Topographic e�ects on exploration seismic data �

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Figure �� Synthetic seismograms with a �eld topographic structure�

Fu� L� Y�� ����� ��D boundary element seismic modeling in complex geology ��th Ann� Internat� Mtg�� Soc� Expl� Geophys�� ExpandedAbstracts� �������

Fu� L� Y�� Mu� Y� G�� and Yang� H� J�� ����� Forward problem of nonlinear Fredholm integral equation in reference medium viavelocity�weighted wave eld function Geophysics� ��� ��������

Kennett� B� L� N�� ����� On the nature of regional seismic phases�I� Phase representations for Pn� Pg� Sn� Lg Geophys� J�� �����������

Lay� T�� and Wallace� T� C�� ����� Model global seismology Academic Press� Inc�McLaughlin� K� L�� and Jih� R� S�� ����� Scattering from near�source topography teleseismic observations and numerical simulations

Bull� Seis� Soc� Am�� ��� ����������McMechan� G� A�� and Chen� H� W�� ����� Implicity static corrections in prestack migration of common�source data Geophysics� ���

��������Ronen� J�� and Claerbout� J�� ����� Surface�consistent residual static estimation by stacking�power maximization Geophysics� ���

��������Sanchez�Sesma� F� J�� and Campillo� M�� ����� Topographic e�ects for incident P� SV� and Rayleigh wavesTectonophysics� ���� �������Wang� B�� Cheng� S� W�� Pann� K�� and Deng� H� L�� ����� Estimating large statics by a simpli ed stacking power approach using local

optimization ��th Ann� Internat� Mtg�� Soc� Expl� Geophys�� Expanded Abstracts� ����������Wu� R� S�� and Aki� K�� ����� Scattering characteristics of elastic wave by an elastic heterogeneity Geophysics� ��� �������Wu� R� S�� ����� Wide�angle elastic wave one�way propagation in heterogeneous media and an elastic wave complex�screen method J�

Geophys� Res�� ��� ��������Wu� R� S�� ����� Synthetic seismogram in heterogeneous media by one�return approximation Pure and Applied Geophys�� ��� ��������

Topographic e�ects on exploration seismic data �

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Figure �� Synthetic seismograms for anomalous topographies�

shot by shot along the line to assist in designing an optimal source�receiver geometry in the light of the near�surfacecondition� obviating the near�surface e�ects as much as possible� The implementation of this scheme is facilitatedwith topographic elevation data and a rough near�surface velocity distribution obtained by refraction statics analysisor other methods� Another method is the inverse scattering extrapolation of full wave�elds to deal with strongnear�surface scatterings caused by rugged free surface and near�surface heterogeneities�

Acknowledgements�

The support from the U�S� Department of Energy � Basic Energy Sciences and the facilities supported from the W�M�Keck Foundation are appreciated�

References

Aki� K�� ����� Local site e�ects on strong ground motion� In Von Thun� J� L�� Ed�� Earthquake engineering and soil dynamics II�Recentadvances in ground motion evaluation Am� Soc� Civil Eng�� New York� ��������

Berryhill� J� R�� ����� Wave�equation datuming Geophysics� � ���������

Bevc� D�� ����� Flooding the topography Wave�equation datuming of land data with rugged acquisition topography Geophysics� �������������

Bouchon� M�� Schultz� C� A�� and Toksoz� M� N�� ����� E�ect of three�dimensional topography on seismic motion J� Geophys� Res������ ����������

Clouser� R� H�� and Langston� C� A� ����� Modeling observed P�Rg conversions from isolated topographic features near the NORESSarray Bull� Seis� Soc� Am�� ��� ��������

Topographic e�ects on exploration seismic data �

ered the pros and cons of various alternative modelingmethods� we prefer to combine the boundary integralequation with the Lipmann�Schwinger integral equationin the background medium to handle the near�surfacee�ects on wave propagation� The former is very conve�nient to deal with the traction�free condition and cangive a full description of arbitrarily rugged topographywith irregular acquisition geometry� but only suitableto model wave propagation in piecewise homogeneousmedia �Fu� ��� The latter can be used to handlegeneral heterogeneous media �Wu and Aki� ��� Itcan be solved approximately by the generalized screenmethod �Wu� �� �� and accurately via a velocity�weighted wave�eld �Fu et al�� ��� All computations ofsynthetic seismograms presented in this paper are per�formed in the frequency range � � �� Hz� with receiversalong the free surface� and the source at depth �� mbelow the free surface� To make the e�ect of topogra�phy clear� direct arrivals from the source to receivers areremoved�

