seismic modeling aseg 082001 andrew long

ASEG 15th Geophysical Conference and Exhibition, August 2001, Brisbane. Extended Abstracts

Understanding elastic wavefield recording by detailed 3D surveyplanning and simulation

Andrew S. Long* Hans-Jurgen Hoffmann Bingwen DuPGS Seres AS, Australia PGS Seres AS, Norway PGS Seres AS, [email protected] [email protected] [email protected]

INTRODUCTION

Wavefield propagation in an inhomogoneous medium is acomplex phenomena, that must be understood if we are toextract information about both the sedimentary structures ofprospective hydrocarbon provinces, and the elastic propertiesof the rocks and fluids of interest. A cursory examination ofhistorically published “seismic survey planning” literatureyields an overwhelming emphasis upon fundamentalgeometric issues – offset requirements, simple criteria forestimating spatial sampling requirements, required recordlengths, etc. Such criteria are no longer sufficient, makingsimplistic and unrealistic assumptions about the Earth, andshed no light upon the dynamic aspects of wave propagation.Seismic survey planning is now a rigorous project that willincorporate all relevant knowledge of the geology, acquisitionsystems, processing requirements and interpretation objectives– all accounted for whilst honouring geophysical integrity andaccuracy. We summarize modern state-of-the art tools andtechniques that offer powerful insights into the application andoptimization of 3D seismic technology. For simplicity, wewill focus most attention upon marine seismic techniques.However, all the principles are equally relevant for landseismic techniques.

SUMMARY OF MODELLING TOOLS

Everything always begins with a detailed understanding of theseismic source, which for marine applications is typically anarray of air guns fired in unison. The output pressurewavefield involves extremely complex mechanical andthermodynamic phenomena. It is critical during any modelingexercise that the so-called far-field signature (an idealisticdescription that can never quite be measured in the field) bedescribable at any azimuth and source emission angle awayfrom the array. This is because of energy directivity effects,which correspond to the direction-dependent output ofradiated energy. Directivity of both the source and receiverarrays must be understood before considering any elasticreflection process wherein amplitude varies with incidenceangle (i.e. recording offset). A thorough “true amplitude”processing sequence would correct for directivity effectsbefore pursuing any kind of AVO-based analysis or elasticinversion scheme. The far-field signature is computed by alinear superposition of notional sources (with appropriate timeshifts and spreading corrections), which are computed becauseof the fundamental fact that the output from an individual airgun in an array can never be directly measured in the field.Interaction effects between the pressure wavefields of each airgun create a complex, time-varying phenomena. Therefore, anumerical integration procedure is required to infer the“notional” source from near-field and mid-field hydrophonemeasurements. Alternatively, it is possible to accuratelymodel the notional sources using a physical modellingalgorithm that accounts for the full time-varying output of anyspecified source array. Sophisticated modeling algorithmshave evolved since the pioneering work of Ziolkowski (1970).Current algorithms use a series of calibrations to controlleddeep fjord measurements of air guns fired in variousconfigurations, and incorporating all interaction,thermodynamic and acquisition system responses. Such amodelling algorithm must be available for survey planning, sothat any possible source array can be accurately simulated andanalyzed.

Likewise, it is essential to understand the full “system”response of the recording hardware (hydrophones, geophones,arrays, streamers, ocean bottom sensors, vertical cables,recording instruments, and any filters involved). Therefore, itshould be possible to separate source and system effects uponthe recorded seismic wavefield from the effects purelyattributable to propagation through the Earth. We may thenfocus upon describing the physical phenomena that affect ourdata – using a variety of Earth models and modelingalgorithms. It is this source-system-model description of thesurvey design process that must be the foundation for allstudies.

SUMMARY

Elastic modelling of seismic wave propagation must bepursued with different algorithms to fully understand allaspects of the recorded information. Modern seismicsurvey planning will utilize a suite of modelling tools,each incorporating the full acquisition system responsefor any given survey. Therefore, the user candiscriminate between acquisition and Earth effects uponthe data. Survey planning no longer simply estimates thebasic configuration of the acquisition equipment. Everyfacet of the seismic method must be replicated andunderstood. Then the data implications of any givenacquisition approach (streamer, land, ocean bottomsensor, vertical cable) can be understood and treatedthroughout the entire processing and interpretationworkflow. In particular, the ability to accurately modelthe Earth reflectivity sequence is critical for AVO,reservoir characterization and time-lapse studies.

