Sound-speed averaging kernels A(r,r0), localized at r0, as a function of the fractional radius, r/R. r/R r0/R=0.0625 0.1250 0.1875 0.2500 0.3125 0.3750 0.4375 0.5000 0.0017331 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.0024510 2.495e-02 7.694e-04 1.791e-03 3.524e-04 5.076e-05 6.348e-05 7.146e-05 5.666e-05 0.0034662 4.993e-02 1.556e-03 3.581e-03 7.045e-04 1.017e-04 1.273e-04 1.432e-04 1.135e-04 0.0044745 8.316e-02 2.625e-03 5.959e-03 1.173e-03 1.701e-04 2.126e-04 2.387e-04 1.892e-04 0.0057761 1.384e-01 4.457e-03 9.895e-03 1.949e-03 2.856e-04 3.552e-04 3.976e-04 3.150e-04 0.0068349 1.934e-01 6.354e-03 1.380e-02 2.722e-03 4.032e-04 4.983e-04 5.561e-04 4.403e-04 0.0080877 2.702e-01 9.114e-03 1.922e-02 3.797e-03 5.711e-04 6.994e-04 7.771e-04 6.148e-04 0.0091733 3.466e-01 1.200e-02 2.458e-02 4.866e-03 7.432e-04 9.018e-04 9.976e-04 7.885e-04 0.0104047 4.443e-01 1.590e-02 3.138e-02 6.229e-03 9.702e-04 1.163e-03 1.280e-03 1.010e-03 0.0115106 5.418e-01 2.001e-02 3.812e-02 7.586e-03 1.205e-03 1.427e-03 1.561e-03 1.231e-03 0.0127341 6.602e-01 2.532e-02 4.621e-02 9.229e-03 1.500e-03 1.752e-03 1.904e-03 1.499e-03 0.0138554 7.780e-01 3.096e-02 5.419e-02 1.086e-02 1.806e-03 2.081e-03 2.245e-03 1.766e-03 0.0150754 9.162e-01 3.801e-02 6.343e-02 1.277e-02 2.180e-03 2.472e-03 2.646e-03 2.077e-03 0.0162095 1.053e+00 4.550e-02 7.250e-02 1.465e-02 2.569e-03 2.867e-03 3.044e-03 2.387e-03 0.0174288 1.210e+00 5.468e-02 8.272e-02 1.680e-02 3.033e-03 3.327e-03 3.501e-03 2.739e-03 0.0185748 1.366e+00 6.445e-02 9.270e-02 1.893e-02 3.517e-03 3.793e-03 3.955e-03 3.088e-03 0.0197962 1.541e+00 7.621e-02 1.037e-01 2.130e-02 4.085e-03 4.325e-03 4.464e-03 3.478e-03 0.0209540 1.714e+00 8.873e-02 1.144e-01 2.365e-02 4.678e-03 4.864e-03 4.970e-03 3.864e-03 0.0221796 1.904e+00 1.036e-01 1.260e-01 2.623e-02 5.364e-03 5.471e-03 5.530e-03 4.288e-03 0.0233492 2.093e+00 1.194e-01 1.372e-01 2.878e-02 6.080e-03 6.087e-03 6.085e-03 4.707e-03 0.0245804 2.299e+00 1.378e-01 1.491e-01 3.154e-02 6.900e-03 6.773e-03 6.691e-03 5.161e-03 0.0257622 2.503e+00 1.575e-01 1.606e-01 3.427e-02 7.755e-03 7.468e-03 7.291e-03 5.609e-03 0.0270008 2.722e+00 1.802e-01 1.726e-01 3.719e-02 8.725e-03 8.236e-03 7.939e-03 6.089e-03 0.0281956 2.938e+00 2.044e-01 1.841e-01 4.008e-02 9.735e-03 9.014e-03 8.581e-03 6.561e-03 0.0294433 3.169e+00 2.321e-01 1.959e-01 4.315e-02 1.087e-02 9.866e-03 9.268e-03 7.061e-03 0.0306521 3.396e+00 2.614e-01 2.072e-01 4.618e-02 1.205e-02 1.073e-02 9.947e-03 7.553e-03 0.0319105 3.637e+00 2.947e-01 2.186e-01 4.938e-02 1.337e-02 1.167e-02 1.067e-02 8.069e-03 0.0331341 3.874e+00 3.300e-01 2.294e-01 