Yoko Hasada

Autoregressive modeling of transfer functions in frequency domain to determine complex travel times

We present a method to determine the complex travel times of impulses in the time domain on the basis of an autoregressive (AR) modeling of superimposed sinusoids in a finite complex series in the frequency domain. We assume that the complex frequency series consists of signals represented by a complex AR equation with additional noise. The AR model in the frequency domain corresponds to a complex Lorentzian in the time domain. In a similar way to the Sompi or extended Prony method, the complex travel times are given by solutions of a characteristic equation of complex AR coefficients, which are obtained as the eigenvector corresponding to a minimum eigenvalue in an eigenvalue problem of non-Toeplitz autocovariance matrix of the complex series. Our method is tested for synthetic frequency series of transfer functions, which show that (1) the complex travel times of closely adjacent pulses in the time domain are clearly resolved, and that (2) the frequency dependence of the complex travel times for physical and structural dispersions is precisely determined by the analysis within a narrow frequency window. These results demonstrate the usefulness of our method with high resolvability and accuracy in the analysis of impulse sequences.

Various Time-Lapse Methods

Various types of time-lapse methods are discussed. The 4D seismic method is the most popular in the time-lapse study. The permanent reservoir monitoring has been carried out in the North Sea, off Azerbaijan, in the Gulf of Mexico, and off Brazil. In these areas, the ocean bottom cable system and repeated shootings by vessels have been used for the time lapse. Each ocean-bottom cable system equips 4000–6000 sensor groups along each cable. The study in the North Sea showed good results. The cross-hole tomography and vertical seismic profile are also used in the time-lapse study. Repeated well logging could be used for the time-lapse study. The interferometric synthetic aperture radar method was used in the time lapse in In Salah, Algeria. New sensors such as distributed temperature sensor and distributed acoustic sensor are also used for the time lapse.

What is Time Lapse

This chapter describes the scope of this book. The terminology of time lapse is explained. 4D seismic method is widely used for the time-lapse study. As an alternative time-lapse method, the Accurately Controlled and Routinely Operated Signal System (ACROSS) methodology is introduced. This book also describes the uniqueness of principle and processing method in ACROSS method. The past approaches to time lapse studied in enhanced oil recovery (EOR) technology and carbon capture and storage (CCS) are reviewed. Weyburn-Midale in Canada, In Salah in Algeria, Sleipner in offshore of Norway are good examples of the time-lapse study associated with CO 2 injection. In addition, there are some small-scale CCS fields such as Nagaoka in Japan, Ketzin in Germany, and Otway in Australia. The objectives of CO 2 -EOR, shale-gas fracking, and permanent monitoring are discussed. The important factors in the time-lapse studies are summarized. The details of each factor are given in Chapter 9 .

Active Seismic Approach by Accurately Controlled and Routinely Operated Signal System

The methodology of the Accurately Controlled Routinely Operated Signal System (ACROSS) and its control system are described. The definition of transfer function and the relation to the ACROSS methodology are explained. The comparison to the 4D seismic method is briefly discussed. Although the conventional seismic processing uses cross-correlation to obtain impulse response functions, the ACROSS processing uses division of observed data by the source signature in spectral domain. The ACROSS seismic source is precisely controlled by an accurate time standard. The chirp signal by the frequency sweep creates a comb of line spectrum. The stacking longer data on each line spectrum enhances the S/N. The data processing for the ACROSS observation is outlined. One important characteristic of ACROSS is the ability of simultaneous generation of vertical and horizontal vibrations. The addition of observed records during clockwise and counterclockwise rotations of ACROSS seismic source synthesizes vertical vibration. The subtraction gives horizontal vibration.

Passive Seismic Approach

In the time-lapse approach, passive geophysical methods are also applied. Microearthquake monitoring has been carried out in the shale gas production. Fracking of shale gas layers could generate microearthquakes. The hypocenter distribution and focal mechanism give the information on the fracture location and the stress field during the fracking process. Finding sweet spots for the best oil recovery from the shale gas layers is one of important tasks to be done. Anisotropy affects the errors on hypocenter determination. The seismic interferometry method has been used for the imaging of deformed regions and the temporal changes in the subsurface. Passive seismic signals generated by microearthquakes, traffic noise, human activities, and wind and weather changes can be used for the time-lapse analysis of Accurately Controlled and Routinely Operated Signal System (ACROSS) measurements. The data of passive seismic signals are obtained by separating the spectral lines of background noise from those of ACROSS signals.

Imaging of Temporal Changes by Backpropagation

If any temporal change of physical properties in a subsurface region occurs, the region of temporal change will behave as a source of scattered wave field. The difference of the waveforms observed at a receiver array before and after the subsurface temporal change creates the residual waveforms. The residual waveforms are backpropagated by reverse-time method to converge to the source of scattered waves. In addition, the cross-correlation of the source wave field and the residual wave field backpropagated from the receiver array is calculated to image the region of temporal change. Four simulations at Ketzin CO 2 storage, steam-assisted gravitational drainage field of Canada Oil Sand, 2-km-depth heavy oil model and 200-m-depth heavy oil model are examined by using this method.

Long Duration Time-lapse Experiment in Al Wasse, Saudi Arabia Using an Ultra-stable Seismic Source

We carried out a long-duration seismic time-lapse experiment consisting of two periods in 2012-2013 and 2015 in a water pumping field in the Kingdom of Saudi Arabia using an ultra-stable ACROSS seismic source and a geophone array. The comparison of travel times and amplitudes of P waves show quite small but distinct temporal variation with time. The maximum change is approximately 1.5 ms during two months both in the first and the second periods. Because the total travel time is 0.2 s, the change of 1.5 ms corresponds to 0.75%. The resolution of travel-time change is ~0.1 ms and it is good resolution to detect the change of subsurface caused by CO2 or high-temperature H2O injection to the heavy oil reservoir. We also discuss the NRMS repeatability of the observation system using the first arrivals at the stations within 700 m from the source and found that the NRMS repeatability was better than 5% during 2 month periods. The source itself might have roughly 2% NRMS repeatability. The NRMS repeatability is based on the waveform change. The present result supports that the ACROSS source has excellent repeatability well enough to discuss the time lapse of the subsurface.

Chapter 20 – Automatic Travel Time Determination from a Frequency-domain Transfer Function: The Sompi Event Analysis

Abstract We have developed a method to extract “events” localized in a time domain from a transfer function in the frequency domain, which is a part of the basic analysis in ACROSS (Accurately-Controlled Routinely-Operated Signal System). In response to the limitations with respect to the practical application shown in the previous procedure, we designed a revised version of this method, based on maximum likelihood estimation. The basic theory, including the revision, is presented here, along with a practical procedure for automatic travel time determination. We then submitted this revised version to a numerical test, the results of which supported the validity of this method for analysis of transfer functions involving plural “events” in the time domain.