-wave velocity.

Figure 4. Marmousi2 S-wave velocity.

Figure 5. Marmousi2 density.

Hydrocarbons. Since one ofour primary goals was to pro-vide a realistic model to eval-uate the impact of prestackdepth imaging on AVO, weintroduced a series of hydro-carbon layers into the struc-tural model. We display thesehydrocarbons as red (gas) andgreen (oil) in Figures 2 and 6.The hydrocarbons are dis-tributed within the complexfaulted zone at differentdepths, and also in the simplestructure on the flanks. Theselayers vary in their size,shape, structural complexity,and hydrocarbon content(Table 3).

We introduced gas andvarying GOR oil using stan-dard fluid substitution tech-niques. In order to simplifythe fluid substitution calcula-tions, we assigned eachhydrocarbon-bearing layer asingle value for P-wave veloc-ity by calculating the value atthe average depth of the unit.Furthermore, we assumedthat all hydrocarbon layers are normally pressured, at a tem-perature of 95° C, with a mudweight of 10 lb/gallon, a watersaturation of 30%, and an API of 30. The gas/oil ratio isexpressed in cubic feet of gas per barrel at the surface(used/maximum).

In Table 4 we show the results of our fluid substitution.Hydrocarbon substitution results in a drop of the P-wavevelocity, a minor increase of the S-wave velocity, and a smalldecrease of the density. The VP/VS ratio and acoustic imped-ance values both decrease after fluid substitution.

Comparison of the fluid substitution results for the anticli-nal hydrocarbons and the original Marmousi model illus-trates that the original model possessed incredibly largechanges in velocity and density that cannot be supportedby fluid substitution. We assume that these somewhatextreme values were emplaced into the model to ensure avery strong reflectivity response for these units.

Other model features. We also introduced several sandunits that should not be detectable by P-wave data alone.


The units have P-wave and den-sity values identical to the sur-rounding layers so that there isno P-wave impedance change.The shear-wave values weremodified from the values givenby the transforms in order toexhibit a small shear waveimpedance change.

Synthetic data generation. Themajor acquisition objectives forMarmousi2 were to create a highquality, multicomponent, high-frequency, elastic synthetic dataset over a complex structuralmodel. In order for syntheticseismic data to be useful for cal-ibrating data-processing algo-rithms, the modeling processmust accurately emulate thephysical experiment. At the veryleast, the forward modelingmethods must be more accuratethan the inverse methods thatwill be tested.

The elastic wave equationsdescribe the propagation of bothcompressional and shear waves,and implicitly handle mode con-versions. Forward modelingwith the elastic wave equationsshould therefore provide datawith many of the events seen inreal data, including primaries,multiples, diffractions, con-verted waves, head waves, sur-face waves, interface waves, andcomplex scattering. By using anelastic model we will be able tobetter evaluate multicomponentprocessing workflows, theimpact of converted waves on P-wave velocity analysis and imag-ing, multiple suppression in thepresence of S-waves and con-verted waves, and AVO.

For reasons of computationalcost, we did not include 3D effects, and for reasons of sim-plicity, we did not include anisotropy and attenuation. Sinceone of our goals is to provide the horizons and layer para-meter models to other researchers, who may wish to gener-ate subsequent (and more complex) versions of this model forinternal or public use, we encourage others to embrace thistask and share their results.

Geometry. We acquired a full set of elastic shot records overthe model. We show the spacing of the sources and receiversin Table 5 and Figure 7.

The source is a synthetic air gun with a firing depth of10 m. The sailing direction for the source vessel is from lowvalues of X (left) to high values of X (right).

