To estimate seismic hazard, the basic law of seismicity, the Gutenberg–Richter recurrence relation, is applied in a modified form involving a spatial term: <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\log N\left( {M,\;L} \right)=A - B\left( {M - 5} \right) + C\log L$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mo>log</mo> <mi>N</mi> <mfenced close=")" open="(" separators=""> <mrow> <mi>M</mi> <mo>,</mo> <mspace width="0.277778em"/> <mi>L</mi> </mrow> </mfenced> <mo>=</mo> <mi>A</mi> <mo>-</mo> <mi>B</mi> <mfenced close=")" open="(" separators=""> <mrow> <mi>M</mi> <mo>-</mo> <mn>5</mn> </mrow> </mfenced> <mo>+</mo> <mi>C</mi> <mo>log</mo> <mi>L</mi> </mrow> </math> </EquationSource> </InlineEquation>, where N(M,L) is the expected annual number of earthquakes of a certain magnitude M within an area of linear size L. The parameters A, B, and C of this Unified Scaling Law for Earthquakes (USLE) in the Himalayas and surrounding regions have been studied on the basis of a variable space and time-scale approach. The observed temporal variability of the A, B, and C coefficients indicates significant changes of seismic activity at the time scales of a few decades. At global scale, the value of A ranges mainly between −1.0 and 0.5, which determines the average rate of earthquakes that accordingly differs by a factor of 30 or more. The value of B concentrates about 0.9 ranging from under 0.6 to above 1.1, while the fractal dimension of the local seismic prone setting, C, changes from 0.5 to 1.4 and larger. For Himalayan region, the values of A, B, and C have been estimated mainly ranging from −1.6 to −1.0, from 0.8 to 1.3, and from 1.0 to 1.4, respectively. We have used the deterministic approach to map the local value of the expected peak ground acceleration (PGA) from the USLE estimated maximum magnitude or, if reliable estimation was not possible, from the observed maximum magnitude during 1900–2012. In result, the seismic hazard map of the Himalayas with spatially distributed PGA was prepared. Further, an attempt is made to generate a series of the earthquake risk maps of the region based on the population density exposed to the seismic hazard. Copyright Springer Science+Business Media Dordrecht 2014
