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"Inversi seismik deterministik sudah banyak digunakan dalam lapangan eksplorasi dan pengembangan. Metode ini digunakan sebagai salah satu cara untuk karakterisasi reservoir dengan menghilangkan efek wavelet sehingga dapat membantu interpreter untuk memetakan struktur bawa permukaan dengan lebih baik. Akan tetapi, metode ini memiliki limitasi karena menggunakan impedansi rata-rata dari layer seismik dimana pada umumnmya nilai impendansi lebih kecil daripada impedansi data sumur sehingga dihasilkan model inversi yang tidak sesuai. Metode inversi stokastik menggunakan konsep geostatistikal, dimana variogram berperan penting dalam menghasilkan output yang sesuai. Pada inversi stokastik dihasilkan banyak realisasi inversi yang digunakan sebagai basis dalam analisis uncertainty, tiap realisasi akan sama pada tiap lokasi sumur yang digunakan namun akan berubah seiring dengan bertambahnya jarak spasial dari lokasi sumur. Metode inversi stokastik akan diaplikasikan pada lapangan gas “K” yang terletak di lepas pantai cekungan Bonaparte, Indoensia Timur. Data yang tersedia antara lain, sebagian dari 3D PSTM angle gather dengan luasan 1,300 km2, 3 sumur dengan data P-Sonic, S-Sonic, densitas, Gamma Ray, dan log resistivitas. Tambahan data berupa report komplesi dan report well testing tersedia untuk beberapa sumur. Lapangan gas “K” terletak pada undeformed continental margin Australia yang melampar kearah lndonesia, dimana secara geologi lapangan “K” terletak pada area Timur dari Sahul Platform dan memiliki struktur berupa tiltef fault block. Lapangan ini memiliki reservoir batupasir formasi Plover yang tersaturasi gas dengan hidrokarbon kolom cukup signifikan, dimana reservoir terdeposisi pada lingkungan shallow marine pada umur Middle Jurasic. Target utama pada lapangan gas “K” merupakan strukutural trap berupa horst block, tilted fault block yang berada dibawah sub-unconformity di umur Palaezoic. Penerapan metode inversi stokastik pada lapangan gas “K” menghasilkan kelebihan yang cukup signifikan dibandingkan dengan inversi deterministik. Reservoir pada lapangan gas “K” terdiri dari batupasir dengan persilangan shale tipis. Metode inversi stokastik dapat membedakan antara batupasir yang tersaturasi gas dengan intraformational shale tipis yang tidak teresolusi oleh seismik dan inversi deterministik. Hasil realisasi dapat digunakan untuk analisis uncertainty dengan probabilitas P10, P50, dan P90 dari facies yang dihasilkan.

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Deterministic seismik inversion method has been successfully used in various projects in exploration and development. This method enables the interpreter to get better understanding of subsurface by omitting the wavelet and tuning effects therefore quantitative reservoir properties can be generated. However, this method has significant limitation by generating average impedances of each layer, and the range of values is smaller than the impedance from the wells therefore the inversion will not produce results that are not within the calibration range. Stochastic seismik inversion is done by conditioning well data and reproducing spatially varying statistics using variogram which could overcome the deterministic limitation. This method generates multiple realizations of high-frequency elastic properties that are consistent with both seismik amplitude and well data. In such instances, stochastic seismik inversion method could provide the uncertainties associated with the models that have been generated. The proposed method is applied in “K” gas field which located in the offshore Bonaparte Basin, Eastern Indonesia. The available dataset for this work includes : part of PSTM 3D which cover 1,300 km2 in angle gather, and 3 wells with compressional sonic, shear sonic, density, gamma ray, and resistivity logs. Additional well completion and well testing reports are available for some wells. Geologically, the “K” field is located within relatively undeformed Australian continental margin that extends into Indonesian waters. It lies on the eastern extremity of the Sahul Platform and occupies a large tilted fault block bounded to the east and south by the Calder-Malita Grabens. This field contains a significant gas column, reservoired within shallow marine, highly mature, quartzose sandstone of the Middle Jurassic Plover Formation. Potential targets in the area may be large folds, horst blocks, tilted fault blocks ad sub-unconformity traps in the Palaeozoic section. The application of stochastic seismik inversion showed significant benefits compared to deterministic especially in “K” gas field where the reservoirs are stacked sandstone with intraformational shale. Some of the reservoir and all the intraformational shales are below seismik resolution. Stochastic seismic inversion able to distinguish those features, in addition the inverted volumes with multiple realizations with ranking criteria for P10, P50, and P90 of facies could be utilized to reduce the risk associated with exploration plan and field development."

