GEOPHYSICAL RESEARCH LETTER,VOL. 20, NO. 7, PAGES 631-634, APRIL 9, 1993 Degrees2, 4, 6 Inferred from Seismic Tomography JEAN-PAUL MONTAGNER Seismological Laboratory, Institut de Physique du Globe, Paris, France BARBARA ROMANOWICZ Seismographic Station, University oy Caliyornia, Berkeley, Caliyornia, U.S.A. Lateral heterogneities of geophysical fields (gravity, magnetic, seismic velocities...) are usually expended into spherical harmonics. Free oscillation and geoiddata show that heterogeneity in thedeep Earth's mantle is dominated by degree 2. However, its geographical pattern and its location at depth is still questionable. Recent tomographic models of seismic velocity, anisotropy and anelasticity obtained from GEOSCOPE andGDSN data,make it possible to gainmore insight on thisproblem.They show that at depth larger than 400km -I- 100kin,thedegree 2 andt a less extent, thedegree 6 arise as the most important features. Thesenew models alsodisplay a large degree 4 for radial nnisotropy at large depths. A simple flow pattern can explain thepredominance of these different degrees 2, 4, 6 andit is shown that degrees 2, 4, 6 in the transition zone are not independent. They are comparedto the corresponding degrees of the hotspot distribution and geoid. A possiblerelation between the degree 2 of velocity andthe degree 4 of radial anisotropy is alsodisplayed. However, the different location of degree 2 in theupper mantle andthe lowermantle is still puzzling. 1. INTRODUCTION In order to compare different geophysicalparameters, it is usual to expand them into spherical harmonics Y?• where 1 is the angular order and m the azimuthal order. Each de- gree is also characterized by its power spectrum Pt related to the amplitude of anomalies. Degree 2 (l = 2) is the most important lateral deviation with respect to a laterally ho- mogeneous sphere. In Seismology, the importance of degree 2 was demonstrated from the location of poles of long pe- riod normal mode eigenfrequencies [Masterset al., 1982]. The geoid also presents a largedegree 2 [Lerch et al., 1983] which has been so far attributed to deep-seated anomalies in the lower mantle. However, the origin at depth is still controversial. Masters et al. [1982] prefer it to be located in the transition zone between 400 and 660km. Romanowicz et al. [1987], display a maximum in degree 2 in the depthrange 200-400km. On the other hand, Kawakatsu [1983] sees the degree 2 as a consequence of surface tectonics. However, these observationsfrom normal modes only provide infor- mation on even degrees and it was necessary to wait for the first globaltomographic models [Woodhouse and Dziewon- ski, 1984; Nata• et al., 1986] to be able to compare even degrees to odd degrees.It turns out that degree2 becomes predominant in the uppermantle(in the transition zone for Woodhouse and Dziewonski [1984], at shallower depth for othermodels (see Romanowicz [1991]).This contrasts with Copyright 1993 by the American Geophysical Union. Papernumber92GL01204 0094-8534/93/92 GL-012 04503.00 more surficial parameters such as plate velocitieswhich dis- play a regular decrease of power with angular order(see for example, Hager and O'Connell, 1979). More recent tomographic models of the upper mantle [Woodhouse and Dziewonski, 1989; Montagnerand Tani- moro, 1991, hereafter referred as MT; Romanowicz, 1990; Roult et al., 1990]confirm the importance of degree 2 in the transition zonebut new observations can be made: Degree6 appears to be an important degree at long period [T>200s; Montagner and Tanimoto, 1990] and at largedepths [M2•. The model AUM (anisotropic upper mantle model) of MT gives both the Vsv-modeland the radial anisotropy (• = •q•-•qv ). Figure I presents the power spectra of • for AUUl•I¾ It must be noted that the spherical harmonic expan- sion of •, shows that degrees 4 (and 5) become predominant below 300km. The same result arises if we consider the mod- elsof NataI et al. [1986] and of Roultet al. [1990] (though only even angular order distributions are available for this model). Therefore, these different observationsmake it possibleto address some generaland basicquestions: What is the origin at depth of degree 2, of degree 6? Is there any relationship between degree 2 and degree 6? in the upper mantle? in the lower mantle? How can we explain the predominance of degree 4 (and 5) for radial anisotropy? In this paper, we show how to relate the degree 2 of seismic velocities with degree6 of velocitieson one hand and hotspot distribution and with degree 4 of radial anisotropy on the other hand. In order to illustrate our discussion, we will consider two recent tomographicmodels, the model AUM of MT and the modelMDLSH of Tanimoto [1990] for the whole mantle. 2. A SIMPLE FLOW MODEL Let us consider a very simple flow pattern with two upgo- ing and two downgoing flows along the equator (figure 2a). Upgoing flow is associated with arbitrary slow velocities (- 10%)anddowngoing flow with high velocities (-]-10%). The width of plumes is about 20 degrees. This simple model is not meant at this stage, to represent any realistic convec- tion model but to illustrate some predictions from such a simple pattern. When a spherical harmonics expansion is performed on this simple velocity distribution, a large de- gree 2 is naturally found, but, more surprisingly the second most importantdegree is degree 6 (figure 2b). This relative predominanceof degree 6 with respect to degree4 doesnot depend on the shape (width and amplitude) of the upgo- ing and downgoing flows, which only affectsthe decreasing slope of the power spectrum with angular order. A physi- cal understanding of that statement[Bercovici et al., 1991] stemsfrom the fact that a degree6 flow pattern can present upgoing and downgoingflows exactly at the same place as those of degree 2; such is not the casefor degree4. 631