After summarizing the main modelling algorithms, wedescribe their integrated use within survey planningexercises, with emphasis upon addressing the elasticproperties of the recorded seismic wavefield.

Key words: Modelling, elastic, acoustic, survey design.

Understanding elastic wavefield recording for survey planning Long and Hoffmann


It is essential to make a distinction at this point betweenacoustic and elastic reflectivity. Theory states that afterignoring some trivial thermodynamic processes, there are 21unique stress-strain relationships (or elastic rock constants)that are required to fully describe the deformation of ananisotropic material subject to a seismic impulse. Forconvenience, isotropic assumptions are typically made,reducing the requirement to only 2 constants (Bulk and ShearModulus). Each of the elastic moduli can be cast in terms ofinstantaneous P- and S-wave velocities (Vp, Vs), and density,as each of their vector values are a direct function of the three-dimensional particle motion. Correspondingly, any non-normal incident seismic wave at an interface will always becomprised of reflected and transmitted P-waves and S-waves.Therefore, mode conversions affect every reflection – which iswhy any P-P AVO study based purely upon Vp informationalone is inherently subject to inaccuracy. In the case of anormal incidence P-wave at an interface, there will be notraction force across the interface, and no conversion toreflected or transmitted S-wave energy. In this unique casethe reflection amplitudes are purely a function of theimpedance contrast (impedance = Vp times density), andwould be addressed by acoustic modelling. Clearly, any finiteoffset, full wavefield modeling exercise must be elastic.

There are essentially three main types of modeling techniquesthat are required to address all aspects of elastic seismic wavepropagation: 1. Recursive reflectivity methods based uponKennet (1983), 2. Ray tracing methods (e.g. Cerveny, 1985),and 3. Full wavefield methods – which are typically basedupon finite-differencing schemes (e.g. Virieux, 1989).

Recursive reflectivity methods are typically “1D” in nature,assuming a flat Earth model. However, they incorporate theoffset dimension, and are amenable for very accurate modelingand simulation of elastic CMP gathers. Source-receiverdirectivity, mode conversions, surface multiples, and interbedmultiples may each be selectively incorporated into themodeling. Unlike ray tracing methods, which are a highfrequency approximation to the wave equation, and breakdown in the vicinity of the critical angle, recursive reflectivitymethods incorporate refraction energy. There is essentially nolimit upon the number of, or thicknesses of layers within thespecified model – each interval layer containing uniquely-defined elastic parameters. However, due to the tau-p domainimplementation of the method, run time can become excessivewith very complicated models. The method is ideal foraddressing the full wavefield interplay between signal andnoise upon recorded gathers, and for amplitude-based studiessuch as AVO modeling, fluid substitution, converted-wavefeasibility studies, etc.

Most AVO feasibility studies will use the followingdiagnostics: Comparison of real vs. modelled PP and PS AVOcurves, frequency-dependent thin layered target responses, andangle range gathers and stacks. The ability to calculate thefull frequency-dependent interaction of various seismicwavefields, even in the presence of thin layering, makes thereflectivity method a valuable complement of any exercise.Furthermore, the incorporation of a rock physics modellingcapability into the algorithm allows any relationships betweenrock properties and AVO attributes to be established for P-Por P-S data. By updating the elastic properties of discrete(target) layers within a 1D model, the user can generate a suiteof synthetic datasets. Then the use of AVO attribute cross-plots, AVO attribute histograms and AVO signature

likelihood displays (e.g. Figure 2) will provide the user withan understanding of the sensitivity of event reflectivity andAVO attributes to rock property variations.

Ray tracing methods may be separated into two separateaspects: kinematic ray tracing (ray path geometry and arrivaltimes) and dynamic ray tracing (geometrical spreadingfactors, wavefront curvature, and amplitude coefficients alongthe ray paths). A layered 2D or 3D model is built, each layercontaining unique interval anisotropic elastic parameters. Theray path and traveltimes along a ray path within a continuousblock of a model are calculated by solving a series ofdifferential equations (the kinematic ray tracing system). Thevelocity function in the block determines the ray behaviour,e.g. a constant velocity (homogeneous layer) yields straightray paths, whereas a linear velocity yields circular rays. Whenthe ray path and traveltimes have been calculated by akinematic ray tracer, one may optionally use a dynamic raytracer to calculate dynamic ray quantities (ray attributes). Thiscalculation is performed along an established ray path, using asimilar system of equations as used for the kinematic raytracer.

