Seismo-acoustic anomalous interference pattern in shallow water

In shallow water layered leaky waveguide, the sound energy below the cut-off frequency is coupled to the seismic sound field. Very low frequency (VLF) sound is propagated in both water-borne and bottom-trapped modes. Under these circumstances, the interference characteristics of sound field and its application are different from those of medium and high frequency, which is the subject of this study. In a multi-channel seismic exploration experiment in the South Yellow Sea, an anomalous interference pattern for the VLF band, e.g., the waveguide invariant of interference striations changes from positive to negative with increase of frequency, was observed in the range-frequency domain. Numerical simulations and modal analyses show that the anomalous interference pattern corresponds to the interference between waterborne modes and bottom-trapped modes, because the group velocity for these two types normal modes change differently in the VLF band.


Introduction
Since the concept of waveguide invariant was proposed by Chuprov [1] in 1982, it has been used in both passive and active sonar processing [2], source ranging [3], geoacoustic inversion processes [4], and array signal processing [5].
The waveguide invariant changes with ocean sound speed profiles.For examples, in Pekeris waveguide [1], the waveguide invariant value is approximately 1, on the other hand  is nearly −3 in a surface duct [6].It is also shown that in complex hydrological environment, such as sea with stratified sound speed profiles (SSPs) or range-dependent environment parameters, the sound field interference structure is complex, and the corresponding waveguide invariant values are difficult to be described with a fixed constant [7].The normal mode coupling caused by internal solitary lead to additional components in the intensity interference structure, which can lead to a very complicated acoustic interference pattern and result in multiple peaks in the distribution of  [8].
As waveguide invariant theory was established and developed with normal mode point of view [7], the interference between two normal modes can also be analyzed with the concept of waveguide invariant.If there are more than one type of normal modes with different dispersion properties in the waveguide, the mn  of mode pairs corresponding to the different types will behave differently [9].
Recently, Knobles et al. [10] identifies a feature in the interference pattern of surface ships over the VLF portion of the spectrum.
Below the cut-off frequency of the duct, the influence of the ocean bottom is not only bottom sediment but also geoacoustic parameters for ocean basement.Up till now, the distributions of waveguide invariants for seismo-acoustic sound field have been less researched.Seismic streamers used in petroleum exploration provide a quick and convenient method for sound intensity map measurement.In this paper, we not only focus on the frequency points discovered by Knobles et al., but also discuss the fringe pattern characteristics of seismic sound waves in the frequency range of 20-50Hz using the data of multi-channel seismic exploration experiments in the Qianliyan uplift zone near Qingdao, Yellow Sea, China.

Derivation of waveguide invariant
According to normal mode theory in layered range independent ocean environments, the total pressure at distance r and depth z is a sum of normal modes

Ir p r p r A r A r A r k
For each pair of mo es, one can efine the following quantity: The slope of these fringes can be etermine by fin ing the irection of constant intensity in the plane.
( ) Inserting Equation (2) into Equation ( 4), the wavegui e invariant mn  for mo es n an m can be efine as [6] ( ) ( ) ( ) is the ifference in the group slowness.Therefore, wavegui e invariants can also represent the ispersion characteristics of normal mo es.

VLF interference pattern
A range-in epen ent test mo el, inclu ing water, se iment an basement, is consi ere for a etaile explanation of the formation of the VLF interference pattern, as shown in Table 1.The source an receiver epths are set up in accor ance with the experimental con itions escribe in Sec. 3. The mo al functions an ispersion cures are evaluate using the numerical KRAKEN co e [11] an presente in Figure 1.In shallow water stratifie leaky wavegui e, VLF soun propagates as waterborne mo es an bottom-trappe mo es.One can conclu e from Figure 1(a) that at 30Hz the first mo e is waterborne mo e, while the secon to fifth mo es are bottom-trappe mo es.The phase velocity of the bottom-trappe mo es is bigger than that of the waterborne mo e, an the phase slowness ifference between the mo es is always positive, as shown in Figure 1(c).The group velocity of waterborne mo es is negative ispersion while that of bottom-trappe mo es is positive ispersion as shown in Figure 1( ).The group slowness ifference between the mo es changes from positive to negative as the frequency increases, an equal to zero at the crossover point.The correspon ing values of wavegui e invariant, calculate using Equation ( 5) are summarize as follows: where 0 f is the frequency at the crossover point of group velocity ispersion curves of waterborne mo e an bottom-trappe mo e, which is consistent with the feature previously obtaine on the New Englan continental shelf [10].The wavegui e invariant for waterbrn mo e an bottom-trappe mo es are shown in Figure 1(b).Wavegui e invariants change from positive to negative with the increase of frequency.2(a), it is the waterborne mo e (mo e 1) an bottom-trappe mo e (mo e 2), whereas in Figure 2(b), for the higher frequency ban s, it is both waterborne mo e (mo e 1 an mo e 2).Both plots show regular interference pattern.The slope of striations changes from positive to negative with frequency in Figure 2(a), while in Figure 2(b) it is always positive.This special interference structure is relate to the characteristics of mo al propagation an ispersion in the se iment layer, so it is a goo characteristic for geoacoustic parameters inversion.