5.253e-02 1.474e-02 1.262e-02 1.138e-02 8.575e-03 0.0344045 4.122e+00 3.698e-01 2.401e-01 5.585e-02 1.626e-02 1.365e-02 1.213e-02 9.102e-03 0.0356438 4.366e+00 4.117e-01 2.501e-01 5.912e-02 1.783e-02 1.469e-02 1.287e-02 9.616e-03 0.0369277 4.620e+00 4.587e-01 2.598e-01 6.253e-02 1.955e-02 1.580e-02 1.364e-02 1.015e-02 0.0381837 4.868e+00 5.083e-01 2.688e-01 6.590e-02 2.134e-02 1.693e-02 1.440e-02 1.066e-02 0.0394824 5.126e+00 5.633e-01 2.773e-01 6.942e-02 2.329e-02 1.814e-02 1.518e-02 1.119e-02 0.0407563 5.377e+00 6.212e-01 2.849e-01 7.289e-02 2.530e-02 1.935e-02 1.596e-02 1.171e-02 0.0420712 5.635e+00 6.852e-01 2.920e-01 7.650e-02 2.749e-02 2.064e-02 1.675e-02 1.223e-02 0.0433641 5.886e+00 7.524e-01 2.981e-01 8.007e-02 2.974e-02 2.194e-02 1.753e-02 1.273e-02 0.0446967 6.142e+00 8.261e-01 3.034e-01 8.378e-02 3.216e-02 2.331e-02 1.834e-02 1.324e-02 0.0460099 6.391e+00 9.034e-01 3.078e-01 8.747e-02 3.464e-02 2.468e-02 1.912e-02 1.373e-02 0.0473617 6.643e+00 9.879e-01 3.112e-01 9.129e-02 3.731e-02 2.612e-02 1.991e-02 1.421e-02 0.0486965 6.886e+00 1.076e+00 3.136e-01 9.510e-02 4.003e-02 2.757e-02 2.068e-02 1.467e-02 0.0500689 7.130e+00 1.172e+00 3.151e-01 9.906e-02 4.293e-02 2.908e-02 2.147e-02 1.513e-02 0.0514266 7.365e+00 1.272e+00 3.154e-01 1.030e-01 4.589e-02 3.058e-02 2.222e-02 1.557e-02 0.0528211 7.599e+00 1.381e+00 3.147e-01 1.071e-01 4.901e-02 3.214e-02 2.298e-02 1.599e-02 0.0542029 7.822e+00 1.494e+00 3.130e-01 1.113e-01 5.218e-02 3.369e-02 2.372e-02 1.639e-02 0.0556209 8.042e+00 1.615e+00 3.102e-01 1.156e-01 5.551e-02 3.528e-02 2.445e-02 1.678e-02 0.0570284 8.251e+00 1.741e+00 3.064e-01 1.200e-01 5.888e-02 3.685e-02 2.515e-02 1.713e-02 0.0584716 8.455e+00 1.877e+00 3.015e-01 1.245e-01 6.239e-02 3.846e-02 2.583e-02 1.747e-02 0.0599066 8.646e+00 2.017e+00 2.958e-01 1.292e-01 6.592e-02 4.005e-02 2.649e-02 1.778e-02 0.0613768 8.831e+00 2.167e+00 2.892e-01 1.340e-01 6.957e-02 4.165e-02 2.713e-02 1.807e-02 0.0628413 9.001e+00 2.322e+00 2.818e-01 1.390e-01 7.323e-02 4.322e-02 2.773e-02 1.833e-02 0.0643406 9.163e+00 2.486e+00 2.736e-01 1.442e-01 7.698e-02 4.479e-02 2.831e-02 1.857e-02 0.0658365 9.309e+00 2.656e+00 2.650e-01 1.495e-01 8.070e-02 4.631e-02 2.885e-02 1.877e-02 0.0673671 9.445e+00 2.835e+00 2.559e-01 1.551e-01 8.449e-02 4.781e-02 2.936e-02 1.895e-02 0.0688961 9.565e+00 3.020e+00 2.467e-01 1.609e-01 8.822e-02 4.925e-02 2.983e-02 1.910e-02 0.0704598 9.671e+00 3.215e+00 2.374e-01 1.669e-01 9.197e-02 5.065e-02 3.026e-02 1.922e-02 0.0720239 9.761e+00 3.415e+00 2.284e-01 1.732e-01 9.563e-02 5.198e-02 3.065e-02 1.932e-02 0.0736227 9.836e+00 3.624e+00 