Ray tracing may be classified as an approximate solution tothe general wave equation, valid for high frequencies (refer toCerveny, 1985). This means that the seismic wavelength mustbe considerably shorter than the “length of the smallest detailsin the model”. Therefore, it may be a requirement that aninterface(s) are smoothed prior to ray tracing. Most raytheoretical methods pertain to so-called geometrical rays, i.e.following the geometrical law of reflection/transmission(Snell’s law) at all interfaces. Another ray family arediffracted rays, which follow Keller’s law of edge diffractionat a pre-defined diffraction point, i.e. at a point where two ofthe model interfaces intersect (refer to Klem-Musatov, 1994).

The power of the ray tracing method lies in the ability torecord all geometric aspects of each ray segment, including amultitude of associated dynamic parameters – these arecollectively referred to as ray attributes. For any given modelinterface, the distribution of reflection (P-P) or conversion (P-S) points, incidence/takeoff angles, and ray density statisticscan be analyzed in a variety of statistical and graphicalfashions. In particular, illumination analyses (e.g. Figure 3)are a powerful tool that can be used for all types of seismicexperiments, allowing the optimization of subsurface (P-P orP-S) fold coverage both prior to, or during an actual seismicexperiment (assuming that appropriate a priori 3D structuraland elastic information is available for model building). Lima(2000) describes the “real time” updating of a complex 3DEarth model during a production marine 3D seismic survey,using immersive visualization technology to QC thevessel/streamer deployment for optimal fold coverage at thetarget depths. This approach is equally applicable to anyseismic technology – vertical cable, multi-component OBC,land, etc.

Unfortunately, ray tracing methods are not ideal for detailedreflectivity or amplitude studies (e.g. AVO). Whilst themethods serve valuable functions for optimizing surveygeometries, investigating illumination and imaging challenges,and for contributing to a suite of seismic processing issues,either recursive reflectivity methods (for simplified 1D Earthmodels) or “full wavefield” (usually finite-difference) methods(for 2D and 3D Earth models) should be used.

Understanding elastic wavefield recording for survey planning Long and Hoffmann


Although expensive, a fully visco-elastic (2D or 3D) finite-difference modelling program will simulate seismic wavepropagation in complex models with all wave types (P- and S-waves, refracted and converted waves, diffractions, multiplesand prism waves) and all couplings (reflections andtransmissions) included. Source array directivity can also beincorporated. A grid-based Earth model is used, with assignedattributes of P- and S-wave velocity, density, and P- and S-wave absorption. The main cost in finite-difference modellingis associated with the spatial step size used. As the step sizeincreases, the maximum frequency achievable withoutnumerical dispersion (fmax) decreases. While fmax is inverselyproportional to the grid step size, computational cost increasescubically for 2D, and quartically for 3D. Therefore, suchmodelling should be pursued judiciously, using source andreceiver configurations that have been optimized by (muchcheaper) ray tracing exercises with the same Earth model.

No attributes are produced by finite-difference modelling,however, wavefield snapshots can be output from any stage ofwave propagation, allowing an improved understanding of thecomplex phenomena involved. Synthetic data recorded willyield the highest possible simulation of the full wavefield, andthe technique is ideal for studies of P-P/P-S attenuation,anisotropy and fracture analysis (when appropriatelyprogrammed).

Figure 1 compares a single shot gather recorded from the samemodel, as yielded by reflectivity, ray tracing and finite-difference modelling. In each case elastic mode conversionsare allowed, and primaries only (no multiples) are allowed.

INTEGRATION OF TOOLS FOR SURVEY PLANNING

Using the source-system-model approach at all times, a typicalsurvey planning exercise begins with the assimilation of allavailable geological and geophysical data. Ideally, a full suiteof well logs will be provided, enabling an accurate reflectivityanalysis of the seismic response and resolution of the targetlithology and fluid characteristics. Such studies are ofparticular significance for converted-wave ocean bottom cable(4C OBC) surveys, where we seek to understand thedifference between P-P and P-S reflection events. Anyexisting seismic data of relevance will be incorporated into theanalyses at this stage, as there is no substitute for real data thatincorporates the full wavefield response of the target Earthmodel. However, the use of real data in the overall surveyplanning scheme is typically limited, as we are stronglyconstrained by the acquisition parameters used, which willlikely be quite different to those for any new survey. 4C OBSsurvey planning will almost always have no precedent, whichis why the availability of full wavefield logs (including S-wave sonics) is critical. For all survey planning scenarios, theunavailability of full log data will demand some kind ofprediction of the elastic model parameters, and consequently,the integrity of all (P-P and P-S) reflectivity and AVO resultswill be at best approximate.

