IUGG 2011 Final presentation

Lateral Scattering: Multimode-Multistructure Method:

Lateral Scattering: Multimode- Multistructure Method G. Gurung 1 , F. Schwab 2 , B.G. Jo 1 1. Chonbuk National University, Republic of Korea. 2. University of California, Los Angeles, USA.

0. Contents:

0. Contents Introduction Scope Fundamental assumption Multi-modal method Feasibility studies Lateral scattering Energy-balancing Transmission coefficients Time series

1. Introduction:

1. Introduction Multimode- multistructure method Application of modal procedures 3-D heterogeneous structure Variable surface curvature. Treatment of lateral heterogeneity Treatment of variable surface curvature Computation time and storage. Standardized representation.

2. Scope:

2. Scope Justify of the fundamental assumption. Variable curvature Lateral heterogeneity Surface azimuthal direction of propagation. K = S / D ratio Describe modal, lateral scattering method. Introduce energy-balancing concept. Accuracy in theoretical seismograms

3. Fundamental Assumption:

3. Fundamental Assumption Ratio between the lateral extent and the depth of penetration. Lateral extent ( S ) = 1.5 x Depth of penetration ( D ) Ratio K = S / D S D

4. Multi-modal method:

4. Multi-modal method Mode 2 Mode 3 Mode 4 Mode 5 Mode 1 Curvature

5. Feasibility of our method:

5. Feasibility of our method Frequency (Hz) 0 0.05 0.10 6.5 5.0 3.5 Phase velocity (km/sec) Frequency (Hz) 0 0.05 0.10 0.010 0.005 0 Error in phase velocity (km/sec) Error in C is 0.002 km/sec Error in C is 0.006 km/sec Error in C is 0.008 km/sec Increasing errors Experimental error = C (true R ) – C (Fixed R ) True structure Fixed structure

6. Lateral scattering:

6. Lateral scattering Modal scattering due to subsurface lateral changes in the structure. Modal scattering due to lateral topographic changes. Vertical scatterers

6.1 Alsop’s M-discontinuity step model:

6.1 Alsop’s M-discontinuity step model Representative of a single step in the structure. Compute scattering coefficients.

6.2 Transmission: Alsop’s method:

6.2 Transmission: Alsop’s method Frequency (Hz) 0 0.05 0.10 Transmission coefficient 1.6 1.0 1.4 0.8 Transmission coefficient obtained by Alsop. It is important to note that all scattering to body waves is ignored.

6.3 Tranmission: our method:

6.3 Tranmission : our method x = – S /2 x = + S /2 Range of lateral averaging S / D = K When – S /2 < x < + S /2 the averaged structure varies smoothly with x from x = – S /2 to x = + S /2 x = 0 At x = 0 the structure is a simple lateral average of the two quarter spaces

6.4 Energy-balancing:

6.4 Energy-balancing x = – S /2 x = + S /2 Range of lateral averaging S / D = K x = 0 Frequency (Hz) 0 0.05 0.10 Transmission coefficient 1.6 1.0 1.4 0.8 Alsop’s T without energy balancing Our transmission coefficient clearly looks smaller than that of Alsop’s. Once we balance the energy-density flux between – S /2 to x (0 –) and + S /2 to x (0+) , then our transmission coefficient will match with Alsop’s. T with energy balancing

6.5 FD Method: Sloping Moho model:

6.5 FD Method: Sloping Moho model Sloping Moho model. Homogenenous on sides, heterogeneous in the middle. Downdip and updip propagation Region of strong lateral variation Far side Far side

6.6 Transmission Factors:

6.6 Transmission Factors Amplitude spectrum at a given station normalized by the spectrum at the first station. Sensitive indicator of subsurface variation. Frequency (Hz) Transmission Factors Downdip Propagation Updip Propagation

6.7 Optimum K = S/D value:

6.7 Optimum K = S/D value Downdip Propagation Updip Propagation Path K ( unitless ) Path K ( unitless ) L0 – L4 1.50 L0 – L4 1.00 L0 – L5 1.50 L0 – L5 1.00 L0 – L6 1.50 L0 – L6 1.00

6.8 Comparision with Boore’s Phase velocity results (Downdip):

6.8 Comparision with Boore’s Phase velocity results ( Downdip )

6.9 Comparision with Boore’s Phase velocity results (Updip):

6.9 Comparision with Boore’s Phase velocity results ( Updip )

6.10 Comparision with Boore’s Time series results:

6.10 Comparision with Boore’s Time series results

6.11 Comparision with Boore’s Time series results:

6.11 Comparision with Boore’s Time series results

Conclusion:

Conclusion In using the multimode- multistructure methods to treat 3-D varying structures with variable surface curvature, currently practical procedures require a fundamental assumption (lateral averaging and surface curvature based on conservation of energy defined by S/D = K ). The optimum fundamental assumption of K = 1.3 ± 0.5 The overall goal is to attain the highest possible accuracy in the 3-D structural models and this requires an accuracy of 3.6-3.7 sig. fig. (an error of 0.15% ~ 0.20 %) in the theoretical seismogram. Our lateral scattering results shows a successful correlation with the finite-difference results, however, our limits are much less that the ideal 3.6-3.7 sig. fig. accuracy that we seek. The accuracies in the phase comes to 2.8-3.5 sig. fig. for downdip propagation, and 2.8-2.9 sig. fig. for the updip propagation. The accuracies in the amplitude comes to 1.3-1.8 sig. fig. for downdip propagation, and 1.4-1.8 sig. fig. for the updip propagation. 1.0 2.0 3.0 4.0 5.0 6.0 1.5 1.05 1.005 1.0005 1.00005 1.000005 s Measured value True value