2.197e-01 1.798e-01 9.926e-02 5.325e-02 3.099e-02 1.938e-02 0.0752240 9.893e+00 3.839e+00 2.120e-01 1.865e-01 1.027e-01 5.442e-02 3.129e-02 1.942e-02 0.0768601 9.934e+00 4.062e+00 2.053e-01 1.936e-01 1.062e-01 5.551e-02 3.154e-02 1.942e-02 0.0785009 9.956e+00 4.290e+00 2.002e-01 2.010e-01 1.094e-01 5.648e-02 3.174e-02 1.940e-02 0.0801768 9.959e+00 4.527e+00 1.970e-01 2.086e-01 1.124e-01 5.735e-02 3.190e-02 1.936e-02 0.0818599 9.944e+00 4.767e+00 1.962e-01 2.165e-01 1.153e-01 5.809e-02 3.199e-02 1.929e-02 0.0835784 9.909e+00 5.015e+00 1.984e-01 2.247e-01 1.179e-01 5.871e-02 3.204e-02 1.921e-02 0.0853063 9.854e+00 5.266e+00 2.040e-01 2.330e-01 1.202e-01 5.917e-02 3.203e-02 1.910e-02 0.0870699 9.779e+00 5.523e+00 2.137e-01 2.417e-01 1.222e-01 5.949e-02 3.197e-02 1.898e-02 0.0888467 9.684e+00 5.782e+00 2.282e-01 2.504e-01 1.239e-01 5.965e-02 3.186e-02 1.884e-02 0.0906598 9.567e+00 6.046e+00 2.483e-01 2.593e-01 1.252e-01 5.964e-02 3.169e-02 1.869e-02 0.0924970 9.430e+00 6.311e+00 2.746e-01 2.683e-01 1.261e-01 5.945e-02 3.147e-02 1.854e-02 0.0943713 9.271e+00 6.578e+00 3.083e-01 2.774e-01 1.266e-01 5.910e-02 3.121e-02 1.837e-02 0.0962731 9.092e+00 6.846e+00 3.502e-01 2.864e-01 1.266e-01 5.856e-02 3.090e-02 1.821e-02 0.0982133 8.891e+00 7.113e+00 4.015e-01 2.952e-01 1.262e-01 5.783e-02 3.054e-02 1.806e-02 0.1001750 8.670e+00 7.375e+00 4.628e-01 3.038e-01 1.252e-01 5.694e-02 3.015e-02 1.791e-02 0.1021760 8.429e+00 7.635e+00 5.357e-01 3.119e-01 1.237e-01 5.588e-02 2.973e-02 1.778e-02 0.1041979 8.170e+00 7.887e+00 6.207e-01 3.195e-01 1.217e-01 5.467e-02 2.928e-02 1.766e-02 0.1062597 7.893e+00 8.132e+00 7.197e-01 3.264e-01 1.192e-01 5.333e-02 2.882e-02 1.756e-02 0.1083435 7.600e+00 8.365e+00 8.329e-01 3.324e-01 1.162e-01 5.187e-02 2.836e-02 1.750e-02 0.1104682 7.290e+00 8.587e+00 9.626e-01 3.374e-01 1.127e-01 5.033e-02 2.790e-02 1.746e-02 0.1126147 6.968e+00 8.794e+00 1.109e+00 3.411e-01 1.088e-01 4.875e-02 2.746e-02 1.746e-02 0.1148029 6.633e+00 8.985e+00 1.273e+00 3.434e-01 1.046e-01 4.715e-02 2.706e-02 1.750e-02 0.1170123 6.290e+00 9.157e+00 1.456e+00 3.441e-01 1.001e-01 4.559e-02 2.670e-02 1.758e-02 0.1192643 5.936e+00 9.307e+00 1.661e+00 3.430e-01 9.545e-02 4.412e-02 2.641e-02 1.771e-02 0.1215363 5.580e+00 9.434e+00 1.884e+00 3.400e-01 9.082e-02 4.281e-02 2.620e-02 1.788e-02 0.1238516 5.217e+00 9.535e+00 2.131e+00 3.351e-01 8.629e-02 4.170e-02 2.609e-02 1.809e-02 0.1261850 4.857e+00 9.607e+00 2.398e+00 3.281e-01 8.209e-02 4.088e-02 2.610e-02 1.836e-02 0.1285624 4.496e+00 9.650e+00 2.688e+00 3.191e-01 7.837e-02 4.039e-02 2.624e-02 1.867e-02 0.1309555 4.141e+00 