The trouble with segmentation David D. Jackson, UCLA Yan Y. Kagan, UCLA Natanya Black, UCLA

Troubles Segment model never predicted anything successfully. Segment model never predicted anything successfully. Segment boundaries not defined properly Segment boundaries not defined properly As mapped: place where something changes or changed at least once along fault As mapped: place where something changes or changed at least once along fault As applied: impenetrable barrier As applied: impenetrable barrier Earthquakes don’t stay on faults, let alone on segments Earthquakes don’t stay on faults, let alone on segments Segment model leads to demonstrably wrong conclusions about magnitude distribution, unless very generous allowance is made for alleatory uncertainties. Segment model leads to demonstrably wrong conclusions about magnitude distribution, unless very generous allowance is made for alleatory uncertainties.

Some definitions required (in advance!) for a testable hypothesis Polygon to define segment boundary Polygon to define segment boundary Polygons to define non boundaries Polygons to define non boundaries Definition of rupture Definition of rupture Surface slip above threshold? Surface slip above threshold? Aftershock zone? Aftershock zone? Geodetic slip above threshold? Geodetic slip above threshold? Compare penetration ratio for boundary vs. non boundary Compare penetration ratio for boundary vs. non boundary Enters and stops Enters and does not stop Segment boundary Not boundary

Problems in applying Magnitude- dimension regressions to forecasting  Assumes fault length (or segment length) = rupture length.  Data are not for quakes for which fault length = rupture length.  Requires better definition of rupture length.

Earthquakes don’t stay on existing faults Examined post-1975 earthquakes in Southern California of magnitude 6.0 or greater. Examined post-1975 earthquakes in Southern California of magnitude 6.0 or greater. Assessed pre-earthquake fault length from geologic maps, aerial photographs, and fault evaluation reports. Assessed pre-earthquake fault length from geologic maps, aerial photographs, and fault evaluation reports. Compared pre-earthquake fault length to rupture length. Compared pre-earthquake fault length to rupture length.

Problems Faults are complex. Faults are complex. Rupture does not always break the surface. Rupture does not always break the surface. Rupture may continue beyond the mapped fault traces. Rupture may continue beyond the mapped fault traces. Landers fault group

Events Seven events met the study criteria: Seven events met the study criteria: Hector Mine Hector Mine Landers Landers Big Bear Big Bear Joshua Tree Joshua Tree Northridge Northridge Superstition Hills Superstition Hills Elmore Ranch Elmore Ranch Hector Mine Rupture (USGS Images)

Southern California Observations Four end member scenarios:

Elmore Ranch: Type D Aerial photos used to constrain pre- earthquake fault length (Red) Aerial photos used to constrain pre- earthquake fault length (Red) Rupture length overlaid, mapped in yellow. Rupture length overlaid, mapped in yellow.

Elmore Ranch Earthquake 8.25 km of rupture occurred on previously unmapped faults. Rupture connected ‘along-strike’ fault sections. Fault possibly buried under alluvium.

Hector Mine: Type C Rupture broke beyond the Lavic Lake fault, into an alluvial basin Rupture broke beyond the Lavic Lake fault, into an alluvial basin Rupture stopped at the end of the basin. Rupture stopped at the end of the basin. Was the fault buried under alluvium? Or breaking through new rock? Was the fault buried under alluvium? Or breaking through new rock?

*Superscript letter refers to a reference 5 out of 7 events broke beyond the originally mapped fault trace.

