We have estimated seismic hazard throughout New Mexico using instrumental data collected from 1962 through 1995. Based on the distribution of seismicity, we divided the whole area into two source zones, an ~6000 km2 area located in the central Rio Grande rift which was designated as the Socorro Seismic Anomaly (SSA), and the remainder of the state (RNM). A total of 477 independent earthquakes with M_D >= 2.0 (133 within the SSA) were used to obtain a universal b for the entire state. For this computation, we assumed a Poisson distribution with upper and lower bound magnitudes of 6.5 and 2.0, and a magnitude bin size of 0.1. We divided the state into 20 km x 20 km areas and evaluated seismic hazards on the basis of these blocks. Seismic hazard estimates were obtained by combining the temporal probability of occurrence with the spatial probability of occurrence and a relation between ground acceleration and magnitude (Joyner and Fumal, 1985). Results have been presented in the format of maximum horizontal ground accelerations at 10% probability of exceedance in a 50 year period. We have determined variations in these seismic hazard estimates arising from uncertainties in (1) the fitted slope b and (2) the maximum magnitude earthquake assumed in the recurrence relationship. The variation of the fitted slope b for the whole area, 0.6675±0.0314 (1 s.d.), resulted in minimal changes on the level of seismic hazard estimates. For example, the highest level of estimated ground acceleration for the entire area ranged only ±0.006g (1 s.d.) from a mean value of 0.212g. Changes in maximum magnitudes had larger but still moderate effects on the overall estimates of seismic hazard. The decrease in the highest level of seismic hazard obtained by reducing the maximum magnitude from 6.5 to 6.0 was -0.009g and the increase in hazard by increasing the maximum magnitude to 8.0 was +0.04g.

We have examined the effects of incorporating pre-instrumental data from 1860 through 1961 on seismic hazard estimates for the SSA. The fitted slope b derived from the pre-instrumental catalog for the SSA yielded a slighter lower value, 0.6454, than that obtained from the instrumental data but within the range of the first standard deviation. The cumulative number of events N at magnitude 4.0, the starting magnitude for seismic hazard estimates, in the recurrence model also showed only ~7% changes between the two models. Thus no drastic changes in hazard estimates are expected by including pre-instrumental data into the evaluation process.

Probabilistic Seismic Hazard Map for New Mexico

Figure 1 shows the earthquake epicenters for the New Mexico area for events with magnitudes ³ 1.3 for the period 1962 through 1995. It is clear that earthquakes have occurred throughout this region and that on the basis of the seismicity, boundaries between the major physiographic provinces are not defined. Among the recorded 1606 events, 572 fall inside the boundary of the SSA. The ~6000 km² SSA occupies less than 2% of the total area of the state but accounts for about one third of the state's seismicity. Based on the distribution of seismicity, we divided the region into two source zones, the SSA and the RNM. Our tests indicate that a cut-off magnitude of 2.0 assures completeness of data throughout the region with a substantial margin of safety. Dependent events were removed from the earthquake catalog using time and space windows of 7 days and 4 km for the SSA and 7 days and 25 km for the RNM.

After removal of dependent events, the remaining 477 independent earthquakes with M_D >= 2.0 (133 within the SSA) were used to obtain a universal b for the entire state. For this computation, we assumed a Poisson distribution with upper and lower bound magnitudes of 6.5 and 2.0, and a magnitude bin size of 0.1. Figure 2 shows the maximum likelihood slope b (Bender, 1983) for both the SSA and the RNM. Note that the two source zones have about the same slope b, the SSA is 0.6927 and the RNM 0.6568. To simplify the computation process, we used a universal b of 0.6675 for the whole area, which is about the mean b for the two source zones.

We divided the region into small blocks of 20 km x 20 km² and evaluated seismic hazards on the basis of blocks. The size of the block was set so that it was large enough to accommodate the maximum horizontal epicentral error for nearly all recorded earthquakes. Computational errors that arise when a gridded zone contains no events were avoided by assigning a level of background seismicity for the SSA and RNM equal to 25% of the average observed in each of these two source zones. Therefore, the cumulative number of events N in the recurrence model for each block is the combination of 75% of the events that occurred within the block and 25% background seismicity. Seismic hazard estimates were obtained by combining the temporal probability of occurrence with the spatial probability of occurrence and a relation between ground acceleration and magnitude (Joyner and Fumal, 1985). For each block, probabilities of occurrence were calculated for ground accelerations ranging from 0.05g to 0.4g at 0.05g intervals. Desired values of probability of ground acceleration were then interpolated directly from the curve. In this study, a total number of 1330 probability-ground acceleration curves were evaluated.