Experimental data analysis
This section presents an example of the abnormal interference pattern of a single shot signal recor e using a towe hy rophone array.We show the time omain signal representing the sound pressure in Figure 3(a).The seismic profiles in icate that the epth of basement surface increases from west to east.

Conclusion
This paper escribes an abnormal interference phenomenon of the VLF soun fiel in shallow water.A three-layer range-in epen ent mo el was use to interpret the anomalous interference.Results in icate that anomalous interference pattern can be generate when the environment supports both un erwater mo e an bbottome-trappe mo e propagation, an the group velocity for these two type normal mo es change ifferently with frequency.In the VLF ban , the group velocity of waterborne mo es is negative ispersion while that of bottom-trappe mo es is positive ispersion.Therefore, as another expression of the ispersion characteristics, the interference structure of the two type normal mo es is no longer a striation, an its slope is nonlinear with frequency.It was shown that the acoustic feature is closely relate to the ispersion of the bottom-trappe mo es.

where m k an m 
are the horizontal wave number an mo al function, respectively, m  is the mo al attenuation coefficient.The expression of acoustic intensity the ifference in the phase slowness between mo es n an m; an

Figure 1 .
Figure 1.The VLF bands (20-50Hz) model analysis.(a) Depth functions of the first five modes, the modes are calculated at 30Hz.(b) The distribution of 1,2  (c) Phase velocity dispersion curve and (d) Group velocity dispersion curves.The phase velocity of the bottom-trappe mo es is bigger than that of the waterborne mo e, an the phase slowness ifference between the mo es is always positive, as shown in Figure1(c).The group velocity of waterborne mo es is negative ispersion while that of bottom-trappe mo es is positive ispersion as shown in Figure1().The group slowness ifference between the mo es changes from positive to negative as the frequency increases, an equal to zero at the crossover point.The correspon ing values of wavegui e invariant, calculate using Equation (5) are summarize as follows:

Figure 2 .
Figure 2. The range-frequency interference pattern for mode 1 and mode 2 at VLF band is shown in Figure (a) and Figure (b) is 150-200 Hz.(c) Phase velocity dispersion curve and (d) Group velocity dispersion curves at 150-200 Hz.Plotte in Figure 2(a) an Figure 2(b) are the range-frequency interference pattern from 5 to 10 km for frequencies 20-50 Hz an 150-200Hz, respectively.The interference mo e pairs iffer in the two figures; in Figure 2(a), it is the waterborne mo e (mo e 1) an bottom-trappe mo e (mo e 2), whereas in Figure 2(b), for the higher frequency ban s, it is both waterborne mo e (mo e 1 an mo e 2).Both

Figure 3 .
Figure 3. (a) The single shot gather for the air-gun source.(b) The interference pattern of the received signal for 20-50 Hz band.(c) The interference pattern of the received signal for 150-200Hz band.The soun intensity in the range-frequency omain correspon ing to the receive ata is shown in Figure 3(b) an Figure 3(c), respectively, in the frequency ban s of 20-50 Hz an 150-200Hz.The interference patterns in Figure 3(b) an Figure 3(c) are almost i entical over the smallest range (0-1km), representing the Lloy mirror effect.This is a near-fiel effect that is insensitive to environmental characteristics.This is consistent with previous research results [6].At longer istances, both figures 3(b) an 3(c) show the evolution towar s a wi er interference pattern.However, the slope irection an egree of the interference fringe in Figure 3(b) are very ifferent from the irection an egree of the constant slope of the common interference fringe in Figure 3(c).These spectrographs show a neste set of fringes whose vertices occur at a specific frequency: Figure 3(b) is about 29Hz.The fringe slope is consistent with equation (6).

Table 1 .
Parameters of range-independent test model.