Examples

Figure shows a �at free�surface model and the cor�responding synthetic seismograms� We see that themain e�ect of a �at free surface is the reverberationsbetween the free surface and the re�ecting boundaries�The energy of the secondary sources due to the free�surface re�ection is almost the same as that of the �rstsource� This e�ect is mainly related to the source depthand dominant frequency of the source wavelet� In thecase of a �at free surface� the reverberation has a sim�ple and regular form� However� the situation will be�come anomalously complicated when the free surface isrugged� On the other hand� when receivers are moved tobelow the free surface� the secondary re�ections downgo�ing from the free surface near the receivers can severelyimpair the seismic data� Figures �a and �d show anuplifted free�surface model and its corresponding seis�mograms� respectively� This topographic structure canfocus secondary sources� Strong scattered waves can beseen in the near subsurface� depending on the shape ofthe free�surface structure� We will show later that thecondition becomes formidable in the presence of severalirregular free�surface structures� A near�surface low�velocity anomaly �see Figures �b and �e� can increasethe time shift of re�ections� intensify multiple�scatteringe�ects� and cause a waveform delay due to the presenceof secondary sources� From Figures �c and �f� we seethat the �at free surface can decrease these undesirede�ects to some degree�

Figure � illustrates the wave propagation in a �eld topo�graphic structure in the western areas of China� Becauseof strong glacial erosion� these areas have the greatestrelief of any of the world�s oil �elds� where the di�er�

ences in elevation often reach over several hundreds ofmeters� and often have such seismic data as in Figure �bacquired under conditions of the topography shown inFigure �a� The problem becomes more serious on weath�ering soil �i�e�� sharp rugged loess and desert� than rigidground� However� a considerable improvement can beobtained in these areas if the data acquisition is designedalong a �at ground between ridges� This suggests thatthe undulation of the earth�s surface is a substantial fac�tor to control the seismic data quality� Figures �c � �eshow the corresponding synthetic seismograms with thesame topography� but with a hypothetical near�surfacevelocity structure� A number of the free�surface velocityanomalies can intensify the topographic e�ects� even de�stroy re�ections from the depth� In addition� this irreg�ular topography and related low�velocity anomalies pro�vide a good platform for multiply scattering of upgoingre�ections from deep layers� These scattered waves cancontaminate the signals and form relatively strong noisesin the middle or deep part of a seismic section� Detailedcomparisons among Figures �c� �d� and �e in the light ofFigure �a indicate that the topographic shape controlsthe distribution of these unwanted scattered wave�elds�It should be stressed that in comparison with the realdata of Figure �b� the levels of the near�surface e�ectscalculated almost systematically underestimate the ac�tual e�ects observed in the �eld� The main reasons ac�counting for this discrepancy is that our modelings arebased on a ��D topographic geometry and without theenergy loss through nonelastic processes in near�surfaceweathered layers� In addition� the presence of a free sur�face can tremendously increase interconversions betweendi�erent wavetypes �Lay and Wallace� �� while ourcomputations only account for scalar wave propagation�

Discussions and Conclusions

In this paper� we attempt to apply the method of syn�thetic seismograms to characterize topographic e�ectson exploration seismic data and have shown that themajor e�ects of the near�surface scatterings are the gen�eration of irregular scattered noises� These strong near�surface scatterings can seriously decrease the energy ofvalid signals and signi�cantly increase noise levels thatmask the interesting re�ections� This type of noise can�not be removed using conventional methods due to itsirregularity� and hence impairs the performance of staticcorrection and wave�equation datuming� We have alsoshown that the distribution of the near�surface e�ectsis controlled by the topographic shape which exerts astrong directivity on the di�racted wave�eld away fromthe topography� Particularly� the near�source geometryappears to be critical to the topographic e�ects on ex�ploration seismic data�Two approaches are suggested tocompensate for these e�ects� One is that before seismicdata acquisition� some numerical modelings can be done

