What is Lg?
According to Ewing, Jardetsky, and Press (1957), Lg is:
"The Lg phase is a short-period (1 to 6 sec) large-amplitude arrival in which the motion is ... transverse ... and vertical. The phase occurs only when the earthquake epicenter and seismograph station are situated to make the path entirely continental. The velocity of Lg is 3.51 km/sec, a value essentially equal to the velocity of shear waves in the upper continental crust..."
In recent time, Brian Kennett has spent more effort than anyone to understand the Lg phase. He has developed complex higher-mode wave generation and propagation software to study Lg. Here are a few of his additions (Kennett, 1983) to the properties of Lg:
"The Sg waves grade at later times into a longer period disturbance composed of higher mode surface waves, the Lg phase. There is no clear distinction between the Sg and Lg phases..."
"At a distance of 980 km... Sg is not very strong, but a well-developed Lg is seen. At the same range, long-period records are dominated by fundamental mode Love and Rayleigh waves, which in areas with thick sedimentary sequences can have significant energy at very low group velocities."
"The group slowness extrema for the first few higher mode branches at frequencies above 0.10 Hz lie in the velocity range of 3.1 to 3.6 km/sec and lead to a characteristic high-frequency wavetrain of Lg."
Since Lg is a prominent phase in Eastern North America seismograms out to distances of 1000 km, Nuttli (1973) developed the Lg magnitude scale. Atkinson and Boore (1987) suggest that the original Nuttli definition be named mN. Nuttli's formulas are:
mN = 3.75 + 0.90 log(D) + log(A/T) for 0.5º < D < 4º
mN = 3.30 + 1.66 log(D) + log(A/T) for 4º < D < 30º
where A is peak ground displacement in microns, T is period of peak motion in sec, and D is epicentral distance in degrees (1 deg=111 km). Note that Nuttli found that amplitude decay shows two different exponents, a log slope of -.90 at distances closer than 444 km, and a much stronger decay of log slope -1.66 for greater distances. For the purposes of OhioSeis regional monitoring, we mainly need to be concerned with the formula out to 444 km. Also note that Nuttli defined the scale at distances as close as 55 km, Lg can not exist at these near source distances. Clearly, we are measuring Sg amplitudes at distances less than 200 km. Thus, as the Lg wave emerges from the Sg phase, mN "follows" the Sg into the Lg. The original usage of "mbLg" makes this behavior explicit in the designation.
Lets try to make some sense from these definitions by first looking at schematic travel time curves:
Lets now try to understand how Lg grows beyond the Moho reflected critical distance.
First look at the standard sketch of ray paths for the Sg and Sn phases.
But can the direct Vs wave, Sg, really propagate long distances without turning into a Rayleigh wave? And what about the multiply-reflected waves trapped in the crust?.
This complex wave interference produces Lg.
Lets now return to the use of Lg for magnitudes.
If we use different instruments which have different high-frequency cut-offs and we extend the region such that there are spatial variations in attenuation, then we observe tremendous scatter in the individual magnitude determinations. Robert Hermann has studied these practical and theoretical aspects of Lg for many years. Hermann and Kijko (1983) produced a modified version of the Lg magnitude formula:
mLg = 3.81 + 0.833*log(D) + 48.2*g*D + log(A)
where D is distance in degrees, A is the "sustained" max peak amplitude in microns, and g is a frequency and regional dependent attenuation coefficient. Hermann and Kijko argue that the above definition is better than the original mN, though Atkinson and Boore (1987) disagree and say that mN is better. The Canadians use mN, we've been using the Hermann and Kijko as applied to the nominal Lg in our OhioSeis seismograms.
But is it really Lg?
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