Practical issues of reverse time migration: true-amplitude gathers, noise removal and harmonic-source encoding

Transcription

1 Submiion number: 3784 Practical iue of revere time migration: true-amlitude gather, noie removal and harmonic-ource encoding Yu Zhang, CGGVerita, Houton Jame Sun, CGGVerita, Singaore Summary We analyze the amlitude behavior of revere-time migration and how that modifying the initial-value roblem into a boundary-value roblem for the ource wavefield, lu imlementing an aroriate imaging condition, yield a true-amlitude verion of RTM. We alo dicu different way to ure the migration artifact. inall we introduce a harmonic-ource hae-encoding method to allow a relatively efficient delayed-hot or lane-wave RTM. Taken together, thee yield a owerful true-amlitude migration method that ue the comlete two-way acoutic wave equation to image comlex tructure. 70 th EAGE Conference & Exhibition Rome, Ital 9-1 June 008

2 Introduction Recentl revere-time migration (RTM) ha drawn a lot of attention in the indutry. Unlike one-way wave equation migration, RTM doe not need to deal with the theory of ingular eudo-differential oerator. A traightforward imlementation of RTM correctly handle comlex velocitie and roduce a comlete et of acoutic wave (reflection, refraction, diffraction, multile, evanecent wave, etc.). The RTM roagator alo carrie the correct roagation amlitude and imoe no di limitation on the image. In the at, the trong migration artifact and the intenive comutational cot have been the two major roblem that revented RTM from being ued in roduction. In thi abtract, we firt formulate RTM baed on inverion theory and then we addre ome olution to ure the low frequency migration artifact. At the end, we rooe harmonic-ource migration a a way to imrove the efficiency of delayed-hot RTM. True-amlitude revere-time retack deth migration We firt formulate RTM baed on the theory of true-amlitude migration. To migrate a hot record Q( x, y; x, y ;, with the hot at ( x, y, z = 0) and receiver at ( x, z = 0), we have to comute the wavefield originating at the ource location and oberved at the receiver location. ecaue the ource wavefield exand a time increae and the recorded receiver wavefield i comuted backward in time, we denote them by and reectively in the following two-way wave equation: 1 r r r ( x x ) f (, = c t δ (1) and 1 r = ( ; ) 0, x t c t () ( x, z = 0; = Q( x, y; x, y ;, where c = c( x, z) i the velocit f ( i the ource ignature, and i the Lalacian oerator. To obtain a common-hot image with correct migration amlitude, we need to aly the deconvolution imaging condition (Zhang et al., 005) r r 1 r R( x) = dt, (3) 1 r r where i defined a the invere of the wavefield. Thi imaging condition i imle to aly in the frequency domain for one-way wave equation migration. However, it i difficult to imlement in the time domain for RTM. In ractice, the cro-correlation imaging condition r r r R( x) = dt (4) i often referable for reaon of tability. Although thi doe not aear to be conitent with true-amlitude migration, Zhang et al. (007a) roved that the imaging condition (4) i a roer choice to obtain true-amlitude angle gather from wave equation baed migration. However, for thi to occur, equation (1) need to be modified accordingly a 1 r ( ; ) = 0, x t c t (5) r r t ( x, z = 0; = δ ( x x ) f ( t' ) dt'. 0 Thi equation i different from the conventional wave equation (1) for the forward wavefield, becaue the ource at the urface i treated a a boundary condition intead of a right-handide forcing term in the equation. In ummar we rooe the following algorithm to outut true-amlitude angle-domain common-image gather from RTM: 70 th EAGE Conference & Exhibition Rome, Ital 9-1 June 008

3 1. Comute forward and backward wavefield and by olving the two-way wave equation (5) and ();. Aly the cro-correlation imaging condition (4) during the migration; 3. Ue an exiting method, e.g. Sava and omel (003), to outut angle-domain commonimage gather. The migration outut then rovide angle deendent reflectivity in the ene of the high frequency aroximation. To how how true-amlitude angle-domain RTM work, we aly it to a -D horizontal reflector model in a medium with velocity c = ( z) m /. The inut i hot record over five horizontal reflector. The hot i in the center of the ection and the receiver cover the urface in an aerture of 15000m on each ide. The amlitude variation acro travel time and lateral ditance i due only to geometrical reading lo. We migrated the hot record uing the common-hot RTM algorithm () and (5) with the imaging condition (4). At an image location, we tack all the migrated common-image hot gather to generate the uburface offet gather, and then convert them to the uburface reflection angle gather hown in igure 1. The normalized eak amlitude along the reflector in the angle domain are hown in igure. It i clear that the amlitude in the angle domain recover the reflectivity accurately over a large angular range, aide from edge effect. igure 1: A migrated angle domain common-image gather. igure : Normalized eak amlitude v reflection angle curve along the migrated reflector. Noie removal from true-amlitude migration oint of view It ha been oberved that the conventional cro-correlation imaging condition (4) roduce trong low-frequency migration artifact in RTM. igure 3a how a direct alication of RTM to the 004 P -D data et (illette and randberg-dahl, 005). The migration artifact aear mainly at hallow deth and everely mak the migrated tructure. They are mainly generated by the cro correlation of reflection, backcattering wave, head wave and diving wave. The non-reflecting wave equation (ayal et al., 1984) wa rooed to ure the artifact in ottack RTM by avoiding the normal-incidence reflected energy from an interface. However, thi technique i not effective for retack deth RTM becaue the underlying mechanim of how the noie i generated are different. Other technique have been rooed in the literature, uch a velocity moothing, high-a filter (Mulder and Pleix, 003), Poynting vector (Yoon, et al., 004), directional daming term at the interface (lecher et al., 005) etc. In ractice, we find they are either difficult to imlement roerly or have the drawback of ditorting the ectrum or amlitude of the migrated image undeirably. Liu et al. (007) rooed a new imaging condition to olve the roblem: decomoe the wavefield into one-way comonent and only cro-correlate the wave comonent that occur a reflection. In 3-D, fully decomoing the wavefield into different direction i comutationally intenive, therefore only ugoing and downgoing comonent are ued in ractice. Thi incomlete decomoition remove ome teely diing reflector for comlex tructure (igure 3b). Here we oint out that ureing migration artifact i imle if we outut angle gather. The migration artifact have the common feature that the ource wavefield correlate to the 70 th EAGE Conference & Exhibition Rome, Ital 9-1 June 008