"This is the expanded second edition of a successful textbook that provides a broad introduction to important areas of stochastic modelling. The original text was developed from lecture notes for a one-semester course for third-year science and actuarial students at the University of Melbourne. It reviewed the basics of probability theory and then covered the following topics: Markov chains, Markov decision processes, jump Markov processes, elements of queueing theory, basic renewal theory, elements of time series and simulation. The present edition adds new chapters on elements of stochastic calculus and introductory mathematical finance that logically complement the topics chosen for the first edition. This makes the book suitable for a larger variety of university courses presenting the fundamentals of modern stochastic modelling. Instead of rigorous proofs we often give only sketches of the arguments, with indications as to why a particular result holds and also how it is related to other results, and illustrate them by examples. Wherever possible, the book includes references to more specialised texts on respective topics that contain both proofs and more advanced material.Readership: Advanced undergraduates, graduate students, lecturers and researchers in mathematics, statistics, actuarial sciences and economics."

"This volume first introduces the mathematical tools necessary for understanding and working with a broad class of applied stochastic models. The toolbox includes Gaussian processes, independently scattered measures such as Gaussian white noise and Poisson random measures, stochastic integrals, compound Poisson, infinitely divisible and stable distributions and processes.Next, it illustrates general concepts by handling a transparent but rich example of a "teletraffic model". A minor tuning of a few parameters of the model leads to different workload regimes, including Wiener process, fractional Brownian motion and stable Levy process. The simplicity of the dependence mechanism used in the model enables us to get a clear understanding of long and short range dependence phenomena. The model also shows how light or heavy distribution tails lead to continuous Gaussian processes or to processes with jumps in the limiting regime. Finally, in this volume, readers will find discussions on the multivariate extensions that admit a variety of completely different applied interpretations."

"Selected papers submitted by participants of the international Conference “Stochastic Analysis and Applied Probability 2010” ( www.saap2010.org ) make up the basis of this volume. The SAAP 2010 was held in Tunisia, from 7-9 October, 2010, and was organized by the “Applied Mathematics & Mathematical Physics” research unit of the preparatory institute to the military academies of Sousse (Tunisia), chaired by Mounir Zili. The papers cover theoretical, numerical and applied aspects of stochastic processes and stochastic differential equations. The study of such topic is motivated in part by the need to model, understand, forecast and control the behavior of many natural phenomena that evolve in time in a random way. Such phenomena appear in the fields of finance, telecommunications, economics, biology, geology, demography, physics, chemistry, signal processing and modern control theory, to mention just a few. As this book emphasizes the importance of numerical and theoretical studies of the stochastic differential equations and stochastic processes."

"Mathematical methods based on the theory of stochastic processes have long been used effectively in telephone traffic modeling. Today's modern network traffic, which is distinctly different from traditional voice traffic, generates challenging mathematical and statistical problems. Stochastic Modeling in Broadband Communications Systems provides a concise overview of stochastic models and mathematical techniques for solving these problems and enhances readers' overall understanding of communication systems. The book also presents an excellent introduction, particularly for students and professionals in probability and applied mathematics, to a huge area of interesting problems and models arising from modern developments in broadband channel transmission systems. The author's clear presentation is based on sound mathematical reasoning, and he has taken special care to make the material easily accessible to readers unable to devote hours of time on rigorous mathematical detail and generality. Topics include models ranging over different time scales of calls, bursts, and cells; different protocol layers for transport, control, and applications; mechanisms for queuing, collisions, delay, and loss; and the effects of buffering, retransmission, multiplexing, and traffic control. Comprehensive exercises are provided at the end of each chapter."