9.660e+00 2.999e+00 3.082e-01 7.537e-02 4.033e-02 2.654e-02 1.902e-02 0.1333932 3.792e+00 9.637e+00 3.333e+00 2.955e-01 7.329e-02 4.075e-02 2.701e-02 1.942e-02 0.1358443 3.455e+00 9.579e+00 3.686e+00 2.815e-01 7.241e-02 4.172e-02 2.767e-02 1.985e-02 0.1383404 3.127e+00 9.485e+00 4.061e+00 2.666e-01 7.295e-02 4.331e-02 2.852e-02 2.032e-02 0.1408416 2.817e+00 9.355e+00 4.450e+00 2.516e-01 7.514e-02 4.553e-02 2.957e-02 2.082e-02 0.1433880 2.522e+00 9.188e+00 4.859e+00 2.371e-01 7.927e-02 4.847e-02 3.084e-02 2.134e-02 0.1459294 2.248e+00 8.986e+00 5.277e+00 2.244e-01 8.545e-02 5.207e-02 3.230e-02 2.187e-02 0.1485159 1.993e+00 8.748e+00 5.709e+00 2.145e-01 9.398e-02 5.642e-02 3.398e-02 2.242e-02 0.1510996 1.761e+00 8.477e+00 6.144e+00 2.091e-01 1.049e-01 6.139e-02 3.583e-02 2.297e-02 0.1537282 1.550e+00 8.172e+00 6.587e+00 2.097e-01 1.184e-01 6.706e-02 3.788e-02 2.354e-02 0.1563557 1.365e+00 7.840e+00 7.025e+00 2.184e-01 1.343e-01 7.324e-02 4.005e-02 2.410e-02 0.1590281 1.200e+00 7.477e+00 7.463e+00 2.375e-01 1.529e-01 7.995e-02 4.236e-02 2.467e-02 0.1616960 1.061e+00 7.093e+00 7.888e+00 2.690e-01 1.738e-01 8.695e-02 4.473e-02 2.523e-02 0.1644086 9.437e-01 6.684e+00 8.303e+00 3.163e-01 1.970e-01 9.423e-02 4.715e-02 2.578e-02 0.1671135 8.493e-01 6.263e+00 8.694e+00 3.810e-01 2.218e-01 1.014e-01 4.954e-02 2.633e-02 0.1698629 7.751e-01 5.825e+00 9.063e+00 4.676e-01 2.483e-01 1.086e-01 5.188e-02 2.688e-02 0.1726002 7.210e-01 5.383e+00 9.399e+00 5.771e-01 2.754e-01 1.153e-01 5.406e-02 2.742e-02 0.1753817 6.842e-01 4.933e+00 9.702e+00 7.149e-01 3.030e-01 1.214e-01 5.608e-02 2.795e-02 0.1781457 6.635e-01 4.489e+00 9.962e+00 8.808e-01 3.297e-01 1.267e-01 5.782e-02 2.848e-02 0.1809533 6.561e-01 4.047e+00 1.018e+01 1.081e+00 3.554e-01 1.310e-01 5.927e-02 2.901e-02 0.1837391 6.600e-01 3.621e+00 1.034e+01 1.314e+00 3.785e-01 1.340e-01 6.035e-02 2.953e-02 0.1865678 6.726e-01 3.206e+00 1.045e+01 1.586e+00 3.986e-01 1.357e-01 6.105e-02 3.005e-02 0.1893711 6.915e-01 2.815e+00 1.051e+01 1.894e+00 4.145e-01 1.360e-01 6.131e-02 3.056e-02 0.1922166 7.146e-01 2.442e+00 1.050e+01 2.244e+00 4.257e-01 1.347e-01 6.114e-02 3.106e-02 0.1950343 7.391e-01 2.100e+00 1.044e+01 2.629e+00 4.311e-01 1.319e-01 6.055e-02 3.154e-02 0.1978934 7.636e-01 1.783e+00 1.031e+01 3.059e+00 4.303e-01 1.277e-01 5.955e-02 3.201e-02 0.2007226 7.856e-01 1.501e+00 1.012e+01 3.520e+00 4.229e-01 1.224e-01 5.822e-02 3.244e-02 0.2035924 8.041e-01 1.247e+00 9.872e+00 4.023e+00 4.088e-01 1.160e-01 5.659e-02 3.284e-02 0.2064303 8.174e-01 1.030e+00 9.570e+00 4.551e+00 3.884e-01 1.091e-01 5.481e-02 3.321e-02 0.2093077 8.247e-01 