4 receiver wavefield roagating in the ooite direction, which imlie that the reflection angle i 90º. Therefore the artifact can be removed by tacking the migrated angle gather with a far-angle mute (igure 3c). Another imle and oular way to remove the migration artifact i to aly the Laacian filter to the tacked migrated image. It remove the migration artifact effectively without hurting tee di. To ee how thi technique work, we recall the well-known relation k x + k y + k z = 4ω co θ / v, (6) where θ i the reflection angle and v i the local interval velocity. Equation (6) ay that alying a Lalacian filter to the tacked image i equivalent to alying a co θ weight to the angle gather. According to (6), to correctly utilize thi technique without ditorting the migrated ectrum and amlitude, we have to aly a 1/ ω filter to the inut data and recale the migration outut by a v factor. igure 3d how the reult of alying the above mentioned technique to P -D dataet. igure 3a: Direct image from RTM. igure 3b: Image of decomoed imaging condition igure 3c: 0º-60º tacked image. igure 3d: Image of Lalacian filter lu roer re and ot migration roceing Delayed-hot, lane-wave, and harmonic-ource RTM or common-hot migration, the cot equal the cot of migrating a ingle hot time the number of hot migration. Variou aroache have been rooed to reduce the number of hot, thu reducing the roject cycle time and cot. Combining hot by line-ource ynthei in the inline direction (delayed-hot migration) or in both inline and croline direction (lane-wave migration) roduce atifactory reult if enough -value are ued (Whitmore 1995). One may conider alying imilar technique to RTM to imrove it efficiency. However, ince we erform RTM in the time domain, delayed-hot or lane-wave RTM require a long time adding for long ail line and large value of. Thi can low down rather than eedu the roce coniderably. To avoid thi roblem, Zhang et al. (007b) introduced a new hae-encoding cheme that doe not uffer from the long time adding roblem. Thi new hae-encoding algorithm i theoretically equivalent to the delayed-hot migration and we called it harmonic-ource migration. or a tyical roduction roject in Gulf of Mexico, the eedu ratio of harmonic-ource migration veru common-hot migration could be a factor of -3. We have alied thi migration to both one-way wave equation migration (Soubara, 006) and RTM. igure 4 comare the reult of a one-way 70 th EAGE Conference & Exhibition Rome, Ital 9-1 June 008

5 wave equation migration to RTM both uing harmonic-ource encoding with a dee water GOM dataet. In general, RTM give better image of the teely diing alt flank. The ediment underneath the alt overhang are extended cloer to the alt flank boundarie. We attribute thee imrovement mainly to the high-angle or turning-wave roagation abent in the one-way wave equation migration. Concluion We have analyzed the amlitude behavior of revere-time migration. We have hown that modifying the initial-value roblem into a boundary-value roblem for the ource wavefield lu imlementing an aroriate imaging condition yield a true-amlitude verion of RTM. We have alo dicued different way to ure the low frequency migration artifact. inall we have introduced a harmonic-ource hae-encoding method which allow a relatively efficient imlementation of delayed-hot or lane-wave RTM. Taken together, thee yield a owerful true-amlitude migration method that ue the comlete two-way acoutic wave equation to image comlex tructure. igure 4: Real data from GOM with image from one-way wave equation migration and RTM. Reference ayal, E., Koloff, D. D. and Sherwood, J. W. C., [1984], A two-way nonreflecting wave equation: Geohyic, 49, illette,. J. and randberg-dahl, S., [005], The 004 P velocity benchmark: 67 th Ann. Mtg.: EAGE, 035. letcher, R.., owler, P., Kitchenide, P. and Albertin, U., [005], Sureing artifact in retack revere time migration, 75 th Ann. Mtg.: SEG, Liu,., Zhang, G., Morton, S. and Leveille, J., [007]. Revere-time migration uing one-way wavefield imaging condition, 77 th Ann. Mtg.: SEG, Mulder, W. A. and Pleix R.-E., [003] One-way and two-way wave equation migration, 73 rd Ann. Mtg.: SEG, Sava, P. C. and omel, S., [003], Angle-domain common-image gather by wavefield continuation method: Geohyic, 68, Soubara, R. [006], Modulate-hot migration, 76 th Ann.Mtg: SEG, Whitmore, N. D., [1995], An imaging hierarchy for common angle lane wave eimogram: Ph.D. thei, Univerity of Tula. Yoon, K., Marfurt, K. J. and Starr, W., [004], Challenge in revere-time migration: 74 th Ann. Mtg.: SEG, Zhang, Y., Sun, J. and Gra S., [007b], Revere-time migration: amlitude and imlementation iue, 77 th Ann. Mtg.: SEG, Zhang, Y., Xu, S., leitein, N. and Zhang, G., [007a], True amlitude angle domain common image gather from one-way wave equation migration: Geohyic, 7, S Zhang, Y., Zhang, G. and leitein, N., [005], Theory of true amlitude one-way wave equation and true amlitude common-hot migration: Geohyic, 70, E th EAGE Conference & Exhibition Rome, Ital 9-1 June 008