ADAPTIVELY PARAMETERIZED 3D MODELS OF THE EUROPEAN UPPER MANTLE FROM SURFACE WAVE TOMOGRAPHY Abstract The ultimate goal of our project is to determine a new model of seismic velocities in the crust and upper mantle underlying Europe and the Mediterranean Basin; we present here our current progress limited to the upper mantle. We use a global data set of fundamental-mode Rayleigh- and Love-wave dispersion data with period range from 35s to 300s and an especially good coverage around Switzerland and over central Europe. We present phase-velocity and 3D radially anisotropic shear-velocity maps at a global scale and for Europe obtained by a new algorithm for upper-mantle surface-wave tomography based on adaptive parameterization. Our inversions involve regularization via roughness minimization. J. Schäfer (schaefer@ erdw.ethz.ch), L. Boschi, E. Kissling Conclusions and Outlook Regularization To obtain stable solutions from the inversion of an ill-conditioned inverse problem it is essential to regularize the problem by using a priori information. Thus we damp the horizontal, and, in the 3D case, vertical roughness of the solution. C µ D h λ D v ⎛ ⎝ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ δ p = δ t 0 0 ⎛ ⎝ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ (1) The roughness operator R for an adaptive parameterization and a spherical harmonic framework is defined e.g. by Boschi and Dziewonski (1999). By differentiation the roughness damping operator is found: ∂R( δ p ) δ p lm = 2l (l + 1) δ p lm (2) The translation to a pixel framework, as used in this study, is given by δ p lm = δ p i A i , lm i ∑ (3) Substitution of (3) into (2) delivers the horizontal roughness damping operator D h in an adaptive pixel framework: D h i , lm = 2 l (l + 1) A i , lm (4) C : tomographic coefficient matrix D v : vertical roughness damping, minimizes difference between vertically neighboring pixels D h : horizontal roughness damping, as defined by (4) l , m : degree and order of spherical harmonic coefficients δ p lm / i : phase-slowness heterogeneities in the spherical harmonic framework/pixel framework A i , lm : spherical harmonic coefficients of the pixel i Adaptive Parameterization Advantage Size of each parameterization pixel depends on the local density of seismic data coverage: higher parameterization density in regions with dense data coverage lower (computationally cheap) parameterization density in regions with lower coverage parameterization is everywhere optimal, both in terms of its computational cost, and of approximately uniform model resolution Implementation We first define a “coarse” grid with equal-area pixels of 5˚ latitudinal extent. The finer grids are each defined by subdividing the coarser pixel in four pixels (Figure 1). The adaptive grid is obtained in two steps. First the number of hitcount is determined for each pixel of the finest grid. In the next step we check if an assumed threshold value is reached: if not, pixels are combined to a coarser pixel. This procedure is continued till the hitcount for all pixel is above the threshold or the biggest pixel size is reached. In the 3D case we restrict the adaptive grid to Europe since the size of the matrix we have to invert otherwise reaches our computational limits. 5˚ 2.5˚ 1.25˚ Fig. 1: Pixel of the four grids. 0 2000 4000 6000 8000 10000 12000 14000 > 15000 hitcount Fig. 2: Grid we use for 3D inversions. Adaptivity is limited to Europe. On the right the corresponding hitcount map is shown. Acknowledgements Parts of the computations where conducted on a cluster operated by the University of Southern California for which we thank Thorsten Becker and John Yu. References • Artemieva, I. (2006), Global 1°x1˚ thermal model TC1 for the continental lithosphere:Implications for lithosphere secular evolution, Tectonophysics, 416, 245–277 • Boschi, L. , and A. Dziewonzki (1999), High- and low-resolution images of the Earth's mantle: Implications of different approaches to tomographic modeling, Journal of Geophysical Research, 104, 25,567-25,594 • Boschi,L., Fry, B., Ekström, G., and D. Giardini (2009), The European Upper Mantle as Seen by Surface Waves, Surveys in Geophysics, 30, 463-501 •Tesauro, M., M. K. Kaban, and S. A. P. L. Cloetingh (2008), EuCRUST-07: A new reference model for the European crust, Geophys. Res. Lett., 35, L05313 3D Inversions -10 -5 0 5 10 % heterogeneity sensitivity kernel 9 layers and an inversion for 2 parameters (vertical and horizontal shear velocity v SV and v SH ) results in 18 times as many parameters to invert for! Computational limits are reached much faster than in the 2D case. We restrict the adaptive parameterization to Europe to keep the inverse problem computable. For inversions we use a large shared memory, multi-CPU server with ~30GB RAM. # pixel layer RAM necessary to store the matrix [GB] 2D 3D 3D 20000 0.75 can be easily computed on a desktop 20000 241 extremely expensive 4300 11 still about 2.2 times as many pixel as in inversions with a 5˚x5˚ grid The model resolution is more precisely described by the sum of entries of C associated with the pixel than through a simple hitcount (i.e. length of rays crossing the pixel). Azimuthal coverage has to be determined to identify smearing effects. Layer thickness should not be constant but change depending on the sensitivity kernels. U23D-0057 Fig. 7: Phase-velocity heterogeneities for Rayleigh-waves with a period of 35s for Germany and Switzerland. On the left obtained from teleseismic and on the right from ambien noise data (Verbeke et al., talk Dec. 17., 4.15pm, room 2011). -10 -5 0 5 10 % -10 -5 0 5 10 % Implementing 3D Inversion with Radial Anisotropy Two layers defined around the maximum of the kernel map the heterogeneity with the same amplitude. One layer defined around the maximum of the kernel maps the heterogeneity with a larger amplitude than surrounding layers Fig. 5: Adaptively parameterized, radially anisotropic 3D model on a global scale and for the high resolution region Europe. 3D inversions are still work in progress and unfortunately no reasonable results were achieved up to now. Our 2D models are characterized by a good correlation with independent geophysical observables (e.g. topography, Moho depth and estimates of lithospheric thickness). The resulting model for the upper mantle will be complemented by an ambient noise study of the crust, also developed within our group at ETH. Once crustal effects are adequately accounted for, we expect to obtain a very high resolution image of the lithosphere- asthenosphere boundary. Phase-velocity Maps Fig. 4: Phase-velocity heterogeneities for Love waves with a period of 35s for Europe on the top and globally on the right Fig. 3: Phase-velocity heterogeneities for Rayleigh waves with a period of 75s for Europe on the top and globally on the right 700 750 750 800 800 800 850 900 900 900 950 50 950 950 1000 1000 1000 1000 1050 1050 1050 1050 1050 1100 1100 1100 1100 1150 1150 1150 1150 1150 1200 1200 1200 1200 1200 1250 1250 1250 1250 isolines represent temperature at 100 km depth (geothermal data: TC 1, Artemieva, 2006) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 misfit 0.0 0.1 0.2 normalized image roughness 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 misfit 0.0 0.1 0.2 normalized image roughness l-curve curvature l-curve -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 correlationcoefficient 0.0 0.1 0.2 normalized image roughness correlation with temperature at 100km depth Rayleigh waves, 75s 10 10 10 15 15 15 15 15 15 15 20 20 20 20 20 20 20 20 20 20 25 25 25 25 25 25 25 25 25 25 25 30 30 30 30 30 30 30 30 30 30 30 30 30 30 35 35 35 35 35 35 35 35 35 40 40 40 40 40 40 40 45 45 45 45 45 45 50 50 55 0 5 0 5 0 isolines represent crustal thickness (crustal model: EuCRUST-07, Tesauro, 2008) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 misfit 0.0 0.1 0.2 normalized image roughness 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 misfit 0.0 0.1 0.2 normalized image roughness l-curve curvature l-curve -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 correlationcoefficient 0.0 0.1 0.2 normalized image roughness -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 correlationcoefficient 0.0 0.1 0.2 normalized image roughness -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 correlationcoefficient 0.0 0.1 0.2 normalized image roughness Moho depth topography basement depth correlation with crustal properties Love waves, 35s heterogeneity z sensitivity kernel V SV V SH work in progress ... 100km 100km 150km 150km Fig. 6: Uniformly parameterized, radially anisotropic 3D model on a global scale and for the high resolution region Europe from Boschi et al. (2009). 0.625˚