The probabilistic seismic hazard map we present here (Figure 3) is in the format of maximum horizontal ground accelerations at 10% probability of exceedence in a 50 year period. The highest ground acceleration is 0.21g and the lowest is near 0g. Like the distribution of seismicity, the physiographic provinces are not identifiable from the seismic hazard map. The area inside the SSA has the highest level of seismic hazard, 0.21g. Along the major population corridor of the state from Albuquerque to Santa Fe, the maximum ground acceleration is ~0.1g, which is equivalent to Modified Mercalli intensity VI-VII effects.

Uncertainties in Probabilistic Seismic Hazard Estimates

To evaluate our seismic hazard estimates, we examined some factors that could have affected probabilistic seismic hazard estimates.

Deviations of the maximum likelihood slope b. The compiled earthquake data for the hazard estimates were not measured in exact magnitude but in magnitude intervals of 0.1. To avoid bias for estimating b using the sample mean magnitude, we adopted a distribution function (Bender, 1983) for our hazard analysis. For our analysis, we divided the magnitude range between 2.0 and 6.5 into 45 intervals of width Ĉm of 0.1 for the observed 477 events. The probability of a particular combination of 477 events for a given slope b value becomes

where , N = total number of events,

and k_i = number of earthquakes in the ith magnitude interval with upper and lower bound magnitudes of 6.5 and 2.0 and a magnitude bin size of 0.1.

The maximum likelihood slope b can be derived from the first derivative of the distribution function. Figure 4 shows the distribution of b values for the recurrence relation based on instrumental data for the whole area. Maximum likelihood slope b derived from the distribution function yielded 0.6675±0.0314 (1 s.d.). Shown in Figure 5 are the estimated seismic hazards with the fitted slope b +/- one standard deviation. Deviations in ground accelerations attributed to 1 s.d. change in fitted slope b (~5%) were found to be minimal. For example, the highest level of estimated ground acceleration for the entire area ranged only ±0.006g (1 s.d.) from a mean value of 0.212g.

Maximum magnitude earthquake. For our short-term seismic hazard estimates, we assumed that an event of magnitude 6.5 on a blind fault was far more probable than a much stronger scarp producing earthquake of magnitude 6.75 or greater. However, to determine the effect of the maximum magnitude earthquake on seismic hazard, we performed some tests. For maximum magnitude earthquakes of 6.0, 7.0 and 8.0, we re-computed the maximum likelihood slope b value using the same procedure described in the earlier section. Values of maximum likelihood slope b for different maximum magnitudes are shown in Figure 6. As shown in the figure, the fitted slope b value has an asymptote of 0.672 as maximum magnitude increases. Figure 7 shows results of probabilistic hazard estimates for maximum magnitude earthquakes of 6.0, 7.0 and 8.0 using the corresponding fitted slope b values. Changes in maximum magnitudes had larger but still moderate effects on the overall estimates of seismic hazard. The decrease in the highest level of seismic hazard obtained by reducing the maximum magnitude from 6.5 to 6.0 was -0.009g and the increase in hazard by increasing the maximum magnitude to 8.0 was +0.04g.

Recurrence Model Derived from Pre-Instrumental Data

We have examined the effects of incorporating pre-instrumental data from 1860 through 1961 on seismic hazard estimates for the SSA. We compiled an event list contains 23 earthquakes for the 102 year period. We elected to include only events with intensity V or greater effects to ensure completeness of data. Maximum intensity scale values in the pre-instrumental data were converted to magnitudes using a modified Gutenberg-Richter relationship

M = 2/3 Imax + 0.5.

