Estimation of Sea Surface Temperature (SST) Using Marine Seismic Data

Abstract

Not much attention is given to direct wave arrivals in marine seismic data that are acquired for petroleum exploration and prospecting. These direct arrivals are usually muted out in routine seismic data processing. In the present study, we process these direct arrivals to accurately estimate soundspeed in near-surface seawater and invert for sea surface temperature. The established empirical equation describing the relationships among temperature, salinity, pressure and soundspeed is used for the inversion. We also discuss processing techniques, such as first-break picking and cross-correlation for the estimation of soundspeed, that are well known among petroleum-industry geophysicists. The accuracy of the methods is directly linked to the data quality and signal processing. The novelty in our approach is in the data conditioning, which consists essentially of spectral balancing based on a wavelet transform that compensates for spherical spreading and increases the signal-to-noise (S/N) ratio. The 2D seismic data used in this paper are from the offshore Krishna-Godavari Basin east of India. We observe a significantly higher soundspeed of 1545 m/s for near-surface water than the commonly used value of ~1500 m/s. The estimated temperature (from velocity) is about 30 °C. Interestingly, the estimated temperature matches well with the temperature recorded in the CTD profile acquired in the study area during the month of May, the month corresponding to the acquisition of seismic data. Furthermore, the estimated temperatures during different times of data acquisition correlate well with the expected diurnal variation in temperature.

Appendices

Appendix

Sound waves in water attenuate due to spherical divergence and dispersion. Furthermore, direct arrivals on near offset receivers are most often affected by bubble pulses, making them difficult to pick with automated pickers. Therefore, wavelet shaping is performed to increase accuracy in time-delay estimations. Conventional time or frequency domain processing, steps such as automatic gain control (AGC) or predictive deconvolution, tend to amplify noise along with the signal. For non-stationary signal analysis, time–frequency variant operators are preferred for wavelet shaping. In this case, the wavelet transform is naturally suited because the wavelet adapts to the frequency content of the signal providing improved control over both resolution and stability. There is a redundancy of scale which is effectively exploited to control noise amplification while performing the inverse wavelet transform, thus giving a stable algorithm for spectral balancing.

Spectral Balancing in the Wavelet Transform Domain

A continuous wavelet transform is often used for time–frequency representation of a time domain signal. This is preferred over a Short-Time Fourier transform as it does not require a user-specified window length and the analyzing wavelet adjusts itself to the frequency content in the signal to optimize the time–frequency resolution (Sinha et al. 2005). In order to balance the time–frequency content throughout the record length, a smoothed spectrum surface is generated. The original time–frequency spectrum is balanced with respect to the smooth surface (Sinha 2014). A brief description of the method follows.

The time scale spectrum for a signal $f(t)$ is obtained by taking the inner product of a family of wavelets $\psi_{\sigma ,t} (t)$ with the signal.

$$F_{W} (\sigma ,\tau ) = \langle f\left( t \right),\psi_{\sigma ,t} \left( t \right) = \mathop \int \limits_{ - \infty }^{\infty } f\left( t \right)\frac{1}{\sqrt \sigma }\psi \left( {\frac{t - \tau }{\sigma }} \right){\text{d}}t,$$

(5)

where $\sigma$ is the scale and $F_{W} (\sigma ,\tau )$ is the time-scale map. The inverse of the above transform of the above exists when the analyzing wavelet satisfies the “admissibility condition” given by

$$C_{\psi } = 2\pi \mathop \int \limits_{ - \infty }^{\infty } \frac{{\left| {\widehat{\psi }(\omega )} \right|^{2} }}{\omega }{\text{d}}\omega < \infty .$$

(6)

The function f(t) is reconstructed as

$$f(t) = \frac{1}{{C_{\psi } }}\mathop {\iint }\limits_{ - \infty }^{\infty } F_{W} \left( {\sigma ,\,\tau } \right)\psi \left( {\frac{t - \tau }{\sigma }} \right) \frac{{{\text{d}}\sigma {\text{d}}\tau }}{{\sqrt {\sigma \sigma^{2} } }} .$$

(7)

Spectral balancing of the signal is achieved by modifying $F_{W} (\sigma ,\tau )$ before applying Eq. (7) for the inverse continuous wavelet transform. Essentially, a time and frequency dependent operator is obtained by smoothing the power scalogram$\left| {F_{W} (\sigma ,\tau )} \right|$. For this purpose, we have used a 2D Hamming filter to construct the operator. Margrave et al. (2011) discuss other ways to construct a time–frequency varying 2D filter for spectral enhancement. In this trace-by-trace processing algorithm, we have used the Morlet wavelet which is a commonly used wavelet in seismic data applications. The wavelet is essentially a plane wave modulated by a Gaussian window (Morlet et al. 1982).