A suite of 2D and 3D elastic models are then constructed, thecomplexity and accuracy of which are dictated by the amountof available data for model building. It is often the case that anew 3D survey will occur in a relatively virgin area, so themodels built will be by necessity simplistic, and theexperience and technical skill of the survey planninggeophysicists will be of particular importance. Fundamental3D issues like subsurface fold and illumination, analyses of

acquisition footprints, shooting direction etc., are all typicallyaddressed by dynamic 3D ray tracing and processing. Generaloffset and spatial sampling requirements can be addressed byall the modelling methods, depending upon the complexity ofprimary and noise interference at larger offsets, and upon thedetail of resolution and AVO criteria specified for the survey.Each acquisition parameter is addressed individually by avariety of real data and modelling tests, and an understandingof the overall wavefield phenomena for the target area willdevelop. In areas of existing seismic data, incorporation of thereal navigation data will increase the relevance of anymodelling results.

High-end studies involving reservoir characterization, fractureanalysis and reservoir monitoring feasibility studies all requirethe full wavefield modelling power of 2D and 3D visco-elasticfinite difference algorithms, and will involve comprehensivelog analysis, rock physics investigation, and seismicmodelling, greatly expanding upon the scope of exploration-scale survey planning

CONCLUSIONS

Seismic survey planning has evolved to become a complexprocess that must incorporate all available geological andgeophysical data for a study (survey) area, and will demand acomprehensive understanding of wave propagation principles.Depending upon the nature and complexity of the study, theeffort required will correspondingly vary, however, at alltimes, a full consideration of the elastic characteristics of therecorded seismic wavefield must be honoured. Overall, thekey is that a comprehensive suite of elastic modelling tools areavailable, all incorporating the source-system-model concept,and all equally able to simulate the full range of acquisitionapproaches possible (multi-source, multi-streamer systems,ocean bottom sensors, vertical cables and fixed geometries).

REFERENCES

Cerveny, V., 1985, The application of numerical modelling ofseismic wavefields in complex structures, In: Seismic shearwaves, Part A: Theory, (Ed.) G. Dohr, Handbook ofgeophysical exploration, (Eds.), K. Helbig and S. Treitel,Geophysical Press, London, p. 1-124.

Kennet, B., 1983, Seismic wave propagation in stratifiedmedia, Cambridge University Press

Klem-Musatov, K., 1994, Theory of seismic diffractions,(Eds.) F. Hron and L. Lines, SEG, Tulsa, OK, USA.

Lima, Y., 2000, Using VR tools to quality control seismicacquisition surveys, Offshore, August, 136.

Virieux, J., 1989, P-SV wave propagation in heterogeneousmedia: Velocity-stress finite difference method, Geophysics51, 4, 889-901.

Ziolkowski, A., 1970, A method for calculating the outputpressure waveform from an air gun, Geophys. J. R. Astr. Soc.21, 137-161.


Figure 1. Example of the synthetic shot gathers output from the three main modelling algorithms. Using the simple elastic 1Dmodel on the left in all cases, the results are shown (from left to right) from 1D reflectivity, 2D dynamic ray tracing, and 2Dvisco-elastic finite-difference modelling. Note that ray tracing is by far the fastest method, but yields the least events. Incontrast, finite difference modelling is the most expensive, but yields the most complete representation of the full wavefield.

Figure 2. Example PP (left) and PS (right) AVO likelihood plots for a target reservoir horizon. Such analyses can be used fora 1D elastic model based upon well log data. Integration of rock physics programs can be used to pursue fluid substitutionand lithology perturbation studies at discrete intervals, and the generation of a suite of synthetic data and diagnostic displayssuch as those shown here.

Figure 3. Example PP and PS reflection strength at the top of an anticlinal feature. This result is derived from dynamic 3Dray tracing, and simulates the ideal migrated amplitude response at the target horizon. Note the differences in illuminationdue to the fundamental differences in PP and PS ray path geometries. The “ring” of sparse illumination in both casescorresponds to the pinchout of onlapping strata in the full 3D model (only the target horizon is plotted here).

PS-converted wavesPP-waves

seismic modeling aseg 082001 andrew long

Technology