8.427e-01 9.210e+00 5.114e+00 3.620e-01 1.019e-01 5.295e-02 3.353e-02 0.2121517 8.253e-01 6.898e-01 8.805e+00 5.692e+00 3.313e-01 9.518e-02 5.120e-02 3.382e-02 0.2150342 8.189e-01 5.661e-01 8.352e+00 6.294e+00 2.971e-01 8.931e-02 4.966e-02 3.408e-02 0.2178816 8.055e-01 4.729e-01 7.866e+00 6.897e+00 2.624e-01 8.506e-02 4.855e-02 3.431e-02 0.2207667 7.852e-01 4.054e-01 7.344e+00 7.510e+00 2.289e-01 8.299e-02 4.801e-02 3.453e-02 0.2236154 7.591e-01 3.626e-01 6.804e+00 8.109e+00 2.008e-01 8.374e-02 4.822e-02 3.475e-02 0.2265008 7.272e-01 3.402e-01 6.242e+00 8.698e+00 1.810e-01 8.795e-02 4.933e-02 3.502e-02 0.2293486 6.914e-01 3.355e-01 5.678e+00 9.255e+00 1.741e-01 9.604e-02 5.146e-02 3.535e-02 0.2322323 6.518e-01 3.450e-01 5.108e+00 9.785e+00 1.848e-01 1.086e-01 5.477e-02 3.578e-02 0.2350774 6.106e-01 3.649e-01 4.552e+00 1.026e+01 2.177e-01 1.256e-01 5.922e-02 3.634e-02 0.2379574 5.680e-01 3.923e-01 4.004e+00 1.069e+01 2.789e-01 1.476e-01 6.496e-02 3.709e-02 0.2407980 5.264e-01 4.235e-01 3.485e+00 1.106e+01 3.720e-01 1.738e-01 7.179e-02 3.805e-02 0.2436725 4.857e-01 4.562e-01 2.987e+00 1.136e+01 5.048e-01 2.045e-01 7.978e-02 3.926e-02 0.2465071 4.479e-01 4.871e-01 2.529e+00 1.158e+01 6.788e-01 2.385e-01 8.856e-02 4.072e-02 0.2493747 4.130e-01 5.147e-01 2.104e+00 1.172e+01 9.032e-01 2.756e-01 9.813e-02 4.249e-02 0.2522017 3.825e-01 5.365e-01 1.726e+00 1.177e+01 1.176e+00 3.138e-01 1.080e-01 4.452e-02 0.2550608 3.562e-01 5.520e-01 1.387e+00 1.174e+01 1.508e+00 3.528e-01 1.179e-01 4.685e-02 0.2578789 3.349e-01 5.597e-01 1.098e+00 1.162e+01 1.892e+00 3.900e-01 1.275e-01 4.938e-02 0.2607282 3.182e-01 5.596e-01 8.503e-01 1.141e+01 2.340e+00 4.248e-01 1.364e-01 5.214e-02 0.2635361 3.062e-01 5.518e-01 6.505e-01 1.111e+01 2.839e+00 4.547e-01 1.440e-01 5.498e-02 0.2663743 2.985e-01 5.364e-01 4.913e-01 1.074e+01 3.401e+00 4.787e-01 1.503e-01 5.789e-02 0.2691710 2.947e-01 5.147e-01 3.738e-01 1.029e+01 4.008e+00 4.946e-01 1.545e-01 6.070e-02 0.2719971 2.940e-01 4.871e-01 2.916e-01 9.770e+00 4.671e+00 5.017e-01 1.568e-01 6.337e-02 0.2747818 2.957e-01 4.555e-01 2.427e-01 9.200e+00 5.366e+00 4.988e-01 1.567e-01 6.573e-02 0.2775951 2.992e-01 4.206e-01 2.212e-01 8.575e+00 6.104e+00 4.854e-01 1.542e-01 6.772e-02 0.2803675 3.036e-01 3.846e-01 2.227e-01 7.921e+00 6.856e+00 4.619e-01 1.495e-01 6.922e-02 0.2831676 3.083e-01 3.480e-01 2.423e-01 7.234e+00 7.630e+00 4.286e-01 1.428e-01 7.017e-02 0.2859271 3.124e-01 3.129e-01 2.745e-01 6.542e+00 8.395e+00 3.878e-01 1.345e-01 7.052e-02 0.2887135 3.155e-01 2.797e-01 3.155e-01 5.841e+00 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