Calibration of the local magnitude scale ($$M_L$$) for Brazil

Abstract This study presents the calibration of a local magnitude scale ( $$M_L$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>L</mml:mi> </mml:msub> </mml:math> ) for Brazil, based on seismic data recorded between 2014 and 2023 by the Brazilian Seismographic Network (RSBR) and local networks operated by the Seismological Observatory of the University of Brasília (SIS/UnB). The dataset comprises 1083 seismic events and 155 stations, totaling 7193 vertical-component seismograms. Events were selected at hypocentral distances from 15 to 2400 km and magnitudes ranging from 1.0 to 4.3 $$m_R$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>R</mml:mi> </mml:msub> </mml:math> . A fixed depth of 15 km was assumed, consistent with typical intraplate earthquake depths observed in stable continental regions and commonly adopted in previous magnitude scale studies in Brazil. Only events recorded by at least four stations were considered to ensure reliability. All waveforms were standardized by applying the Wood-Anderson instrument response, allowing for the measurement of maximum amplitudes of the S–Lg wave complex. An inversion was performed using the logarithmic and linear dependence of amplitude on distance, resulting in an empirical local magnitude equation $$M_{L} = \log _{10}(A_{\text {WA,mm}}) + 1.0188 \log _{10}(R/100) + 0.00062 (R - 100) + C \pm S$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>L</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:msub> <mml:mo>log</mml:mo> <mml:mn>10</mml:mn> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>A</mml:mi> <mml:mtext>WA,mm</mml:mtext> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>+</mml:mo> <mml:mn>1.0188</mml:mn> <mml:msub> <mml:mo>log</mml:mo> <mml:mn>10</mml:mn> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>/</mml:mo> <mml:mn>100</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.00062</mml:mn> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>-</mml:mo> <mml:mn>100</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>+</mml:mo> <mml:mi>C</mml:mi> <mml:mo>±</mml:mo> <mml:mi>S</mml:mi> </mml:mrow> </mml:math> . The derived attenuation curve aligns with those from regions with similar tectonic settings. Station-specific correction terms were also estimated. These corrections enhance the model’s applicability for routine seismic monitoring across Brazil.