Acoustical Modeling of Gunshots Including Directional

Information and Reflections Robert C. Maher

Electrical and Computer Engineering Montana State University - Bozeman

Outline • Introduction

• Gunshot Acoustical Characteristics

• Recorded gunshots – Reverberation and reflections – Directional characteristics

• Directional modeling

• Conclusion

Gunshot Analysis Applications

• Real Time Tactical Information – Gunshot Detection – Sniper Localization

• Forensic Reconstruction

– Timeline Assessment – Shooter Location and Orientation – Firearm Classification

Gunshot Evidence Issues Near the Shooter

• Mechanical Action • Muzzle Blast • Supersonic Projectile (shock wave) • Surface Vibration • Reflections • Microphone Type and Location • Audio Recording Issues (e.g., codecs)

Supersonic Projectile

=

==

M

cVM

M1arcsin

numberMach

θ

Bullet Trajectory

Shock Wave Cone: Mach 3.0

( velocity V )

Shock Wave Front Trajectory

( velocity c )

θM, fast θM, slow

Shock Wave Cone: Mach 1.05

Shock Wave Front Trajectory

( velocity c )

Example Recording

A

B

C

Gun Barrel

Shock Wave Trajectory

3.7 meters

6.3 m

eter

s

θM = 23

B’

X

Microphones

L R Bullet speed at muzzle: 2728 ft/sec (831.5 m/sec)

Speed of sound (c): 1075 ft/sec (328 m/sec)

Mach Number (V/c): 2.54

Mach Angle (θM): 23.2°

Ground Reflection (cont.)

0 5 10 15 20 25 30 35 40 45 -0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Time [ms]

Am

plitu

de [l

inea

r sca

le]

Ch 1 R Ch 2 L

L R

Muzzle Blast

Muzzle Reflection

Shock Wave

Shock Wave Reflection

Directional Effects

• Gunshot sound levels and waveform characteristics vary with firearm type and azimuth with respect to the barrel.

• Off-axis levels are typically 15-20 dB lower than on-axis levels.

• Waveforms from a particular firearm can vary substantially as a function of azimuth

Directional Effects (cont.)

357 Handgun

0 1 2 3 4 5

180

170

139

130

94

85

49

40

9

0

Time [ms]

Azi

mut

h [d

eg]

Different Firearms On-Axis

0 2 4 6 8 10

22

p38

p9mm

p357

p40

p10mm

p45

12ga

223

308

Time [ms]

Sound Level vs. Azimuth

0 45 90 135 180125

130

135

140

145

Azimuth [deg]

Mea

n S

ound

Lev

el [d

B re

20u

Pa]

30822312ga

Effects Due to Surroundings • A simple idea: “just convolve a gunshot

recording with the 1-D acoustical impulse response between shooter and microphone”

• But this is the problem: the gunshot sound is highly directional, so a 3-D spatial/directional impulse response is required.

Anechoic Recording On-Axis

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Time [sec]

Am

plitu

de [L

inea

r Sca

le]

(extrapolation)

Anechoic Recording 20 deg

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Time [sec]

Am

plitu

de [L

inea

r Sca

le]

(extrapolation)

Example “alley” scenario

15 m

10 m

3 m

Microphone

North

E

S

W

Firearm

3 m

10 m

Model Result: Barrel to West

0 0.02 0.04 0.06 0.08 0.1-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Time [sec]

Am

plitu

de [L

inea

r Sca

le]

Model Result: Barrel to East

0 0.02 0.04 0.06 0.08 0.1-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Time [sec]

Am

plitu

de [L

inea

r Sca

le]

Recommendations

• Acoustical modeling and reconstruction of a shooting scenario inherently requires the directional characteristic of the firearm.

• Systems intended for gunshot classification also must consider the orientation of the firearm and the acoustical characteristics of the scene.

Conclusions

• Audio forensic examination must anticipate: – Acoustic variation among firearms – Acoustic variation of one firearm at differing

azimuths • Care is needed when applying convolution

– A spatial impulse response is required. • Pristine recordings are unlikely in most

audio forensic scenarios.

Thank you for your attention. http://ece.montana.edu/rmaher/