Characterization of topographic e�ects on exploration seismic dataLi�Yun Fu� and Ru�Shan Wu� Institute of Tectonics� University of California at Santa Cruz

Summary

Using synthetic seismograms� we study the in�uence ofthe widely observed strong scattering noises in complexnear�surface areas� Our studies show that an intensescattering occurs in near surface regions� especially inthe near�source and near�receiver regions� The scatter�ing is dominated� to a great degree� by the e�ect of thefree�surface boundary� and hence forms strong noises inseismic data� Moreover� the sharp rugged free surfacecan greatly impair seismic data� The study through sim�ulating wave scattering by a low�velocity topographicstructure in the western China shows that the topo�graphic e�ect is the most important factor to degradethe quality of seismic data in these areas� Based on theabove studies� we suggest two approaches to deal withthe topographic e�ects on surface seismic data� Oneis the forward modeling of wave propagation to assistin designing an optimal source�receiver geometry be�fore seismic data acquisition� Another is the inversescattering extrapolation of full wave�elds to deal withthe strong scattering by rugged topographies and near�surface heterogeneities�

Introduction

Removing the topographic e�ects on surface seismicdata has long been a formidable task in exploration seis�mics� The widely used static correction to compensatefor topography assumes that waves propagate verticallyin the near surface� Several wave equation�based ap�proaches have been designed to solve this problem forbetter datum correction� In fact� the main e�ect onthe raypath emergence angles is the near�surface veloc�ity� The slower the near�surface velocity is the smallerraypath emergence angles are� As a result� large dif�ferences in elevation along a seismic line lead to largestatics in magnitude� With the methods to handlelarge magnitude statics �Ronen and Claerbout� ��or wave�equation datuming �Berryhill� �� McMechanand Chen� ��� the problem would be solvable� How�ever in most cases� regions with large statics always haveextremely poor signal�to�noise data� In such situations�these methods are not applicable �Wang et al�� �� orlikely to generate strong artifacts �Bevc� ��� Also inthese conditions� residual statics is more likely to pro�duce false structures on the seismic data with large er�rors of datum statics�

To remove the near�surface e�ects on seismic data� a

thorough understanding of wave propagation in the shal�low subsurface region is needed� The near�surface prop�erties are generally controlled by rough free surface� un�consolidated sediment� weathered zone�related attenua�tion� and strong velocity heterogeneities� During the lasttwo decades� signi�cant progress has been achieved bothin the observation and in the evaluation of the e�ects oftopography on seismic waves that are generated by anearthquake or an underground nuclear explosion� for ex�ample� the investigations of both surface ground motion�e�g�� Aki� � Sanchez�Sesma and Campillo� ��and the amplitude� polarization and coda of various seis�mic phases �e�g�� McLaughlin and Jih� � Clouser andLangston� ��� Also to quantify these e�ects� a largenumber of theoretical investigations and numerical sim�ulations of wave di�raction by topographies have beendone �e�g�� Kennett� � Bouchon et al�� ��� Al�though the conditions and motivations in these studiesare signi�cantly di�erent from those of seismic explo�ration� they have provided insight into the topographiccontrol on wave propagation�

For seismic exploration� the major di�erences from theabove applications lie in� �� Source points are generallylocated at about � m to �� m below the free surface� ���The distances between a source and receivers are verysmall� from about �� m to � km� ��� The frequency com�ponents considered for interactions with topographiesare over �� Hz� higher than those in the above stud�ies� These distinctions lead to the fact that the topo�graphic e�ects in exploration seismics are strongly re�lated to the near�source and near�receiver topographicgeometries� and the scattering by irregular topographieshas a large range of ratios of scatterer size to wavelength�The purpose of this paper is to show examples of mainfeatures of topographic e�ects on seismic data throughwave propagation simulations in the near�surface region�

Method for the forward modeling

To model the e�ects of both rugged topography andstrong heterogeneities in the near�surface on wave prop�agation� the method should be selected with the em�phasizes on� �� The rugged free�surface must be ge�ometrically described accurately and the traction�freecondition can be easily implemented in the algorithm���� All forward and backward scatterings� including re�verberations inside strong heterogeneous media� mustbe correctly handled in the modeling� Having consid