Natanya’s rules: Modest adjustments to avoid discrepancies noted above 1) Total length of two faults 5 km apart is the sum of the total length of the two faults (L2), not counting overlapping segments. Plus the distance between the faults (L1) 2) Total length of faults within a 45 degree angle is the sum of both fault lengths. 3) Total length of a fault truncated at an alluvial (Holocene) basin is the length of the fault inferred across the length of the basin. fault

Natanya’s rules correct the immediate problem

Table 1. Superscripts are: Table 1. Superscripts are: a) Ariel photograph a) Ariel photograph b) Dibblee, 1953 b) Dibblee, 1953 c) Jenkins, 1975 c) Jenkins, 1975 d) Rhymer, 1992 d) Rhymer, 1992 e) Fault Evaluation Report e) Fault Evaluation Report f) Sowers et al., 1995 f) Sowers et al., 1995 g) Barnhart and Slosson, 1973 g) Barnhart and Slosson, 1973 h) Hudnut et al., 1989 h) Hudnut et al., 1989 i) Bennett et al., 1995 i) Bennett et al., 1995 j) Hart et al., 1993 j) Hart et al., 1993 k) Jones et al., 1993 k) Jones et al., 1993 l) Trieman, 2002 l) Trieman, 2002 m) Jones et al., 1994 m) Jones et al., 1994 n) Wells and Coppersmith, n) Wells and Coppersmith, The superscript * indicates subsurface rupture. The superscript * indicates subsurface rupture.

Magnitude distribution implied by assuming earthquake magnitude limited by mapped fault length Estimate length of each fault from map Estimate length of each fault from map Estimate Mmax from Wells and Coppersmith Estimate Mmax from Wells and Coppersmith Estimate moment rate for each fault Estimate moment rate for each fault Construct magnitude distribution for each fault (TGR) consistent with moment rate Construct magnitude distribution for each fault (TGR) consistent with moment rate Sum moment rates from all faults Sum moment rates from all faults Compare with observed earthquake magnitude distribution. Compare with observed earthquake magnitude distribution.

Fault traces and earthquakes used to test fault segmentation against earthquake rate. Only earthquakes and faults within the boundary are used for M-F distribution. Fault traces are from Caltrans. Earthquake catalog is from Toppozoda. Red circles represent the location of earthquakes with M >= 5.5.

Observed (red) and theoretical (blue) magnitude-frequency distributions for California. Historic (1800+) and instrumental (1920+) catalogs agree closely. However, the observed and theoretical distributions do not agree, so the assumption of maximum magnitude must be rejected.

Alternative magnitude distributions for a single fault.

Integrated magnitude distribution assuming alternate distributions. A mixed distribution works best, because it allows for earthquakes bigger than allowed under the strict GR or characteristic.

Selection region for “San Andreas fault” earthquakes. We computed the magnitude distribution of earthquakes inside the fault polygon, to test the assumed G- R magnitude distribution.

Magnitude distribution of all earthquakes, and those in the San Andreas polygon. The earthquakes in the polygon do have a GR distribution

Troubles Segment model never predicted anything succesfully. Segment model never predicted anything succesfully. Segment boundaries not defined properly Segment boundaries not defined properly As mapped: place where something changes or changed at least once along fault As mapped: place where something changes or changed at least once along fault As applied: impenetrable barrier As applied: impenetrable barrier Earthquakes don’t stay on faults, let alone on segments Earthquakes don’t stay on faults, let alone on segments Segment model leads to demonstrably wrong conclusions about magnitude distribution, unless very generous allowance is made for alleatory uncertainties. Segment model leads to demonstrably wrong conclusions about magnitude distribution, unless very generous allowance is made for alleatory uncertainties.

Recommendations Forget segmentation until it can pass a test (50 years California; 5 years global) Forget segmentation until it can pass a test (50 years California; 5 years global) Use Natanya’s rules for fault length. Use Natanya’s rules for fault length. Set Mmax = W&C + 1, or 8.1, whichever is less, for all faults Set Mmax = W&C + 1, or 8.1, whichever is less, for all faults Use floating earthquakes, 60% TGR and 40% Fuzzy Characteristic, everywhere. Use floating earthquakes, 60% TGR and 40% Fuzzy Characteristic, everywhere. Use clustering model for time dependence. Use clustering model for time dependence.