Details

Autor(en) / Beteiligte

• Shaw, Herbert R.
• Chouet, Bernard

Titel

Fractal hierarchies of magma transport in Hawaii and critical self-organization of tremor

Ist Teil von

• Journal of Geophysical Research: Solid Earth, 1991-06, Vol.96 (B6), p.10191-10207

Ort / Verlag

Blackwell Publishing Ltd

Erscheinungsjahr

1991

Link zum Volltext

Beschreibungen/Notizen

• A hierarchical model of magma transport in Hawaii is developed from the seismic records of deep (30–60 km) and intermediate‐depth (5–15 km) harmonic tremor between January 1, 1962, and December 31, 1983. We find two kinds of spatial distributions of magma fractions at depths below 5 km, defined by the fractal dimension D3, where the subscript is the embedding dimension. The first is a focused distribution with D3 = 0.28, and the second is a dispersed distribution with D3 = 1.52. The former dimension reflects conduitlike structures where the magma flow converges toward a summit magma chamber and the fractal dimension tends to zero. The latter dimension reflects multifractal clustering of dendritic fractures where hypocentral domains represent subsets of fractures within spherical domains with an average radius of about 1 km. These geometries constitute a percolation network of clustered intermittent fracture and magma transport. The magma volume of the average fracture is about 2 × 104 m3. A tremor model of magma transport is developed from mass balances of percolation that are proportional to tremor durations. It gives reasonable magma fractions and residence times for a vertical drift velocity of 4 km yr−1 and yields patterns of intermittency that are in accord with singularity analyses of the 22‐year time series record. According to the model, sustained tremor is generated by the relaxation oscillations of the percolation network with a dominant frequency of about 1 Hz to obtain internally consistent values of fracture geometry, fracture opening force, and magma supply rate. Calculated tremor frequencies are higher in fracture networks of small volume in harmony with the observed relation between seismic amplitude and dominant frequency of tremor. Tectonic relaxation times of rock stresses versus magma pressures are in fair agreement with the average length of tremor episodes and average period of tremor intermittencies. These observations suggest that a high degree of self‐organization is characteristic of the nonlinear dynamics of fracture percolation and coupled tremor processes. Logarithms of frequencies (in hertz) of high‐amplitude tremor (1‐s period), mean tremor duration (28‐min period), and mean onset interval (14‐day period) are 0, −3.2, and −6.1, implying broadband maxima in the frequency spectrum of transport at intervals of 103. The next longer period of this sequence, which corresponds to eruptions and shallow intrusions, is about 32 years (10 −9 Hz), comparable to the average eruption intermission of Mauna Loa during the last 150 years (about 20 years). This and other evidence suggest that spatiotemporal universality extends from small to large scales in Hawaiian and other magmatic systems. The apparent universal scaling of frequencies may be more than 15 decades in time (1 s to about 60 m.y.) and 10 decades in length (0.1 mm to 103 km).