1. UWBRAD meeting July 1st, 2014 Leung Tsang, Shurun Tan, Tian-Lin Wang An alternative way to explore the density fluctuation effects ---Modeling density profile with Gaussian random process

2. Outline Modeling density profile using a continuous random process Tb frequency dependence Conclusion

3. Modeling density profile using a continuous random process Use random process to generate more reasonable density profile compared to measurement. Marco’s approach: adding Gaussian dumped noise. New approach: adding noise in terms of random process. is a Gaussian random process with exponential correlation function Exponential correlation function: Correlation length,,.

4. DOMEX3 Measurement By Giovanni Macelloni and Marco Brogioni Modeling density profile using a continuous random process Marco’s approach Gaussian dumped noise Gaussian random process with Exponential correlation function Independent identical random variable Does not account for correlation between successive layers Reflection depends on number of layers Both coarse and fine scale feature resembling measurement. Reflection depends on the profile instead of number of layers.

5. Tb frequency dependence (1 realization) Exponential correlation function Layer profile Layer location Mean layer depth Total layers 10-3200m0.01m320,000 2 0-200m0.01 m 20,570 200-500m1m 500m-3200m10m To validate the layer profile setting, we compare the results from profile 1 and profile 2. Results are the same. Interference of coherent Tb against frequency is observed with density fluctuation. Coherent Tb varies around the incoherent Tb. Incoherent Tb of noisy density profile is lower than that of smooth profile. 1 realization For coherent model, when we set the mean layer depth to 0.01m or smaller, the result converges.

6. Tb frequency dependence (200 realizations) Exponential correlation function The interference is almost eliminated by 200 realizations. Tb of noise density profile is lower than that of smooth density profile. 200 realization

7. Tb frequency dependence (use Marco’s density profile ) Use Marco’s density profile 150 realizations Use Marco’s density profile and layer profile 2, where spline interpolation is used to acquire density for finer structure. (20,570 layers) Correlation of density between succeeding layer is ignored. A fixed layer depth of 10 cm is not appropriate for coherent model input. Use Marco’s layer and density profiles (1979 layers) The low frequency feature is different from that of the exponential random process.

8. Conclusions Gaussian random process with exponential correlation function is effective to describe both the coarse and finer structures of density profile while also keeps good agreement with measurement. Averaging smoothes out the interference for coherent model. (for, case) Tb is lower than the smooth density profile when adding noise.