نمايش كانال‌هاي مدفون با استفاده از روش تحليل مولفه‌هاي اصلي

Demonstrating buried channels using principal component analysis

امروزه تحليل سري‌هاي زماني در مطالعات لرزه‌اي داراي كاربردهاي فراواني هستند. با توجه به اينكه زمين در مقابل انتشار امواج لرزه‌اي مانند يك فيلتر پايين‌گذر عمل مي‌كند، موجب تغيير محتواي بسامدي امواج لرزه‌اي با زمان مي‌شود. نمايش زمان – فركانس يكي از ابزارهاي مناسب تحليل سيگنال‌هاي لرزه‌اي با محتواي فكانسي متغير با زمان مي‌باشند. تجزيه طيفي يك داده سه‌بُعدي لرزه‌اي، به‌ازاي هر بسامد مكعبي هم‌بُعد با خود داده لرزه‌اي ايجاد مي‌كند. استفاده هم‌زمان از اين حجم زياد داده، هم از نظر محاسباتي و هم از نظر تفسيري ‌بسيار مشكل است. روش‌هاي گوناگوني براي كاهش حجم داده‌ها و در عين حال استفاده از تمامي اطلاعات موجود در هر مكعب‌هاي تك بسامد وجود دارد. در روش برانبارش رنگي، تصاوير RGB با استفاده از سه مقطع تك‌بسامد مجزا تهيه و اطلاعات مورد استفاده در نمايش، نسبت به روش تك‌بسامد سه برابر مي‌شود. با اين وجود، حجم زيادي از اطلاعات هنوز ناديده گرفته ‌شده است. به‌منظور حل اين مشكل روش آناليز مولفه‌هاي اصلي براي كاهش حجم داده‌ها و استفاده از تمام اطلاعات موجود، پيشنهاد گرديد. در اين مقاله به‌منظور شناسايي كانال‌هاي مدفون در داده‌هاي لرزه‌اي سه‌بعدي ابتدا با توليد تصاوير تك‌بسامد و برانبارش رنگي آنها وابستگي كيفيت تصاوير توليدي آنها به مولفه‌هاي بسامدي انتخابي نشان داده مي‌شود و در ادامه با اِعمال روش تحليل مولفه‌هاي اصلي روي تصاوير تك‌بسامد فقط با توليد يك تصوير كه شامل همه مولفه‌هاي بسامدي است، اين وابستگي برطرف مي‌شود. نتايج به‌دست آمده نشان داد كه تصاوير حاصل از تحليل مولفه‌‌هاي اصلي، جزييات بيشتري دارند و شاخه‌‌هاي كانال را دقيق‌تر از ساير روش‌‌ها نشان مي‌‌دهند.

Spectral decomposition of time series has a significant role in seismic data processing and interpretation. Since the earth acts as a low-pass filter, it changes frequency content of passing seismic waves. Conventional representing methods of signals in time domain and frequency domain cannot show time and frequency information simultaneously. Time-frequency transforms upgraded spectral decomposition to a new level and can show time and frequency information simultaneously. Time-frequency transforms generate high volume of spectral components, which contain useful information about the reservoir and can be decomposed into single frequency volumes. These single frequency volumes can overload the limited space of computer hard disk and are not easy for an interpreter to investigate them individually; therefore, it is important to use methods to decrease volume with no information lost, so frequency slices are separated from these volumes and used for interpretation. An expert interpreter can achieve some information about channel content and lateral variation is of thickness. Since different frequencies contain different types of information (low frequencies are sensible to channel content and high frequencies are sensible to channel boundaries), these slices cannot show this information simultaneously. Therefore RGB images can be produced by plotting three different frequency slices against red, green and blue components. An RGB image, sometimes referred to as a true color image, it is an image that defines red, green, and blue color components for each individual pixel and has intensity between 0 and 1. Although this method obviates some drawbacks of single frequency plots, but it uses only three slices and practically ignores a big part of information and the frequency choice is not clear, so different choices will result to different images. Principal component is a statistical method for identifying patterns in data and expressing them in a way to highlight their similarities and differences. In order to find major patterns in data this technique reduces the number of dimensions of data without the loss of information. Principal component analysis introduces new set of orthogonal axes through data set called “eigenvectors” which data variance along them is maximized and have the importance proportional to their corresponding eigenvalues. The projection of single frequency slices onto eigenvectors is called “principal component (PC) bands”. The amount of total variance that each PC band represents is proportional to its eigenvalue, thus after normalizing the total sum of all eigenvalues, each eigenvalue represents the percentage of total spectral variance that its corresponding principal component can represent. So the first PC band (having largest eigenvalue) best represents the spectral variance in data, the second PC band (having the second largest eigenvalue) best represents the spectral variance in data which is not represented by the first PC and so on. Therefore PC bands with the smallest eigenvalues will represent a small portion of variance and can be deduced as random noise. So choosing the PC bands with the largest eigenvalues can be an effective way for data denoising, image processing and in our case determining the major trends in data set. We can represent more than 80 percent of spectral variation by plotting three largest principal components against red, green and blue components in a RGB image. In this paper, we applied spectral decomposition on land seismic data of an oil field in south-west of Iran using short time Fourier transform (STFT) and S transform. Then we constructed single frequency slices and investigated them. We produced RGB images by color stacking method and improved interpretation. Finally we used principal component analysis to use all the frequency bandwidth. Our results showed that PCA based images showed channel and its branches in a more precise manner than the other methods.