For the pre-instrumental data, the lower and upper bound magnitudes became 3.83 and 6.5 and the magnitude bin size 0.83. A recurrence relationship for the converted pre-instrumental earthquake data was obtained using the same procedure as was applied to the instrumental data (Figure 8). Note that the one standard deviation for the pre-instrumental data is significantly higher than the value estimated from instrumental data because the uncertainty in the measurement of magnitudes for the pre-instrumental data is much higher. The maximum likelihood slope b derived from the pre-instrumental catalog for the SSA yielded a slighter lower value 0.6454 than that obtained from the instrumental data but within the range of the latter at one standard deviation. Figure 9 shows the annual recurrence relationships for the SSA for both instrumental and pre instrumental data. It is clear that the differences between the two curves are very small. The cumulative number of events N at magnitude 4.0, the starting magnitude for seismic hazard estimates in the recurrence model, showed only ~7% difference between the two models. Thus no drastic changes in hazard estimates are expected by including pre-instrumental data into the evaluation process.

Discussions and Conclusions

We used only instrumental data for probabilistic seismic hazard estimates. Based on a 34 year instrumental earthquake catalog which is complete for earthquakes with M_D >= 2.0, we analyzed effects of the uncertainty in the fitted slope b value and the selections of maximum magnitude earthquake on seismic hazard. Results from the analysis of the fitted slope b indicate that at one standard deviation of the fitted slope b value, the effect on the probabilistic seismic hazard estimates is minimal; approximately 5%. Changes in the selection of maximum magnitude earthquake in the recurrence model had larger effects on the hazard estimates; approximately 19% for maximum magnitude 8.0. However, it is highly unlikely that an event with magnitude 7.0 or 8.0 would occur in New Mexico in a 500 year period. A recurrence relationship derived from pre instrumental data for the SSA matched the relationship derived from the instrumental data. Thus we don't expect changes in estimated seismic hazards by incorporating pre-instrumental data into the evaluation process.

References

Bender, B. (1983). Maximum likelihood estimation of b values for magnitude grouped data, Bull. Seism. Soc. Am., 73, 831-852.

Joyner, W.B. and T.E. Fumal (1985). Predictive mapping of earthquake ground motions, in J.I. Ziony (ed.) Evaluating Earthquake Hazards in the Los Angeles Region - An Earth-Science Perspective, U.S. Geological Survey Professional Paper 1360, 203-220.

Lin, K.W., A.R. Sanford and I.C. Tsai (1996). Probabilistic seismic hazard of the Socorro, New Mexico, area of the Rio Grande Rift, New Mexico Institute of Mining and Technology Geophysics Open File Report 82, 30p.

Lin, K.W., A.R. Sanford and I.C. Tsai (1997). Probabilistic seismic hazard estimates for New Mexico using instrumental data from 1962 through 1995, New Mexico Institute of Mining and Technology Geophysics Open File Report 84, 12p.

Figure 1. Seismicity map for New Mexico from 1962 through 1995 for earthquakes with duration magnitude of 1.3 or greater. The total number of events is 1606. Red area indicates the geographical extent of the Socorro Seismic Anomaly (SSA).

Figure 2. Annual recurrence/km2 versus magnitude for both the SSA and the RNM. The two source zones have about the same slope b but the annual seismic density for the SSA is about 15 times greater than the RNM.

Figure 3. Probabilistic seismic hazard map for the State of New Mexico at 10% probability of exceedence in a 50 year period. The highest level of ground acceleration is 0.21g and the lowest near 0g. Seismic hazard in the major population area along the Albuquerque-Santa Fe corridor is ~0.1g.

Figure 4. Distribution of b values for the recurrence relation based on instrumental data. The maximum likelihood slope b is 0.6675 and the standard deviation is 0.0314.

Figure 5. Probabilistic seismic hazard maps for the New Mexico incorporating +/- 1 s.d. uncertainties in the annual recurrence relation (See Figure 4); 10% probability of exceedence in 50 years.

Figure 6. Maximum likelihood slope b of instrumental data with respect to changes in assumed maximum magnitude earthquake. The fitted slope b has an asymptote of 0.672 as maximum magnitude earthquake increases.

Figure 7. Probabilistic seismic hazard estimates with different maximum magnitude earthquakes; 10% probability of exceedence in 50 years.

Figure 8. Distribution of fitted slope b for pre-instrumental data; 1860-1961. The maximum likehood slope b for the 23 event list is 0.6454.

Figure 9. Recurrence relationships for the SSA derived from both instrumental and pre-instrumental data. The fitted slope b for the pre-instrumental data yielded a slighter lower value than the instrumental data.