The source signature is a zero-phase 5-10-60-80 Hz Orms-by wavelet with frequencies up to 80 Hz (Figure 8). Thecomputation of 2D models typically involves the use of a “linesource” due to the limitations of 2D modeling. A line sourcediffers considerably from a “point source” in that it has

1/R1/2 rather than 1/R amplitude decay. Also, it has increasedlow-frequency content proportional to 1/f1/2, and mostimportant, it has a phase rotation of 45°. To better approx-imate the phase and frequency content of 3D propagation,we modify our 2D finite difference source by applying a 45°phase rotation, time shift, and frequency filter to provide afar-field, zero-phase wavelet, consistent with one we wouldobtain if we could afford to model the data in 3D (Figure8).

The data were recorded using receivers located along twohorizontal lines (the streamer depth at 5 m below sea leveland the OBC measurement depth at the water bottom of 450m below sea level), and one vertical location (the VSP). The“streamer” cable recorded a hydrophone response (pressure)at 1361 locations with a group interval of 12.5 m, representinga currently unrealistic 17-km cable. For simplicity, and toallow workers the ability to process data with alternativeacquisition programs such as two ship experiments, thecable also extended all 17 km across the model (including


Figure 6. Hydrocarbon units. (a) Overview shows location of hydrocarbon units and areas shown in greaterdetail in (b) and (c). (b) Location of hydrocarbon units in a relatively simple structural setting. (c) Locationof hydrocarbon units in more structurally complex locations.

in front of the “boat”).The “OBC” cablerecorded pressure, thevertical component ofparticle velocity (VZ),and the horizontal com-ponent of particlevelocity (VX), using ahydrophone and twoorthogonal geophonesrespectively. The OBCcable was fixed at thewater bottom and had1381 locations and agroup interval of 12.32m. The unusual group-ing distance resultedfrom parameterizationdifficulties within themodeling software. Thevertical “VSP” cablerecorded both hydrophone and two-compo-nent geophone responses. In addition, a the-oretical “shear phone” was used. Shearphones do not exist in the real world but canbe simulated in the modeling software,recording a wavefield proportional to theshear wave component of the energy. Thevertical cable was at X=10 300 m, withreceivers from the free surface to bottom ofthe model. Receiver groups were spacedevery 12.5 m in depth, making a total of 281receiver groups. Every receiver was “live”(recorded data) for every shot, so, the offsetdistribution of the data has not been limitedto standard streamer lengths or geometries.

Model boundaries. The data were acquiredwith a reflecting free surface, which simu-lates an air/water interface. The reflectingfree surface is commonly the most significantsource of multiples in marine data. Theremaining boundaries are absorbing, suchthat most energy passing out of the model does not reflectback into the model. The modeling software employs a vari-ation of the Clayton Engquist (1990) boundary conditions.

Calculation grid. We chose our calculation grid based onwell understood limits of numerical accuracy. Grids that aretoo coarse result in a faster computation but with bothnumerical dispersion and numerical anisotropy. The gridsampling is given by

To avoid numerical dispersion, approximately five sam-ples per wavelength are required for the slowest velocity inthe model (Levander, 1988). The slowest velocity is approxi-mately 270 m/s (shear-wave velocity), and the maximum fre-quency is 80 Hz. Theoretically, using five samples perwavelength, a grid size of 0.42 m is required, but this wasimpractical for the assigned computational resources.However, looking more closely at the model, it is clear thatonly a very small portion of the model has velocities with val-ues this low. Amore reasonable average minimum shear wavevelocity is around 400 m/s. The required grid size becomes1 m for 80 Hz, 1.14 m for 70 Hz, and 1.33 m for 60 Hz.


Figure 7. Acquisition geometry for Marmousi2. Diagram is not to scale.

Figure 8. (a) Amplitude spectra and (b) wavelet for the source. The blueline represents the actual modeling source wavelet and also characterizesthe signature in the near field. It was derived from the 5-10-60-80 HzOrmsby wavelet (red line) by applying modifications to provide a far-fieldsignature consistent with a point source rather than a line source. The redline is the initial 5-10-60-80 Hz Ormsby wavelet, and also represents themodeling signature in the far field.

