Electronic Supplement
David J. Jackson and Yan K. Kagan
"Testable Earthquake Forecasts for 1999"
Seismological Research Letters 70(4), 393-403.

The two tables linked below contain probabilistic earthquake forecasts for the northwest and southwest Pacific regions. The tables give the estimated rate density for M > 5.8 earthquakes for the northwest Pacific and southwest Pacific regions as of 00:00 GMT on January 1, 1999. The rate density is the probability of occurrence of magnitude 5.8 and larger earthquakes per unit area per unit time. The tables also give information about the area per square degree, the most probable focal mechanisms, and their uncertainties. Values are specified as a function of latitude and longitude on a 0.5 by 0.5 degree grid.

The eleven columns of the two tables contain the following information:

  1. "Longitude" measured in degrees east of Greenwich.
  2. "Latitude" in degrees south of equator.
  3. "Probability M>5.8 eq/day*km2": Rate of occurrence per square km per day about grid point.
  4. "Area square degree km2": Area of a 1 degree by 1 degree box, in square km.
  5. "Probability M>5.8 eq/y*degr2": Rate of occurrence in events per square degree per year.
  6. "Coef. variation": Coefficient of variation of the rate estimate.
  7. "T-axis Pl": Plunge of the axis of maximum extension.
  8. "T-axis Az": Azimuth of the axis of maximum extension.
  9. "P-axis Pl": Plunge of the axis of maximum contraction.
  10. "T-axis Az": Azimuth of the axis of maximum contraction.
  11. "Rotation angle degree": Focal mechanism uncertainty, degrees.

The value 9.99 in the coefficient of variation column means that there were too few earthquakes in the neighborhood of this cell to estimate the earthquake rate in the normal way. For these cells, the earthquake rate is assigned a generic value computed as follows: 1% of the total earthquake rate was distributed evenly (by area) over the entire region.

The focal mechanism representation is according to Aki and Richards (1980, p. 106). The focal mechanism uncertainty is in degrees of 3-D rotation around the expected mechanism shown in the table. "Rotation angle"=0 indicates that a focal mechanism is not determined for this point, and that the focal mechanism on that line of the table is a generic focal mechanism.

Using these numbers one can calculate the rate (probability per unit time) of earthquakes with magnitude greater than or equal to 5.8 for any region that can be approximated by a combination of 0.5 by 0.5 degree cells centered on the grid points shown in the table. Because the cells are 0.5 by 0.5 degrees, the total rate for any cell is 1/4 of the rate per square degree given in column 5.

For regions that cannot be approximated by a combination of cells, the values in column 3 may be interpolated and integrated over the region to estimate the rate of events within the region.

For a larger magnitude threshold, all rates and probabilities may be adjusted using the magnitude distribution described in the manuscript. For thresholds up to magnitude 8 this distribution is nearly identical to a Gutenberg-Richter distribution with b=1. Thus the rate of events at or above magnitude 6.8 is 1/10 the value given in the table.

We will test the forecast at the end of 1999 using a likelihood function based on the rate of occurrence at the location of each 1999 earthquake. This value can be approximated well by interpolating the values in the tables, but we will compute a more precise version by using the same program used to generate the values in the tables.

Example


Southwest Pacific 1999 Long-term Earthquake Forecast

             Probability     Probability
                 M>5.8           M>5.8       T-axis  P-axis
             eq/day*km^2     eq/y*degr^2     Pl  Az  Pl  Az 
 Longitude         |     Area      |           |       |   Rotation 
    |   Latitude   | square degree |   Coef.   |       |    angle 
    v              v     km^2      v variation v       v    degree 

  110.0   0.0  7.08E-11 12346  0.00032  9.99   8 284  17 192  39.2
  110.5   0.0  6.65E-11 12346  0.00030  9.99  21 311  12 216  45.3
  111.0   0.0  7.85E-11 12346  0.00035  9.99  53 128  34 337  60.6
  111.5   0.0  1.11E-10 12346  0.00050  9.99  55 147  35 334  50.8
  112.0   0.0  1.44E-10 12346  0.00065  9.99  56 159  34 338  46.0
  112.5   0.0  1.76E-10 12346  0.00080  9.82  56 165  34 345  42.4
  113.0   0.0  2.02E-10 12346  0.00091  9.11  56 165  34 346  41.4
  113.5   0.0  2.34E-10 12346  0.00105  8.28  56 165  34 347  41.2
  114.0   0.0  3.11E-10 12346  0.00140  7.05  58 168  32 352  38.8
  114.5   0.0  4.33E-10 12346  0.00195  6.07  59 167  30 353  37.4
  115.0   0.0  5.15E-10 12346  0.00232  5.49  59 167  30 352  37.9
  115.5   0.0  6.27E-10 12346  0.00283  4.88  60 166  30 352  38.6
  116.0   0.0  7.72E-10 12346  0.00348  4.40  59 165  30 351  39.2
  116.5   0.0  1.01E-09 12346  0.00455  3.84  59 165  31 353  40.6
  117.0   0.0  1.36E-09 12346  0.00612  3.28  59 163  31 350  42.2
  117.5   0.0  1.89E-09 12346  0.00854  2.78  59 163  31 347  43.0
  118.0   0.0  2.71E-09 12346  0.01222  2.34  59 161  31 343  42.7
  118.5   0.0  4.08E-09 12346  0.01839  1.94  59 160  31 340  41.2
  119.0   0.0  6.89E-09 12346  0.03105  1.55  60 158  30 336  39.1
  119.5   0.0  1.08E-08 12346  0.04868  1.26  57 165  32 336  31.8
  120.0   0.0  1.45E-08 12346  0.06555  1.05  62 140  27 333  42.4

Forecast files:
Northwest Pacific 1999 Long-term Forecast
Southwest Pacific 1999 Long-term Forecast


 

     

Posted: July 1999