Practical memory and runtimelimitations resulted in a compromise.The final grid spacing was 1.25 m.This gives only 2.7 samples per wave-length for the very highest frequencyand absolute minimum velocity,which will result in some dispersionof the wavefield, in the thin layerbelow the water column. Practicalfolks that we are, we now proclaimour inaccurately modeled isotropicbottom to be a more complexanisotropic dispersive water bottomcomplex. However, for all velocitiesover 400 m/s and all frequenciesbelow ~65 Hz, there should be nonumerical anisotropy or dispersion.

Computation. The University ofHouston provided the computa-tional resources to create the syn-thetic data, with a mix of fundingfrom the Department of Energy’s“Next Generation Modeling andImaging Project,” and SunMicrosystems’ UH GeoscienceCenter of Excellence. Twenty nodesof a Sun 6800 Starfire system wereused for a total of five months. Weperformed finite-difference elasticwave modeling using the E3D mod-eling code developed at LawrenceLivermore National Laboratory. E3Dis second-order accurate in time andfourth-order accurate in space.

The computation time averagedabout 20 hours per shot using 6nodes of the system—i.e., about 41⁄2CPU days per shot. The data wereacquired between September 2002and January 2003, using a total of 5CPU months, which is equivalent to70 000 CPU hours, or approximately8 CPU years!

Results. We simulated and recordedmulticomponent wavefront snap-shots, acoustic surface seismic shotrecords, multicomponent OBC seismic shot records, and multi-component VSP seismic shot records.

The wavefront snapshots were recorded on a 1.25-mgrid covering the entire model. The time interval betweensnapshots is 100 ms, making a total of 50 snapshots withinthe time range of 0.1 – 5.0 s. There are two snapshots foreach shot, representing P-waves and S-waves. Snapshotswere recorded only for every 40th shot, due to their largesize and storage requirements. The 14 snapshot locations arespaced evenly every 1000 m, from 3000 to 15 000 m. Thesnapshot display uses a custom color wheel and blendingto combine the P-waves, S-waves, and velocity (Figure 9).Pure P-wave modes appear with a blue-yellow color scale,pure S-wave modes appear with a pink-green color scale,while mixed mode guided and evanescent waves either fallin between or rotate between the two. The Marmousi2 P-wave interval velocity model is mapped to a gray scaleimage behind the wavefronts. Figure 9 shows a zoomedimage of one snapshot (t=1.4 s) with certain features labeled.

The snapshots clearly show that the water bottom is a strongmultiple generator. The high-velocity beds reflect a largeamount of energy, which reduces energy propagating to thedeeper parts of the model. There is also an abundance ofmode conversion taking place within the subsurface. Thestronger (higher acoustic impedance) events tend to be thesource for much of the mode conversion.

The shot records were recorded with a time sampling of2 ms and a record length of 5 s. Figure 10 shows the surfaceseismic shot record for shot 285 (X=7100 m). Figures 11-13show the OBC shot records, also for shot 285. Certain fea-tures are identified and labeled in the figures. The shotrecords closely resemble real field shot records, both in termsof the number of events and complexity. The elastic mod-eling has appeared to create very realistic data from the syn-thetic model.

The single vertical cable, at X=10 300 m, recorded datafor every shot. Therefore there are 480 records for each ofthe hydrophone, VZ geophone, VX geophone, and shear-


Figure 9. Wavefront snapshot for source 201 (at X=5000 m), and t=1.4 s. Selected downgoing andupgoing P-waves (blue-yellow) and S-waves (red-green) are labeled. P-wave velocity is shown in thebackground in gray scale.

phone receivers. A suite of VSP records for a near-offset loca-tion (shot 412, X=10 275 m, source-to-receiver offset of 25m) is shown in Figure 14. The near offset VSP records showthat energy propagating into the earth is dominantly P-

wave energy, but that considerable mode conversion is tak-ing place.

Conclusion. We have created an updated 2D fully elastic


Figure 10. Streamer pressure, shot record 285 (X=7100 m). Figure 11. OBC pressure, shot record 285 (X=7100 m).

Figure 12. OBC vertical velocity, shot record 285 (X=7100 m). Figure 13. OBC horizontal velocity, shot record 285 (X=7100 m).

extension of the Marmousi model for use in the public andprivate domain by the geophysical research community atlarge. We created Marmousi2 with three goals in mind. First,we expect the synthetic data volume to provide a means forresearchers, software vendors, service providers, and oilcompanies to evaluate, calibrate, and compare new devel-opments in velocity analysis, seismic imaging, AVO, andimpedance inversion. Second, we expect the numerical mod-eling community to use Marmousi2 as a basis for more com-plicated models that will include the effects of attenuation,anisotropy, complex stratigraphy, more sophisticated hydro-carbon fluid substitution formulae, and more innovativeacquisition techniques. While of less interest to practicinggeophysicists, our final objective is to provide a model thatis large and complex enough for researchers to evaluateimprovements in algorithm and computer architecture thatwill form the basis for truly 3D numerical modeling of a real-istic seismic survey. The major limitation of Marmousi2 isthat the data are 2D.

The Marmousi2 model and synthetic data have alreadybeen made available to many researchers throughout theworld.

Suggested reading. “The Marmousi experience: Velocity modeldetermination on a synthetic complex data set” by Versteeg(TLE, 1994). “Seismic amplitude interpretation” by Hilterman(SEG distinguished instructor short course, 2001). “Fourth-order finite-difference P-SV seismograms” by Levander(GEOPHYSICS, 1988). “Rock Physics—The link between rock prop-erties and AVO response” by Castagna et al. (Offset-dependentreflectivity – Theory and practice of AVO anomalies, Investigationsin Geophysics no. 8, SEG, 1993. “Absorbing boundary conditionsfor acoustic and elastic wave equations” by Clayton and

Engquist (Numerical modeling of seismic wave propagation, 13,SEG, 1990; reprinted from Bulletin of the Seismological Society ofAmerica, Volume 67:6, 1529-154). “Shear-wave velocity estima-tion in porous rocks: Theoretical formulation, preliminary ver-ification and applications” by Greenburg and Castagna(Geophysical Prospecting, 1992). “The Marmousi2 model, elasticsynthetic data, and an analysis of imaging and AVO in a struc-turally complex environment” by Martin (Master’s dissertation,University of Houston, 2004), available from http://www.agl.uh.edu/downloads/downloads.htm. The reader can also downloadhorizon files and associated model parameters, gridded veloc-ity and density models, and images of seismic data and snap-shots, as well as information on how to request digital copiesof the synthetics. TLE

Acknowledgment: This work was made possible by the contributions ofmany colleagues and associates. First, we thank the Department of Energyfor funding the “Next Generation Numerical Modeling” project led byLeigh House of Los Alamos National Laboratories. Next, we thank ShawnLarsen and Lawrence Livermore National Laboratories for providing uswith an executable copy of the 3D finite-difference code, E3D, as part ofthis DOE project. The computation was performed at the University ofHouston’s Geoscience Center of Excellence provided by Sun Microsystems.We thank Don Larson at GX Technology for modifications necessary toGX-II to enable such a complicated model to be constructed. We also thankAline Bourgeois at the IFP, and colleagues at Total and GX Technology.Finally, we thank Fred Hilterman for help in modifying the model to addressan expanded suite of geologic problems and yet honor the original goalsof the Marmousi experiment.

Corresponding author: [email protected]


Figure 14. VSP for shot 412, (at 10 275 m, CDP 1645). Source to VSP offset is 25 m. Downgoing energy is dipping to the right side of the figures;upgoing energy is dipping to the left side. (a) Hydrophone records P-waves, (b) theoretical shear phone records S-waves, (c) vertical component geo-phone records both P-waves and S-waves, and (d) horizontal component geophones also records both P-waves and S-waves.

Marmousi2: An elastic upgrade for Marmousi

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